Existentialism Recitation VII

Plato's Symposium
If you've not read the Symposium, I highly recommend it. A symposium in Athens at the time of Plato's writing was a celebratory drinking party. This particular symposium was in celebration of the poet Agathon's recent victory at some drama contest. The topic of the symposium: Love.

Several speakers attempt to characterize love, each seeming to miss something of the phenomenon. Subsequent speakers identify lacunae and add to the characterization of love, culminating with Socrates. Socrates, however, does not give his own characterization of love, but that of a priestess Diotima. Diotima explained - and Socrates relays - that love is meaningful only insofar as it either is or is concerned with what is universal and objective.

But the dialogue doesn't stop with Socrates. Alcibiades, an uninvited influential charismatic Athenian politician at the time, barges into the symposium uttering one of my favorite lines "Gentlemen, I'm drunk." Alcibiades was absolutely adored by the Athenians. He literally seemed to do no wrong. Let me just give one example of this. During the Peloponnesian War, he literally switched sides and joined Sparta against Athens, but then he was later recalled and welcomed back, after which he served as the head general of the Athenian army for several years. Think about that. How persuasive and charismatic do you think someone must be to be able to literally betray you and your nation, but you still welcome them back with open arms? That's like Colin Powell aligning with Iraq halfway through the Persian Gulf War, then returning as if nothing happened, and we all act like nothing happened. It's almost inconceivable. Most of us know how it worked out for George Costanza when he tried to do that with the Yankees…

Anyway, the life of Alcibiades was full of this sort of stuff. It's one of the reasons Socrates spent so much time trying to teach Alcibiades virtue, and why Plato spent so much time talking about him. He was influential, intelligent, and powerful.

But Socrates failed Alcibiades. I think the close of the Symposium makes this clear. Alcibiades enters and finds Socrates sitting next to Agathon. Note, the word "agathos" meant "good" in Greek, so Alcibiades effectively walks in and sees Socrates sitting next to the Good. Alcibiades strolls in and sits directly between Socrates and Agathon, i.e. momentarily blocks Socrates from access to the Good. Alcibiades then offers his speech on love. To my ears, it is heartbreaking. I paraphrase:

I love Socrates; I love this man. He tells me my beliefs are wrong; he shows me they must be, and I believe him. But I return to my life, and find my old beliefs and vices exalted by the Athenians. I am weak. I fall into pride of my skills, supported on nearly every side in my vice. But I know better; the man I love showed me better. The weight of the world is too much though, despite what I know, so I crawl back to my love, weeping, in need. But he is gone, distant, off in contemplation, far away from me. I try to wait for my love. Where can I go, back to the Athenians? They praise vice. To virtue, alongside my love? He won't show me the way. I can only wait alone, knowing virtue but only able to live in vice; knowing my love abandons me when I need him most. Socrates speaks of love as objective and universal. If he's right, then witness love before you. I am love; love is torture. 

Alcibiades has been shown the truth. But convincing a vicious person to be virtuous without showing them how is torture. Socrates failed to show Alcibiades how to be virtuous, and so he failed him as a teacher. I take this, moreover, to be an incalculable failure. Preach virtue, but as long as there are people like Alcibiades - charismatic, influential, persuasive, vicious, people - just as capable of preaching vice, and as long as we're disposed to vice as we seem to be, vice has the upper hand. Socrates spent so much energy arguing against sophists; this is small potatoes. The hard case was Alcibiades, and no answer is given for addressing such a character.

Simone Weil
Why is this relevant to our discussion of Simone Weil? Weil too appeals to love, truth, beauty, and justice as objective, resting this on our intuitions about such things. Weil claims we build idealized legal and social rules, then use these rules to justify moral judgments they can't justify. In a nutshell: Is murder wrong because it's illegal? No. Morality is what is supposed to underwrite the law, not the other way around. Is murder wrong because my culture says so? No, for similar reasons. Where then does morality rest? Your moral judgments. What do these rest on? Intuitions.

How do we find ourselves reversing the priority of morality? We lie to ourselves, of course. We construct legal and social principles for idealized scenarios, and ignore or dismiss evidence that the world doesn't align with those principles. This is doubly problematic. On the one hand, it makes us think we've ready answers to cases of theft, murder, etc. when that's no always so clear. On the other hand, it provides us false confidence in our moral judgments even if we admit that we're ultimately relying on them.

How then do we get out of this bind? Weil seems to be suggesting something like reflective coherent equilibrium for moral judgments, born out of exposure to a variety of moral scenarios; baptized - as it were - by fire. Only then can you trust your moral judgments. This, I take it, motivates much of her criticism directed at individuals who appear to avoid pain, struggle, and tough moral scenarios; they simply don't understand the experiences of agents in those scenarios, and so moral judgments involving those individuals are suspect. Concretely: Do you think you really understand what it's like to think murdering someone is the right thing to do? You can of course describe it; you can of course rely on cultural knowledge and legal discussions about such things; but can you really understand what it's like to think that's the best thing to do in a scenario? Likely not. That suggests you may not understand enough of what's going on in such scenarios to be able to justifiably pass moral judgment, and similarly, legal and social judgment. That's quite the pickle. Perhaps you should expose yourself to more such scenarios, in fact, to gain a fuller picture of the purview of moral judgment…

To be candid, I think Weil is right about this up to a point. Most of us likely don't have sufficient exposure to various moral scenarios to justifiably pass judgment on agents involved in those scenarios, though we do it all the time anyway. Moreover, it's likely most of us haven't reflected carefully on the moral intuitions we have, though we rely on them to make such judgments. I have to disembark from this line of reasoning though once the prescribed remedy is to experience struggle, harm, and pain before passing relevant moral judgment. To see why, let me make this personal, since reading Weil reminds me of my own ways of thinking from about 5 years ago.

Weil's life was one of ostracism, pain, and discomfort. Being raised in such a life gives one what you might call an appetite for discomfort. Contrast this with those who fortunately are raised in more or less comfortable environments, with friends, family, support, etc. Being raised in such a life gives one what you might call an appetite for comfort. Individuals with these respective appetites likely have distinctive expectations and behaviors concerning many aspects of life. Those raised in discomfort find familiarity in further discomfort, and expect it in life, and perhaps may even seek it out. Just as important, they often may not seek out comfort. As an example from my own life of the latter, for many years I rarely took action to make my daily life more comfortable. I didn't purchase a backpack when I started school even though it would've made carrying things easier. I didn't sleep on a bed for many years since the floor seemed fine. Etc. On the other hand, those raised in comfort find familiarity in further comfort and expect it too, often seeking it out.

This is not to say those with an appetite for comfort don't understand discomfort, or vice versa. But there are further distinctions we can draw between them, since it seems those with an appetite for, say, comfort don't thereby have an appetite for pain too. Nevertheless, those raised in comfort acquire what we might call a taste for pain, and those raised in discomfort acquire a taste for pleasure. For example, many watch sensational and uncomfortable news from the comfort of their homes, i.e. watching an Amber Alert without even trying to help, sending thoughts and prayers, etc. On the other hand, some watch comfortable events from a distance without seeking engagement, i.e. enjoying comedy shows rather than Law and Order. In these ways, those with an appetite for discomfort while having life seasoned with a bit of comfort here and there, and those with an appetite for comfort may season like with discomfort. The balancing act between comfort and discomfort should of course be familiar, since they seem these respective phenomena seem mutually dependent. What I'm pointing to here is the dispositions some have towards one or the other. We're creatures of habit, and often find ourselves doing what we've been doing, for better or worse.

Now, Weil seems to be suggesting those with only a taste for pain should learn to develop an appetite for it, since it brings one closer to the objective truth of justice, beauty, and truth. I take the point, but not the prescription. Speaking as someone raised in discomfort for the first 13 years of his life, I can say I've an appetite for pain, and only a taste for pleasure. To put it more phenomenologically, I find exposure to pleasure…difficult. I rarely expect it; my behavior suggests that I contingency plan to minimize discomfort, but each plan I make involves some discomfort by default. As an innocuous example, I never send food back because I don't like it. Never. And yet I believe there have been times when I should have. Importantly, it doesn't seem to me to stem from some virtuous good-hearted character, though it does stem from character. I literally don't think to do such a thing, and if someone points out to me that I should, I dismiss it without much reflection. Now as a less innocuous example, I've difficulty blaming others even when it seems plausible they deserve blame. I still have trouble blaming my stepfather for any of the terrible things he did. In my mind, he's no more blameworthy than the asphalt is for scraping my knee. Bad things are expected, not good. And while my default is not to blame, it is to praise others. Again, I don't expect good things, so I tend to call attention to them when they arise. If you've an appetite for comfort, you might have parallel experiences. For example, you may find it easy to blame but difficult to praise. Similarly, you may carry expectations for how others treat you, e.g. it may not occur to you not to send your food back if it's not to your liking. Of the two of us, I suspect Weil might strongly suggest you avoid pain, and are at risk of overlooking objectivity and true moral intuitions. Moreover, it seems Weil might suggest you experience a bit more discomfort in the effort of gaining better purchase on objectivity.

Perhaps, but I don't think we should take this too far. I think Weil's correct that those with an appetite only for comfort tend to deceive themselves about the world. But I think this charge applies equally to people like Weil and myself, i.e. those with an appetite for discomfort. I've been in therapy for a few years now. Prior to therapy, I'd assumed most people in the world thought roughly the way I did, i.e. had an appetite for pain but a taste for pleasure (though I wouldn’t have put it that way). Through therapy, I realized something like my way of thinking is characteristic of people with PTSD. I'd been rather anti-social most of my life up until then. I'd not had many close friends. I'd convinced myself I didn't need them, in fact. Dependence on others seemed weakness. But I'd been lying to myself. I wanted intimacy, friends, etc. I'd tried for years to form close relationships with people, but they always seemed to fail. I could never figure out why, and I seemed to keep repeating the same patterns. I convinced myself I didn't need such relationships because I was exhausted, because I thought I just couldn't have them. I'd convinced myself I needed to give up on such things and devote my life to something else, namely, philosophy. So I did. And I was successful too, which I think looking back is to the chagrin of our discipline rather than praise of me, since our discipline encourages and rewards such reclusive, productive, behavior. In any event, when I realized others often thought about the world much differently than I did, things began to make sense. I began approaching interactions with others with an open mind. I no longer tried to predict what people might say next in conversation; I stopped expecting people to hurt me. My life became so much more relaxed. Now I can say I do have close intimate relationships, and I understand better how one might acquire them, and why they're important. The point here is that I've been learning to acquire not just a taste for comfort, but an appetite for it. This while I maintain my appetite for discomfort. I'm learning to inhabit two perspectives at once.

And this is why I think Weil's prescription is too narrow. Those with only an appetite for discomfort are just as susceptible to self-deception as those with only an appetite for comfort. For 30 years people in my life have been trying to love me and I couldn't see it. I genuinely didn't think they cared. I see they do now, and I can see why my well-intentioned reasoning, motivated largely by an appetite for discomfort, obscured that truth from me. This is just to say the prescription to acquiring a more honest understanding or moral intuitions in on point. The method for suggesting, I think, should be expanded to include both of these perspectives. But at the same time, I don't think extreme discomfort is anything we should be prescribing. I'm proud I've made it to where I am, I've no idea what my life would be like without the background I have, and I wouldn't change anything that's happened. But I would never wish it on anyone else. Simply put, I think there are many ways to arrive at similar enough positions in life, and one need not go through what I or Weil went through if one wanted to end up like I have or she did. Some trauma is too much to recommend direct exposure. I spent 30 years thinking in an overcontrolled way and believing everyone else thought that way too. That's far too long for someone to spend being so fundamentally wrong.

More to the point, I don't think you need to have direct experience to understand someone like me, or others who have experienced such extremities of life. I focus here, I hope it's clear on the hard cases like Weil and myself, because I think what I'm going to say equally applies to easier cases like being a wage laborer in a factory, or being someone inclined to vote against their interests. We don't need more suffering people; what we need is to think creatively about how to bridge this gap in understanding….

Narrative Themes Revisited
And this finally brings us back to Alcibiades. Socrates was a pillar of virtue, able to ignore vice and keep his eye on virtue despite the vicissitudes of the world. But because only virtue caught his eye, he wasn't able to understand vice enough to compassionately engage with Alcibiades, and in doing so help him reach virtue. Socrates (in the mouth of Plato) obscured vice by making virtue objective and universal. It seems to me a useful ethical theory needs both. It also seems to me a useless ethical theory isn't an ethical theory.

But look, Socrates need not descend to the world, and acquire an appetite for vice to accompany his appetite for virtue. He was surely a creative enough thinker to be able to avoid that sort of excursion. We've already discussed one way in which he could've done this…narrative themes. This is, moreover, the way I encourage you to acquire something more than a taste for discomfort. Your imagination is powerful; use it. Here is some guidance:

  • Step 1: Revisit the discussion of the Binding of Isaac; remind yourself of narrative themes and how they work.

  • Step 2: Reflect on how one might understand extreme suffering without experiencing it themselves.

  • Step 3: Reflect on how narrative theme analysis might've helped Socrates better understand Alcibiades, and how this might've helped Socrates avoid that incalculable failure I mentioned above.

  • Step 4: Reflect on how Alcibiades was already employing something like narrative theme analysis to understand the life of virtue through Socrates, but how this wasn't enough to lead him to virtue.

Between Step 3 and Step 4, you'll gain a better understanding of both the strengths and weaknesses of narrative theme analysis, i.e. where it can be helpful and where it's not so helpful. One major takeaway from this post is that it's more useful than many think, even if it's not always useful. Let's not let perfection get in the way of the good though.

Existentialism Recitation VI

Lies, Deception, and Bullshit

I bet you believe I'm bald. You may not have thought about that before I mentioned it, but surely you believed it before then. Similarly, I bet you believe 256+98076=98332 despite having never thought of this equation before. Call the beliefs you have that you've made explicit to yourself, explicit beliefs, and those beliefs you have that you've not yet made so explicit, implicit beliefs. Sometimes you might learn you've implicit beliefs you'd rather you didn't have. Maria Stewart's speech Why Sit Ye Here and Die? Provides an example of this sort. Among other things, she calls out northern abolitionists who claim to explicitly believe racism is wrong for not hiring black workers. These hiring practices seem to suggest white employers implicitly held racist beliefs. Stewart brings this to light in her speech by pointing to what seems like a performative contradiction. For our purposes, this is a plausible diagnostic for uncovering implicit beliefs.

Beliefs come in a wide variety. You might, for instance, believe the Earth orbits the Sun, or you might believe the Earth does not orbit the Sun. You might even lack any belief about celestial orbits at all. These observations provide shape to types of ignorance, which may be confused with types of belief. For example, you might not have any belief - implicit or explicit - about the number of rings around Saturn, i.e. you might be entirely ignorant about that topic. On the other hand, you might believe there are only two rings around Saturn, i.e. you might have a false belief about that topic. Holding some beliefs crowd out others. If you believe P, then you can't also believe not P or anything that obviously entails not P. If P is true, that's one way to be wrong about P. Another is not having any belief about P, since that entails you don't believe P (or not P).

We have then two axes to help structure not having true beliefs (suppose P is true):

Believe P            Explicit True Belief       Implicit True Belief

Believe not P      Explicit False Belief      Implicit False Belief

No Belief of P     Explicit Ignorance        Implicit Ignorance
Aware            Unaware

You might think it odd to say one could have explicit ignorance, but this isn't so peculiar. There are many things I know I don't know, and know I don't have an opinion about, e.g. capital gains tax. In any event, with that structure in mind, let's think about liars. We know a liar when we see one, right? Maybe. We should be careful, since it seems some things appear like lies but aren't. For example, suppose you ask Kasey if I'm a good logician, and he responds "John? He's always on time!" You might think he's not answered your question. However, what Kasey has plausibly done is invite you to make an inference to conclude that I'm not in fact a good logician. If I were, then he would've said so. But simply because he's not answered your question it doesn't follow he's lied. He wasn't, for instance, trying to deceive you; it's reasonable to think you'd have drawn the inference he invited you to draw. This is rather an example of pragmatic implicature.

The paradigmatic case of a liar, as Sartre understands, is someone who:

(i) Either explicitly or implicitly believes the truth
(ii) Explicitly denies the truth to himself or others
(iii) Accepts that (i) and (ii) are in conflict
(iv) Denies (iii) to himself or others

This is to say Sartre claims there are two levels of deception in paradigmatic cases of lying. Let's consider an example. Suppose it's raining outside and I explicitly believe this. This satisfies (i). Suppose you ask me if it's raining and you are explicitly ignorant of whether it is or isn't. Suppose I say "It's not raining." This satisfies (ii). It seems to follow I'm aware of the conflict between (i) and (ii), and I accept it. "Accepting" is a peculiar attitude one can take towards propositions about the world. You can accept things you think are false, for instance, in pursuit of other goals. For example, a scientist might see a great deal of counterevidence for his favorite theory, but accept that it's true anyway for the sake of further inquiry. Similarly, a lover might accept a partner is faithful despite having overwhelming evidence to the contrary. This is the sense in which the liar can accept two conflicting claims, satisfying (iii). Moreover, you can often understand this in terms of behavior (note, there's no 'explicit' requirement on accepting here). My explicit belief that it's raining and claim otherwise is a performative contradiction, suggesting at least an implicit belief of the sort you'd expect in (iii). To continue the example, suppose I explicitly deny the conflict in (iii). Then I've met all the conditions to be a paradigmatic liar.

Psychoanalysis of Lies

How might be understand this phenomenon at the level of psychology? If Freudian psychoanalytic theory is true, then you've a subconscious id - instincts and drives as part of the mind; arational or irrational - and conscious ego - one intellectual part of the mind; rational. According to the psychoanalytic explanation of lies, both (i) and (iii) fall into the subconscious while (ii) and (iv) are conscious. The subconscious protects itself, and the conscious part of the mind avoids engaging with it, perhaps out of shame, or out of powerlessness (rationality can't even engage irrationality…).

Sartre claims this explanation is inadequate since it seems to require the id have something like a rationality, since otherwise it wouldn't 'know' what desires and instincts it should be protecting in (iii). I think this isn't such a good argument.

  • One response is simply noting the id doesn't need to 'know' anything other than that there are certain bad outcomes correlated with revealing certain instincts and desires to consciousness. But this need not be rational in any robust sense. Neural networks suggest learning may take place without much awareness, as long as background parameters are set up in certain ways.

  • A better response though is to observe that the id need not 'know' anything, since it's plausible the ego is protecting itself by simply not engaging with what it (implicitly) takes to be irrational. You might think the ego must nevertheless know what desires and instincts to ignore, but note the ego might simply be wired - as we are - to avoid disastrous consequences after minimal exposure to them. Children who touch hot stoves often fear all stoves for some time, hot or cold. Similarly, the ego early on might have wrestled with instincts and desires that couldn't be pinned, and were too emotionally costly to engage with. This is to say it’s plausible the ego itself avoids engagement with certain desires and instincts not because they’re being hidden by the id, but because they’re part of the id and unruly.

Which is all just to say I don't find Sartre's motivation compelling. Still, he gets points for offering an alternative explanation all at the level of consciousness for the same phenomenon. To do this, he needs only avail himself of something the Freudian already accepts, namely, the distinction between consciousness and awareness. You can be conscious but not aware. Suppose you're looking for cufflinks in a drawer but can't find them. Later, while driving to a gala, you realize the cufflinks were in the drawer and you overlooked them. The plausibility of this scenario suggests you can perceive cufflinks - and so be conscious - but not be aware of that perception.

***As an aside, this distinction also provides a plausible background against which to explain the truth - I think - of the following claim:

(IMG-PER) It is possible for you to imagine and perceive the same content

Suppose (IMG-PER) is false. Then it's not possible to imagine and perceive the same content. Now suppose you're standing before a white wall. Keep your eyes open and imagine the wall is a slightly darker shade of white than it is. Now slowly imagine the color changing so it is the same color as the actual wall. If (IMG-PER) is false, then it's possible for you to be imagining the darker white wall while perceiving the white wall (since you can perceive and imagine different content at the same time) up until the last moment, in which case you can't be imagining the white wall anymore, but can only be perceiving it. This strikes me as absurd. Hence, I think (IMG-PER) is true. The distinction between consciousness and awareness assists in explaining this phenomenon, since it's plausible you're consciously perceiving and imagining the white wall, but only attending to one of those conscious activities. In other words, it's plausible awareness is limited here.

Bad Faith

Sartre thinks you don't need the id to explain paradigmatic liars. Indeed, the answer he provides should already be familiar to you, since the discussion above about ignorance and implicit beliefs might all occur at a conscious level. To make this clear, consider his example of the waiter who believes himself solely and entirely a waiter. The truth is that he's an autonomous agent capable of choosing, dreaming, etc. in ways that outstrip waiting tables. It's plausible that he at least implicitly believes this, while explicitly believing he's solely a waiter. This might be uncovered by, say, reflecting on how he'd act if he won the lottery. I suspect he'd no longer solely wait tables. Of course, he might find such novel possibilities burdensome, since then he'd need to choose. This is where the tension between his implicit and explicit beliefs enters. He might not recognize this tension, but instead focus solely on being the best waiter he can, so he doesn't have to address his freedom. Indeed, suppose he's pressed to engage in an action not typical of waiters, e.g. rob a bank at gunpoint. Surely he'd not simply act like a waiter in that context. Still, his actions in typical contexts, e.g. gestures, mannerisms, suggest he either explicitly or implicitly denies his freedom to choose for the sake of solely being a waiter.

See if you can examine Sartre's other examples with the table above; it'll be useful to incorporate the category of ignorance in your explanation since - as you may have noted - I didn't…

Sartre suggests bad faith emerges as either focusing on one's facticity or transcendence too much, and there's no way to combine them. We're thus doomed, it seems, to bad faith in most cases. I'd love to explore this, but how about you give it a shot?

Existentialism Recitation V

Metaphysics Revisited

Ontology is the study of being, or what there is. Insofar as it is concerned with what there is, ontology amounts to counting entities. You might count entities at different levels of reality, e.g. tables, people, atoms, and consequently, have ontologies at different granularities. Metaphysicians are often concerned to study the fundamental or base level of reality, i.e. being or beings that underwrite electrons, quarks, etc. Ontologies at higher levels of reality are derived, or applied ontologies. In Being and Time Heidegger restricts his attention to the fundamental level of reality.

This is not, however, to say he is studying fundamental ontology. For there is more to reality than simply counting beings in it, namely, there is also how such beings are structured and relate to each other. Call the study of structure ideology, and consider an analogy to keep these ideas straight: ontology is to ingredients in a recipe, as ideology is to how to combine ingredients in a recipe. You'd count cloves of garlic in a dish, but not mincing. Similarly, you'd count tables and colors in an ontology, but you'd not count as an entity the way a color inheres in a table. This is all to say I take it Heidegger is interested in ideology - the structure of being - rather than ontology - beings. He says as much, though he uses confusing language (he claims he's interested in "Ontological" rather than "ontic" reality; "ontic roughly maps to "ontology" in my sense, and "ideology" in my sense to Heidegger's "Ontology").

Epistemological Puzzles?

In particular, the structure Heidegger is attempting to uncover is the structure of the most important being of all - Dasein - us! That seems a reasonable place to start, given we're of course always viewing things from a subjective perspective, and fundamental metaphysics is no different. But before we can even begin, a host of perennial philosophical puzzles arise. Consider the so-called Problem of Other Minds:

  1. I've direct access to my mind

  2. If (1), then I can be certain I have a mind

  3. I've only indirect access to the 'minds' of others

  4. If (4), then I cannot be certain others have minds

  5. If (1) - (4), then I cannot distinguish between worlds in which only I have a mind and worlds in which I have a mind and others have minds

  6. Hence, I cannot distinguish between worlds in which only I have a mind and worlds in which I have a mind and others have minds

This is quite a puzzle; if (6) is true, then you've no justification - it seems - for claiming to know other people exist. That sounds like philosophy gone crazy. A common response was offered by Bertrand Russell in The Problems of Philosophy. It is to question (4) by asserting that even though we only have indirect access to the minds of others, we can be certain there are other minds by analogy. It doesn't hurt me if I hit you with a hammer in the foot, but you behave as I would. You also look like me, etc. This response by analogy seems plausible, but also weak. Analogies are notoriously susceptible to perspective influence and error. Another response - offered by Heidegger's teacher Husserl - denied (3), claiming that as a matter of fact we do have direct access to other minds. That seems…false…Heidegger thinks the argument itself is ill-posed since he think we're - Dasein's - obviously already encountering the world with others in it. Indeed, it seems we learn about ourselves long after being thrown into it populated by others. This suggests one might start from the opposite direction, deriving the individual from the collective group to which they belong.

More formally, the shift in perspective might be elaborated by supposing you've the task of describing a domain of squares. Squares have points and four lines meeting at right angles. You can approach this task in at least two ways. You might take a mereological starting point, i.e. working from the parts of squares to the whole square; you might take a topological starting point, i.e. working from squares to lines and points. More concretely, suppose you approach this mereologically, say, with only points. Then you can assert that between any two points is a line, some lines form 90 degree angles, and when four such lines form 90 degree angles a square is formed. Suppose instead you approach this mereologically. Then you begin with squares, and you can assert that where any two squares meet there is a line, and where four squares meet there is a point.

One might apply this to the case of Dasein, that entity always discovering itself as a member of a larger group long after becoming a member. This avoids The Problem of Other Minds above, since we seem to - as a matter of fact - have access to other minds once we find ourselves as individuals. Unfortunately, this can't be the story, since it simply reverses the above concern. Call this the Problem of My Mind:

  1. I've only indirect access to my mind

  2. If (1), then I cannot be certain I have a mind

  3. I've direct access to the collective mind 

  4. If (4), then I can be certain there is a collective mind

  5. If (2) and (4), then I cannot distinguish between worlds in which there is only a collective mind and worlds in which I have a mind and there is a collective mind

  6. Hence, I cannot distinguish between worlds in which there is only a collective mind and worlds in which I have a mind and there is a collective mind

This is simply the inverse of the Problem of Other Minds. The problem is that starting from a collective and inferring the existence of an individual runs into the same epistemic worry as starting from the individual and inferring the existence of other minds. Now, you might think this argument is not a strong as The Problem of Other Minds. You might think you've more evidence that you have a mind than that others do. Consider though, many of us trust physics to explain the natural world. Many, moreover, have observed free will - voluntary action of agents - is outside the scope of physics, and is certainly not postulated by any existing physical theory. And from this many conclude there is no such thing as free will. Rather, every decision you've made is explained by particles bouncing off each other, as well as beliefs and desires you never chose but realize you have. This, indeed, is a common position. Note the parallel. If you're willing to infer from the apparent non-existence of free will in the natural world to the lack of free will in your mind, then why not similarly infer from the apparent existence of collective minds to the existence of your own. This is precisely the sort of inference free will skeptics make.

***Response: You've more evidence that there is free will than that there's not, since you seem to engage in free actions all the time. If you're saying there is no free will because physics doesn't say there is, then you're inferring from how things seem from the outside to how things seem on the inside. That is, you're letting the outside world tell you you're wrong about your experiences.***

Is Heidegger susceptible to this problem? Not at all. True, one might start from mereology or topology to model the fundamental ideology of Dasein, but doing either leaves you with an epistemological puzzle. Heidegger thinks the problem is starting from the epistemological stance in the first place while trying to do metaphysics. Naturally, he suggests starting from the metaphysical perspective. And with that, Heidegger claims Dasein and the collective group to which any given Dasein belongs, are mutually dependent on each other, the same way hue, saturation, and brightness are mutually dependent on each other; you can't have one without the other. This is to say, Heidegger rejects (2) and (4), since it presumes a distinction without a difference.

Dasein

Epistemological puzzles aside - for now - we have the assumption of ourselves - Dasein - as exhibiting a three part ontological structure, much like color exhibits hue, saturation, and brightness, and this structure intimately involves collective groups we find ourselves members of. Specifically, Heidegger claims Dasein has been thrown into the world, i.e. influenced by culture imposing dispositions on us as we develop, is presently fallen, i.e. finds itself as a member of a larger group imposing such things on it, and projects to the future, i.e. examines options for how we want our lives to look going forward. The temporal references here are important (this is being and time after all); Heidegger claims time is the form Dasein takes.

We eventually realize we've been thrown into this world, raised by people, adopted beliefs, desires, etc. and experience something like a rising self-awareness. It's like one day you're looking around and realizing you're looking around! Then you realize you've been looking around. But then you realize you have to keep looking around since that's one of the things you do. Importantly, you continuing to look around implicates you in your past and present behaviors. Heidegger calls this being guilty, but it seems to me something more like being responsible. Suppose you've been tapping your foot for a bit in class but haven't realized it until someone points it out to you. Suppose you're a bit embarrassed and don't want to admit you've not been paying attention to your behavior, so you keep tapping your foot. Your tapping after you realize you've been tapping implicates you in your previous tapping. It's as if you become retroactively responsible for the previous tapping, by intentionally continuing to tap. Projecting to the future is like that. We all project and plan for the future, but in doing so we all recognize we've been influenced by culture, etc. By pursuing things like money, fame, respect, etc., we implicate ourselves in past behaviors that align with those pursuits. That’s being guilty; taking responsibility and ownership for your past and present, while keeping an eye to the future.

Epistemological Puzzles Revisited

So far, so good. But Heidegger isn't out of the metaphysical woods yet. He's engaged in fundamental metaphysics, but given each Dasein operates within a limited subjective perspective, this sort of endeavor is susceptible to the question "How do you know that fundamental metaphysical view is true?" More concretely, Heidegger is open to the question "How do you know your characterization of Dasein and its complex ontological structure is true?"

Many philosophers attempt to bridge the gap between epistemology and metaphysics by appealing to something like the following principle:

(IMG) If S imagines P then P is possible

Note first this links a faculty of the mind - the ability to imagine - to whether certain things are possible or not. Possibility is under the purview of metaphysics, and exploring what is possible is a practice many engage in when trying to determine what is actually true. Recall, metaphysicians can't go test claims empirically, they need to use reason and human faculties. If they could test things empirically, they'd know what was possible, since whatever is actually the case is possible. Unfortunately, the other direction doesn't hold. Still, it's hoped that if you can determine what's possible, that's an important step in narrowing down what, say, the actual metaphysical structure of the world is like. Important for us, Heidegger first investigates what is possible before turning to what is actual. Doing that involves something like (IMG).

But is (IMG) true? That depends on what's meant by "possible." Note, we're doing fundamental metaphysics here, so we mean metaphysically possible, i.e. any possible way the world could've been. For example, I could've had hair. That's metaphysically possible. On the other hand, it's not true 2+2=5, and could never be. That's metaphysically impossible. Metaphysical possibility is contrasted with other sorts, e.g. epistemically possible. This is possible with respect to what you know. For instance, Lois Lane believed it epistemically possible that Clark Kent was weak. But that's not metaphysically possible, since he's Superman, and Superman is quite strong.

Returning to (IMG) and thinking about metaphysical possibility, it should be clear (IMG) is too strong. Simply put, I could be mistaken about my imagining. One way to fix this is to introduce a qualification to imagining. For example (taken from Descartes):

(IMG*) If S clearly and distinctly imagines P then P is metaphysically possible

This runs into all sorts of counterexamples not worth discussing. Important for us is the natural move philosophers make to fix principles like this, namely, to fill in the blank:

(*) If S ____ imagines P then P is metaphysically possible

One might refine the type of imagining as Descartes did, or perhaps even try out a different attitude, e.g. supposes, but Heidegger takes a different tact. He appeals to mood. Moods like, say, anxiety, aren't like attitudes. To see why, simply observe one can imagine anxiously or not, or perceive anxiously or not. In this sense, moods are ways in which one engages with the world via attitudes. It's, moreover, independent of content. One might imagine an empty room anxiously or not, and get a different experience each time. And the difference in experiences given the same attitude and content is crucial for why Heidegger thinks moods help here. For he claims anxiety is a mood that discloses the fundamental structure of Dasein. In other words, we have:

(ANX) If S anxiously imagines P then P is metaphysically possible

Now, there's surely an epistemological puzzle to be explored here. Before turning to that, however, we should get clear on what this anxiety thing is. As stated, it's a mood, so that's settled. It's not supposed to be - in Heidegger's understanding - feeling upset or negative, and it's not even supposed to have an object, i.e. something to be anxious about. It's more like a calm state of realizing you're groundless, you're on your own, and you've to accept everything you've done and are doing or not. It's the moment of openness to the possibility of the your future as an intentional agent, while accepting responsibility for every disposition imposed on you as you move forward.

In that respect, anxiety is supposed to be clarifying, the truest mood, the one that discloses reality. It's seeing clearly in a dark room; having a Eureka moment solving a puzzle; etc. Anxiety is that moment you - Dasein - really gets it.

So, do you think (ANX) is true? Consider the sort of argument Heidegger needs to get his metaphysical picture out of the concern that, well, he could be wrong given his limited, finite, epistemic state (let "P" be Heidegger's entire fundamental metaphysical view; let "K" be an operator on sentences that means "S knows that", e.g. "K(P)" means "S knows that P"):

  1. If S anxiously imagines P, then K(S anxiously imagines P)

  2. If S anxiously imagines P

  3. K(S anxiously imagines P)

  4. K(If S anxiously imagines P then P is metaphysically possible)

  5. If K(S anxiously imagines P) then K(P is metaphysically possible)

  6. K(P is metaphysically possible)

  7. P is metaphysically possible

Not all steps are needed here, but I include them for clarity. Consider (1) is needed to link imagining anxiously to being in the right mental state, i.e. knowing, to even recognize that you're anxiously imagining. This is plausible since it seems if anxiety is going to be useful to exploring fundamental metaphysics, then you should recognize anxiety when you're in that mood. (2) is granted for the sake of argument, and (3) follows from (1) and (2) by logic. (4) is the principle (ANX), but again it is only useful if the relevant agent recognizes it's true, since otherwise (ANX) is useless to exploring fundamental metaphysics. (5) follows from (4) by logic, and so (6) follows from (3) and (5) by logic. (7) follows from (6) because 'knows' is factive which is to say if you actually know something then it must be true, i.e. you can't know false things.

Do you think this argument is sound? If so, then Heidegger has no epistemological concern in this area, and anxiety gets us to the nature of the world. If not, then Heidegger may be in trouble, but you'll need to identify where the argument fails. Don't try to dispute the logic, i.e. (3), (5), and (6). I'd be inclined to grant the move from (6) to (7), and (2) for the sake of argument. That leaves (1) and (4) to criticize…

Existentialism Recitation IV

Nietzsche is difficult to parse, given his tendency to hyperbole, aphoristic style, and – as we’ll see, philosophical goals. What follows is an interpretation of Nietzsche’s The Gay Science, which purports to tie together many themes of his work, at least during his so-called middle period.

Hyperbole vs Hyperbole

Let’s situate Nietzsche within some relevant historical context. He was operating on the horizon of a shift in humanistic thinking, that shift moving from optimism and pride in humanity and nature to emphasize the darker side of reality. Where Hegel and Kant had suggested we could think our way to understanding reality, if we only tried hard enough, scholars like Kierkegaard suggested some understanding would necessarily be outside our grasp, and others like Schopenhauer suggested such thinking places too much weight on humanity. The latter believed we’re doomed to failure, and that’s simply our plight.

But Nietzsche’s not obviously a pessimist about human nature and reality in the stripe of Schopenhauer, and he’s not obviously a nihilist about value either. One reason to think he’s not either is his emphasis and defense of natural science as a way to understand the world. That shouldn’t sound like something a nihilist would be inclined to say…

We can reconcile this apparent tension by thinking of Nietzsche as throwing hyperbolic shade on the optimists – who champion the “sweetness and light” of human nature and the scope of rationality – which he finds all around him. To be fair, such optimism had taken a hit by Darwin and others. Nietzsche, however, sees shadows remaining of that old optimism, in the form of what scholars and scientists of his day found desirable to research.

God is Dead…Deal with it…

Nietzsche doesn’t simply say “God is dead”. He goes on to say that we’ve killed him, and we’ll be fighting his shadows for some time. He emphasizes that we’ve killed him – I think – so we take seriously our responsibility for the fallout. I take it he thinks scholars of the time have not paid enough attention to that fallout; they know God is dead, and they’re aware we’ve killed him. But they also believe this deicide entails they’re no longer influenced by the notion of God.  This phrasing is Nietzsche’s rather poetic way of turning attention to the need for continued attention. Put another way, it’s not as if the enlightenment God rid of God and started from scratch. At no point in recorded history has anything ever been so insulated (Cp. Anscombe, Modern Moral Philosophy). As a perhaps more concrete example of this, consider the French Revolution, and the impulse those revolting had to remove religion from its central position in dominant culture, and replace it with reason. That sounds nice, I suppose. But they literally created the Church of Reason, the first state-sponsored atheistic religion. Come on now…you can’t make this stuff up…

In any event, what sort of shadows does Nietzsche have in mind? God was a:

  • Legislator

  • Issued commands

  • That had the force of universal law

Hence, that implied there were:

Scholars of Nietzsche’s time were naturalistic, and so attempting to explain everything in terms of natural science, rather than by making any appeal to, say, supernatural explanations. However, Nietzsche is concerned naturalistic scientists are nevertheless seeking explanations that make most sense if there’s a God in the picture. They hunt “Laws of Nature” e.g. Law of Refraction, Ideal Gas Laws, etc. They privilege one way of understanding the world at the exclusion of all others. And with both laws of nature and privileged perspective, comes purpose in nature. Electrons, they might say, follow a certain trajectory because they’re supposed to…

ASIDE: There are many ways to understand “law” and “supposed to” in this context. Consider, there are laws of chess, such that if you violate them, you simply aren’t playing chess, e.g. moving a rook diagonally. These are called constitutive rules. There are other rules of chess such that violating them doesn’t necessarily mean you’re no longer playing chess, e.g. licking each piece before you move it. These are called regulative rules. The former rules tell you what you must do to engage in a certain practice, while the latter regulate that practice once it’s engaged in.

(Q) Are laws of nature as scientists seem to understand them constitutive, regulative, both, neither?

Naturalistic scientists of the day seemed to be searching for what we might call robust laws of nature, i.e. laws of nature that govern the natural world, much like God’s commanded laws of nature, e.g. “Let there be light!” governed the natural world. We might think of such robust laws of nature as being necessary, that is, having no exceptions. Electrons travel in a particular trajectory at a particular place and time, and there’s no way they couldn’t; it’s the law.

Nietzsche is questioning the need for anything as robust as inviolable laws of nature. He suggests everything science is concerned with can be explained in terms of regular patterns of observable phenomenon. In other words, you don’t need robust laws of nature to explain and predict, say, the migration patterns of geese, electron trajectory, gas movement, etc. Natural scientists need only be engaged – Nietzsche claims – in descriptions of the world, and insofar as laws of nature enter into the description, they’re derived from repeated observations of patterns in nature. It’s fallacious to move from such patterns to governing laws.

By the same token, if there are only regular patterns in nature, then there’s no obvious purpose in nature, and no obviously privileged perspective on nature. Patterns emerge everywhere, and may differ based on one’s perspective. From an economic perspective, one might observe the flow of money entering and existing a hospital one afternoon, while from a disease transmission perspective, one might observe an outbreak.  

Moreover, Nietzsche strongly suggests, these perspectives have no other source than us. God is dead and we killed him. We should take responsibility for that by attending to how we’re still influenced in many ways by our past. But we should also take responsibility insofar as we are the only remaining source of what we take to be objectivity, purpose, and laws….

…by Adopting the Role of God.

Aristotle claimed we’re social creatures by nature, and that anyone who could thrive outside society was either an animal or a God.

Nietzsche suggests we take responsibility by being intentional about our practices, and to take seriously the truth of perspectivalism, the view that there is no privileged perspective on reality. Let’s make sense of this with a stepwise procedure:

1.      Focus on a proper part of reality, all it P
2. View P at either granular, microscopic, macroscopic, interstitial, etc. levels
3.  Divide P into proper parts, call them partitions of P
4.      Focus on a particular partition of P
5.      Say what is true or false within that partition

More concretely:

1.      Focus on Chicago, Illinois
2.      View Chicago, Illinois at the surface level or granular perspective
3.      Divide Chicago, Illinois into, say, buildings, people, pets, etc.
4.      Focus on our classroom
5.      There is at least one human in that classroom; there are no puppies

For contrast:

1.      Focus on Chicago, Illinois
2.      View Chicago, Illinois at quantum perspective
3.      Divide Chicago, Illinois into electrons, neutrons, etc.
4.      Focus on our classroom
5.      There are no humans in that classroom; there are electrons

Note, each of (1)-(4) are independent of each other in an important sense. For example, you need not partition P into the same shapes or sizes, or even consistently. Each provides an impressive degree of freedom with respect to how you look at the same phenomenon. Moreover, fixing each variable as you move down the list, leads to you being able to say more ‘true’ things. In the preceding, at step 3, you can already say there are electrons, by step 4, you can say there is a smaller number of them than you could’ve said in step 3, etc.

This is – I think – how perspectivalism operates in scientific inquiry. Scientists focus on a part of reality, fix variables for focus, then define truth with respect to that partition. This suggests, however, truth is always relative to a partition. In other words, there is no objective truth. And since partitions are determined by our interests, truth ultimately stems from us. So-called ‘laws’ are regular patterns observed in these partitions, and purpose follows from those laws and so our interests.

Acknowledging perspectivalism is the first step in taking on the role of God. But intellectual understanding is insufficient for adopting the role. This is because it’s not enough to simply realize there are multiple equally valid perspectives; one must seek flexibility among them at any given time. Great individuals acknowledge the plurality of perspectives. The best individuals, however, are those who remain flexible in moving among them if needed. I read Nietzsche as advocating such flexibility. Indeed, I read Nietzsche as advocating what the ancient skeptics called the mental state of aporia among these ways of understanding the world.  

There were three major schools of thought operating when the Skeptics were around. Their own school, the Dogmatists, and the Academics. Dogmatists claimed to know things with certainty; Academics claimed to know things were not the case with certainty; Skeptics claimed to know nothing with certainty. Skeptics also claimed they were the only philosophers who were still searching for knowledge since they were the only ones who didn’t claim to have it. They recognized claiming to have knowledge closed off flexibility to alternatives. Skeptics esteemed the journey for truth over the destination. Maintaining flexibility among competing theories and claims about the world was a desirable philosophical goal, and being in the corresponding mental state, the goal they sought. That mental state, as mentioned above, was called aporia. It’s a state of being uncertain – for any claim - whether a claim is true or false. It ain’t easy. Try it out. Try to doubt that you exist…

Nietzsche seems to be just such a seeker of truth, and seems also to be claiming such seeking is the best way to live. Skeptics cultivated virtues of argumentation to help them achieve aporia. It’s plausible to see Nietzsche as gesturing at similar virtues himself.

Traits of a Dancing Star

Let’s examine a few plausible exemplars of ‘overcoming dominant perspectives’ and see if we can line up observed characteristics with claims Nietzsche makes about perspectivalism.

  • Genius and Confidence: Einstein was a genius who changed the world by providing ample evidence for a paradigm shift in physics. But genius isn’t enough. Confidence is needed as well. Einstein’s theory was motivated initially on purely explanatory grounds. It made predictions, but they were difficult to test given the macroscopic scale on which the theory operated. Eddington tested Einstein’s theory eventually, and after empirical predictions confirmed the theory, Einstein was asked what he’d have thought if the results conflicted with his theory. He said, “The world would have been wrong, because the theory is true.” That’s quite a bit of confidence. Some might say too much…but perhaps ‘too much’ confidence is precisely what’s needed to take seriously alternative perspectives.

  • Grit and Diligence: Genius and confidence aren’t enough. Heisenberg had both during his ventures into the quantum world. Many of his discoveries were met with derision by physicists. Later, when his ideas were finally taking hold, he was asked how one changes the minds of old physicists. He said “You don’t, they just die eventually.” Heisenberg maintained his theory in the face of disbelief by peers. That surely must’ve taken quite an emotional toll, but he remained diligent and continued his work. Eventually, he was not only able to overcome an existing – prevalent – view of physics with his novel theoretical claims, but also the derision of his respected peers. In this case, he learned to pick his battles.

  • Cognitive Friction and Exploration: W.E.B. Du Bois couldn’t understand – as a child – why white children wouldn’t play with him. He first thought they believed he wasn’t intelligent, so he achieved academic excellence. They didn’t play. He then thought they believed he wasn’t athletic, so he became an athlete. They didn’t play. Eventually, he inferred the color of his skin was the issue. The white children didn’t notice this, because they didn’t have to explain why other people weren’t playing with them in the same way Du Bois needed to explain that. He experienced cognitive friction that led to a need for an alternative explanatory framework.

  • Etiology of Values and Courage: Joy James observes much literature on race and racism in the U.S. calls for political, economic, and moral change in how, say, Black people are treated. This in turn generates much policy discussion on, say, reparations, respect, etc. James asks, however, why one might want money? That’s a colonizer value. Dignity? That’s a colonizer value. Political change? Colonizer value. James questions whether these values should be the targets for marginalized individuals. They’re the values of the colonizer, and so always play to that advantage. James suggests constructing new values, creatively, as best as one can. One must be wide-eyed and courageous.

  • Errors as Victories: Henkin is known mostly for simplifying a very difficult proof by Kurt Godel. Henkin claimed, however, that his discovery of this proof was an accident. He was intending to do something else entirely, but he recognized the proof for what it was when he saw it. He used that error to overcome.

Let’s take these themes and combine them to gain a picture of the aporia goal. One must exhibit genius, creativity, confidence, remain steadfast, have grit, experience cognitive friction and seek to explore and explain, understand where their values come from and be courageous enough to overcome them, and recognize errors are often how one makes progress. If I didn’t know any better, I’d think Nietzsche was suggesting such as virtues for those elite seekers of aporia

Existentialism Recitation III

Background Concepts

Engagement with the World

I read Kierkegaard as responding to a Hegelian religious tradition that claimed we could understand both the natural and supernatural world with the use of reason. Kierkegaard is, in part, providing a counterexample in the form of a paradox he believes is found in a careful reading of the Binding of Isaac.

In the preface, Kierkegaard sets the discussion up in a useful way. He outlines three types of engagement with the world:

            Aesthetic                        Ethical                          Religious

He claims philistines are under the first, Knights of Infinite Resignation under the second, and those of Faith under the third. There is a preference ranking with the last being considered best. If we think of Kierkegaard as examining ways in which one can have faith, we can make sense of his discussion of previous philosophers like Descartes and the Skeptics, who were known to be distinct with respect to ways of doubting. Consider the following:

Aesthetic                Ethical                          Religious

Simple Doubt         Sophisticated Doubt        Ancient Skeptics

Simple Faith           Sophisticated Faith        Knight of Faith

Simple faith is unreflective, sensory, and, well, philistine. Similar remarks apply to methods of doubt. One might simply doubt to doubt, unreflectively, saying things like “It’s all your opinion” or “Everything’s relative” without much thought. Simple doubters parrot such statements much like those with simple faith parrot sermon or scripture.

More sophisticated are those with ethical faith or doubt. This might be more appropriately called principled faith or doubt, since the important feature is that either emerges from principles. Doubting in a principled manner was what Descartes was doing, one sensory experience at a time, for the purposes of building a grand theory. Similarly, sophisticated faith of this sort seems what the Hegelians were doing, uncovering principles of the natural and supernatural world through reason alone. Importantly, this is a reflective process, requiring great work, and much patience and skill. It is admirable.

Still, sophisticated doubt and faith fall short of religious. Here we have what Kierkegaard will elaborate as the Knight of Faith, who leaps the bounds of logic to accept while resigning the natural world. We find a parallel in ancient skepticism, a school that believed the point of inquiry into truth was to continue searching for it, not to find it. For any argument concluding P they’d give just as good an argument for not P. The point was to generate instability of belief, since that was how one maintained the journey towards truth. The parallel here with the Knight of Faith seems to be that they’re never confident of any, say, acquisition of some principle of the natural or supernatural world. Rather, they’re open towards being wrong even when they believe they’re right. The Knight of Faith is more concerned with the journey rather than the destination.

Sources of Knowledge

The Knight of Faith also differs from that of the Knight of Infinite Resignation with respect to the sort of knowledge they have. Kierkegaard says the latter’s knowledge of God is mediated, while the former has direct access to God. I think of this as a difference between:  

Knowledge by Description

Knowing by Acquaintance

The Knight of Infinite Resignation has mediated access to God through, say, ethical principles like the ten commandments, which is like reading everything there is to read about God as a description. But that falls short of experiencing God directly in an unmediated manner. The Knight of Faith leaps into faith through the absurd, and in that act gains knowledge about God directly, by being acquainted with God.*

*Note: I think an equally good case can be made for thinking Kierkegaard is playing on the distinction between:

Knowing how

Knowing that

I can read every manual on how to play tennis, and so know that I should do this or that in a match, but I won’t know how to play tennis until I actually start playing. Kierkegaard is plausibly understood as claiming the Knight of Infinite Resignation has knowledge that God commands this or that, through ethical principles like the ten commandments, but that the Knight of Faith has knowledge of how God commands this or that, through faith in the absurd. To complicate matters further, it seems plausible given the nature of the absurd and resistance to rational comprehension, the Knight of Faith has knowledge by acquaintance of instances of how God commands through the absurd, but lacks any general descriptive knowledge about how God commands since the nature of the absurd is such that general rules cannot be constructed from instances. 

Philosophical Toolkit

Motivation

Before turning to the story of Abraham, it’s worth briefly discussing a strategy I’ve found useful for understanding direct experiences that I myself have not, and perhaps cannot have. This is relevant here because it’s unlikely any of us have ever experienced what Abraham experienced in this story, and that may make us feel like we can’t really understand what he’s going through. Abraham exhibits faith in the absurd, and it’s plausibly we can’t understand the absurd; that’s the point.

That said, just because we'll never understand, say, a circular square, we can nevertheless understand something being square and something separately being circular. Similarly, we can divide and conquer this story. Specifically, we can make progress by, say, thinking about aspects of the story on analogy with things we have experienced.

I teach a course called the Philosophy of Race and Racism. Clearly, there's a white elephant in the room (me!). I address this immediately when the semester begins, and return to it throughout so we don’t lose sight of it, since it’s certainly relevant to our discussions that a white man is leading them; my views are informed by privilege that I can’t entirely escape. That said, I have something to add to the discussion worth taking seriously that’s not simply that I’ve read lots of relevant literature. I grew up rather poor in a trailer park, have been to jail, was afraid of the police, don’t know my father, was physically and emotionally abused, dropped out of high school, didn’t start college until 22, etc. Simply put, I experienced a lot of traumatic events. They unfortunately and sometimes surprisingly overlap with traumatic experiences many individuals marginalized due to race have. I can speak from direct experience about such events, and in that manner illustrate the intersection of class and race discrimination, from the position of privilege. This is not to compare apples to oranges. I can't speak about what it's like to be a Black woman in America, and I'm not going to act like I can. I can – to some extent - speak about where our harmful experiences intersect with class.

Kierkegaard spends much time outlining how you might go wrong in understanding Abraham. That’s useful, by it’s a description of the scenario by telling you what it’s not. We’re going to try to understand the scenario by saying what it is. I think comprehension is much deeper if you have both. I call doing both in the manner just described Explication.

Explication Strategy

Let’s think about aspects of the Binding of Isaac story:

(1)   Love: I've loved; you have too presumably. I’m assuming Abraham loved Isaac. Consider how strongly you feel towards someone you love, how encompassing that can be, how much you’d be willing to sacrifice for them, and how much you’d be willing to do that happily.

(2)   Sacrifice: This is loss, but for some greater purpose. Abraham is plausibly understood as not simply losing Isaac, but sacrificing him for a great purpose. Think about the greatest sacrifice you’ve made in your life. While not the greatest, I once sacrificed a $200K career for love. It’s easy to see how (1) and (2) interplay in this example. I did so happily; I’d do it again.

(3)   Power: The relevant thing here seems to be overwhelming authority and unwavering power. God can’t be resisted; God is all-powerful. From a positive perspective, this is something inspiring and worth appreciating. I once visited Niagara Falls and felt the sheer awesomeness of the waves crashing over the rocks. I felt small, I felt powerless, but I felt appreciative. I didn’t feel in danger, but I didn’t feel like I wasn’t in danger either.

(4)   Consent: If I asked you whether you wanted to end class early, but before you answered said I’d chop off your arm if you didn’t stay in class, I don’t think it’d count as consent if you said “No.” You can’t consent – I think – under overwhelming threat of violence. Abraham appears to be consenting to sacrificing Isaac. I’m not sure; this seems a place where consent breaks down. God cannot be resisted. The intersection of (3) and (4) seem clear. Niagara Falls wasn’t trying to kill me, or asking some great sacrifice. This isn’t always the case in our experiences.

(5)   Ethical Tension: Here is where we find, I think, the most obvious paradox. In class, this was presented as tension between Abraham being asked to murder Isaac and ethical law prescribing one not murder. I don’t think that’s quite right. “Murder” is typically understood as ‘unjustified killing’ but Abraham is plausibly understood as being asked to justifiably kill Isaac. It’s a sacrifice, and those have a purpose. I think the ethical tension here is more precisely between Abraham being asked to sacrifice his son, which is a violation of parental obligation we all seem to have.

(6)   Faith: Faith not only comes up in religious contexts; faith arises in science as well. There is some measure of faith in assuming one set of axioms explains the world while another doesn’t. Data always underdetermines theory; ultimately we have to make a choice about which theory to choose. Choosing primitives is in part a matter of faith. On the other hand, choices about what you think needs explaining by your theory is also a matter of faith. A very thoughtful Christian friend of mine believes the way he understands the world needs something like God. He has data to explain I don’t recognize, so I don’t feel the pull of this need. He’s primitive data to explain, and that strikes me – as primitive assumptions tend to – as having faith.

Each of these aspects of the story seem things we can understand given we’ve had direct experience with them in various ways. The trouble for us in the Binding of Isaac is putting them all together. Now that we have a handle on these aspects, we’ll be able to see more clearly how Kierkegaard thinks the paradox of faith emerges in the Binding of Isaac.

Binding of Isaac

Which Paradox?

What exactly is the paradox? Let’s explore. Consider the following first pass:

(1) Abraham seeks to murder Isaac
(2) Murder is unjustified killing
(3) Hence, Abraham seeks to unjustifiably kill Isaac
(4) Abraham is a just individual
(5) Just individuals do not seek to do unjust actions
(6) Hence, Abraham does not seek to do an unjust action

Lines (3) and (6) are in conflict, i.e. they generate a paradox. This is a straightforward reading of the text. I don’t think it’s adequate, however, because I don’t think premise (1) is true. I think it’s more plausible that Abraham is asked to sacrifice Isaac. Sacrificing Isaac is not the same as murdering Isaac, since sacrifice might be justified. Murder is – by definition – unjustified. This provides Abraham some flexibility. Replacing “sacrifice” for “murder” and adjusting premises accordingly, we have:    

(1) Abraham seeks to sacrifice Isaac
(2) Abraham is a just individual
(3) Just individuals do not seek to do unjust actions
(4) Hence, Abraham seeking to sacrifice Isaac is not an unjust action

Note, I’ve removed the premise mentioning “murder” since it was irrelevant; I’ve also removed the entailment claiming Abraham seeks to unjustifiably kill Isaac, since that no longer follows given the use of “sacrifice” instead of “murder”. Of course, with these adjustments, there is no obvious paradox. For that, we also need it to be the case that Abraham seeking to sacrifice Isaac is unjust. So far, this doesn’t follow from the premises. But we can strengthen them as follows:

(1)   Isaac is Abraham’s son
(2)   Abraham seeks to sacrifice Isaac
(3)   If S is the parent of S’, and S seeks to sacrifice S’, then S seeking to sacrifice S’ is unjust action
(4)   Hence, Abraham seeking to sacrifice Isaac is an unjust action
(5)   Abraham is a just individual
(6)   If S is a just individual then S does not seek to do unjust actions
(7)   Hence, Abraham does not seek to do unjust actions 

Here we have a conflict between (4) and (7), and so the paradox emerges from Abraham’s parental obligation – which is underwritten by ethical principles – and Abraham following God’s command to sacrifice.  

That said, I still don’t think this is quite right. Consider, if the preceding is all we have to say about Abraham, then it’s not clear how to distinguish him from, say, Agamemnon who sacrificed his daughter Iphigenia. The preceding argument applies just as much to the latter case as to the former. So we must do more work to distinguish Abraham from Agamemnon.  

Fortunately, our explication of aspects of the Binding of Isaac can help us. Above we observed the conflict between ethics and God’s command in this tale. But we also observed the presence of what appears to be another paradoxical element, namely, that between God’s power and Abraham’s ability to consent. That is not mentioned in our argument so far, and may be what we need to distinguish Abraham from Isaac. To contrast, Agamemnon might’ve been dishonored, or shamed by his soldiers and culture, had he not sacrificed his daughter; Abraham on the other hand was being commanded by an all-powerful God. I suspect the consequences for dissenting were far more substantial in the latter case, even those they’re substantial in both. Let’s turn this into an argument:  

(1)   Abraham consents to sacrifice his son Isaac
(2)   Abraham is a just individual
(3)   Just individuals do not consent to do unjust actions
(4)   If S is the parent of S’, and S seeks to sacrifice S’, then S seeking to sacrifice S’ is unjust action
(5)   Hence, Abraham consenting to sacrifice Isaac is an unjust action
(6)   If S is a just individual then S does not seek to do unjust actions
(7)   Hence, Abraham does not seek to do unjust actions
(8)   If G commands S to do an action and G is all-powerful, then S cannot consent to do that action
(9)   Hence, Abraham cannot consent to sacrificing his son Isaac

There are, then, two contradictions lurking here: (i) Abraham consenting to perform an action he cannot consent to; (ii) Abraham being just and yet violating ethical principles by sacrificing his son Isaac. The story of Agamemnon at best has only (ii). That’s sufficient to distinguish them.

It seems to me, moreover, that Agamemnon’s action is calculating in a way that Abraham’s is not. Agamemnon spends much time thinking of the right thing to do; Abraham hears the call of faith, says little, saddles up, and rides to do what he must. It’s claimed by some philosophers that character is that set of habits that underwrite action without need for deliberation. Abraham appears to be acting out of a faithful character; Agamemnon not so much.  

Euthyphro Dilemma 

I take Kierkegaard to be attacking the following claim: 

(M) If God commands x then x is morally permissible

This should seem like an intuitively plausible claim. Consider, if (1) is true, then you can be sure that whatever God commands you to do will be morally permissible. There may, of course, be other things that are morally permissible. That is, there may be morally permissible actions that God hasn't commanded you to do. Whatever the case, the important point is that you have a firm link between what God commands and what is morally permissible. That gives you some surety as to what God thinks is morally okay. Moreover, this is precisely the sort of principle those who think you can simply rationalize your way to knowledge of the supernatural would adopt, i.e. Christian Hegelians.

But the Binding of Isaac is a counterexample to (M).

(1) SUPPOSE: If God commands x then x is morally permissible
(2) God commands Abraham to sacrifice his son Isaac
(3) Hence, Abraham sacrificing his son Isaac is morally permissible
(4) Abraham sacrificing his son Isaac is not morally permissible
(5) Hence, it's not the case that if God commands x then x is morally permissible

We supposed (1) for the sake of finding a contradiction. (2) is true of the scenario, and (3) follows by logic from (1) and (2). (4) is motivated by considering Abraham’s parental obligation to Isaac. But then (3) and (4) are in conflict. If you assume something and that leads to contradiction, you are allowed to assert the negation of what you supposed. Hence, (5) follows since it is the negation of (1). That is to say that (M) is false. I take this to be Kierkegaard’s general argument against (M).

You might have worries about this conclusion though. You can’t rationalize yourself to faith, but that also means God’s commands are something of a mystery, even though they trump ethical principles. We motivated (M) by observing how it links whatever God commands to morality, so you can be sure they don't come apart. But if (M) is false, then you can't be sure. You lose your connection to what God views as morally permissible. But what God thinks is morally permissible may differ widely from what we take ethics to command.

  • Response: God in the Old Testament gave us the commandments. We know what the right thing to do is.

  • Rejoinder: Do we? Abraham might disagree. You might say God has it in mind that we abide by the commandments for the most part, and only deviate when he asks. But that just pushes the question back. We seem to lose track of whether what we think is moral is ok or not. Admittedly, perhaps (M) wasn't so good a rule anyway. According to (M), a plausible reading of the Old Testament has it that homosexuality is morally wrong. But that seems mistaken. That might suggest (M) is false independently. In any event, the point becomes even stronger if (M) is false. If we lose (M), we leave open that what God commands isn't necessarily morally permissible, but we also lose knowledge about what is morally good, i.e. whether the commandments are – in fact – morally right. If (M) is false, what's right is what God says at a time. You might think this is OK if you think God is constant, but the Binding of Isaac suggest God isn’t so constant in command.

Let’s put this point more sharply using a variation of the Euthyphro Dilemma. Modernized a bit, the dilemma is this:

Is A good because God commands it or does God command A because it's good?

This is called a dilemma for a reason. Neither option seems okay. Let’s take them in turn:

  • Suppose A is good because God commands A. Then (M) is false. But we lose our grip on what good means. We're at God's mercy. Perhaps this is to be expected given the reliance on faith, God's power, and our inability to consent. We see some of the issues that might arise on this view. But honestly, the alternative isn't much better. To see why…

  • Suppose God commands A because A is good. Then what is good precedes what God commands. But then there is a standard for goodness independent of what God commands. But then we should be seeking this standard rather than God.

    • Response: Perhaps our only access to the standard is through God.

    • Rejoinder: If that's so, then we're back on the other horn. For we have no access to what's good other than what God allows us to see. But the Binding of Isaac makes trouble for this reading. If there's an independent standard of what's right, it seems plausible that in at least one of these cases God has asked Abraham to do something that is not in accordance with the standard. But then if God is our only access to the standard, we seem in a bad position, since God seems unreliable. 

Ultimately, it seems like if we must choose we should choose the side Kierkegaard lands on. (M) is false, but we lose our grip on the relationship between what's ethical and God's will.

Expanding the Euthyphro Dilemma

The troubling position we find ourselves in might make you seek to reject the conclusion of Kierkegaard's argument. To do that - since it's valid - we reject one or more premises. Which would you reject?

It's not obvious which premise to reject. It looks like a good argument. But perhaps the argument is not as straightforward as outlined above. To see why, consider again the Euthyphro Dilemma and think more carefully about which horn Kierkegaard would accept…

  • If x is good then God commands x. I don't think Kierkegaard accepts this. This would be to put constraints on God. For if God commands x because x is good, then there is an external standard of God outside of God. But then we should be appealing to that standard, rather than God. That standard is - ethically speaking - prior. This doesn't fit with Kierkegaard's notion of God, I think, as unrestricted.

  • If God commands x then x is good. This is something like a divine command view. What good amounts to is just what God says. Then it's trivial that God commands the ethical, since that's the connection. But note, this is essentially (M). If God commands Abraham to murder Isaac, then Abraham murdering Isaac is good. But Kierkegaard clearly thinks it's not good that Abraham murder Isaac. Suppose otherwise. Then Abraham should simply do God's will because it's the right thing to do. He might even be able to explain this to others, e.g. God said to do it, and you know when God says to do something it's right, end of story. Then there’s no paradox. But since Kierkegaard thinks there is a paradox, he must think what God commands Abraham to do is not good. Since this horn entails (M) and Kierkegaard rejects (M), Kierkegaard rejects this horn too.

But now we’re in an even worse spot than before, for we don’t seem to be able to fit Kierkegaard in the dilemma at all! We seem to have a false dichotomy. We've posed and either/or situation and assumed Kierkegaard must be on one side. This need not be so. And I think the reason Kierkegaard isn't susceptible to the dilemma helps illustrate why the above argument might not be as detailed as it should be.

Kierkegaard seems to be operating with at least two notions of "good". There's the notion of good at the level of ethics, and the notion of good at the level of God. Hegelians and Christians at the time seemed to have a unified notion of good. They'd fall into the dilemma, so they'd be urged to pick a side. Kierkegaard has a bifurcated notion of good. There's ethical good, and there's religious good. They might be in tension, but the latter trumps the former when they conflict. This is why Kierkegaard doesn't fall into the dilemma. The dilemma employs a unified notion of good.

Can you think of a way to expand the dilemma to make it apply to Kierkegaard, perhaps by employing two notions of good?

Ultimately though, we need to complicate the above argument for Kierkegaard even in light of this information. Kierkegaard was using premises his opponents accepted. That includes a unified notion of good. But it may soften some of the worry we had about the conclusion. There may be ethical good, and this is what we can come to by reason alone. Then there might be religious good, which is provided by divine insight. When they are in conflict, the divine trumps the rational. But still – Kierkegaard’s opponents might say - we may make headway in understanding what's ethical by using rationality. We just can't assume that we've figured it all out. We need God for that. So, we still have some link to what's ethical, namely what we can uncover with rationality, but we just must remain open to the ethical being trumped sometimes as a matter of faith.

Objections and Exercises

Objection #1:

(1)   The Knight of Faith cannot explain certain harmful choices to anyone
(2)   For any agents S, S’, and choice C, if S cannot explain C to S’, then S cannot justify C to S’
(3)   Hence, Knight of Faith cannot justify certain harmful choices to S’
(4)   If agent S is a member of the moral community, then S must be able to justify harmful choices to other agents in that community
(5)   Hence, the Knight of Faith is not a member of the moral community

The absurd cannot be explained to those who haven’t experienced it. Consider some analogies. There’s a difference between respecting Shakespeare by reading his work and learning others respect him, versus studying the bard intensely and respecting him through that study. Imagine trying to explain to someone who didn’t have that deep appreciation of Shakespeare, why you respect him after your intense study. Similarly, there’s a difference between, say, reading and memorizing love poetry, and actually feeling love. Imagine explaining to someone versed in love who has never experienced it, why you love someone. In both cases, it seems you need direct experience to understand the phenomenon on that level. What applies in these cases seems to apply to Abraham and the absurd. Abraham is presumably not going to be able to explain himself to others, i.e. why he intends to sacrifice Isaac. This is support for (1).

Moreover, it seems (2) is true, since plausibly justifying some choice to someone seems to require being able to explain yourself to them. (3) follows by logic from (1) and (2). And it seems plausible with respect to (4) that being a member of the moral community, that is, an agent who has dignity, deserves respect, is autonomous over their actions, and intends to live in a community alongside others of this sort, requires an ability to justify choices harmful to your fellow community members. (5) follows from the preceding by logic, concluding faith of the sort Kierkegaard has in mind seems to exclude one from the moral community thus understood.

Exercise #1:

Is this sound? If so, all the premises are true. If not, one must be false. I think the weakest is (4). This is partly because it’s ambiguous. Consider to ways to read the premise, based on how we understand the scope of the word “must”:

(4*) MUST [If agent S is a member of the moral community, then S is able to justify harmful choices to other agents in that community]

(4**) If agent S is a member of the moral community, then MUST [S is able to justify harmful choices to other agents in that community]

See if you understand why these are different. As guidance, first assume (4*) is true, and see if that means (4**) is also true, or whether (4**) might be false. Then, assume (4**) is true, and check whether that means (4*) must thereby be true or false. If one of the readings can be true while the other false, then the meanings of the expressions differ.

Once you’ve done this, see whether the argument remains valid if you replace (4) with (4*) in the original argument, or (4**) in the original argument. Remember, an argument is valid just in case if all the premises are true, then the conclusion is also true. Check if it’s sound as well with such replacements.

Objection #2:

(1)   On Kierkegaard’s reading of the Binding of Isaac, God is either not all-knowing or not all-good
(2)   God is both all-knowing and all-good
(3)   Hence, Kierkegaard’s reading is false

This is too quick; I think Kierkegaard has a response. He believes humans are fallen, sinful, limited, and fallible. Moreover, this is a show not tell God. God could've told Abraham the truth about the exercise, but took this as a teachable moment to show Abraham how much faith he has in God, by forcing him to conflict God's command and the ethical. God knows telling fallen things only goes so far, but showing has them feel the force of his word.

This response, however, puts Kierkegaard in another bind. Consider:

(1)   SUPPOSE: Through God all things are possible
(2)   If (1), then God could explain Abraham’s faith to Abraham without the test
(3)   Hence, God could explain Abraham’s faith to Abraham without the test

If Kierkegaard’s response to the first argument is correct, then we’re still left without an explanation for why this show rather than tell all-powerful God tested Abraham when he didn’t have to.

Exercise #2:

There seems to be a conflict here between God understood by Kierkegaard as being all-powerful, and God as being all-good. Re-examine the expanded Euthyphro dilemma above and explain how Kierkegaard might respond to this objection.  

Existentialism Recitation II

Metaphysics Interlude

The word "theory" is frequently used among scientists. I'm sure you've heard of the "Theory of General Relativity" or perhaps the "Germ Theory of Disease" or "Evolutionary Theory." Scientists propose theories often to do two things: (i) Explain existing data; (ii) Make predictions. General Relativity was a unified explanation of much apparently incompatible data; General Relativity makes predictions about, say, how light moves through space. Similarly, the Germ Theory of Disease provides an explanation for a diseases spreading through populations, among other things; the Germ Theory of Disease predicts, say, that if you let someone ill with the flu cough on you, then you'll likely get the flu too.

Sometimes scientists propose theories to explain data that lack any obvious empirical predictions. Murray Gell-Mann suggested the existence of quarks as underwriting the existence of electrons, protons, etc. Other physicists were not exactly kind to this proposal. They criticized Gell-Mann for not providing a theory with empirically testable consequences. Some physicists went as far as to find way to test for the existence of quarks. Turns out, there are good reasons to think there are such things on empirical grounds. Gell-Mann's pet theory was empirically confirmed, and he eventually was awarded many honors for the discovery.

The important thing to note about the preceding history lesson is that scientists propose theories to explain and predict. If explanations are poor, the proposed theory might not seem so good. If predictions are incorrect, the proposed theory might be considered falsified.

So much for how "theory" is used in empirical sciences. This is philosophy! Philosophers engaged in theory building aren't often making empirical predictions. This is especially true among those studying metaphysics. Metaphysics is a branch of philosophy that - roughly speaking - seeks to explain the fundamental nature of the world. A consequence of this approach to theory building is that metaphysicians don't often have the benefit of making empirical predictions. You might take this as a significant cost to metaphysics in general. Why care about theories that can't be empirically falsified?

Because we nevertheless want explanations for the way things are, and empirical sciences don't seem equipped to provide answers to every legitimate question. Suppose we find the "One, True, Scientific Theory." This theory answers any question we might have about the empirical world. Here's one question it won't be able to answer though:

(W) Why is the "One, True, Scientific Theory" true, rather than some alternative theory?

This question outstrips the empirical world. Go ahead, try and think of a way to test (W)…

In any event, it's not like metaphysical theories aren’t falsifiable, at least in some sense. Metaphysical theories still have to explain data, even if they don't make empirical predictions. If they do a poor job, then they're no good. How do we decide? Some cases are more obvious than others. Suppose I want to explain everything by simply saying "God exists and made everything." That's a very simple theory; it explains everything. That doesn't mean it's a good theory; it doesn't make clear how it explains everything…

There are other ways to dispute theories. Theories are comprised of axioms. These are the building blocks. You've likely seen such things before. Euclid's Elements starts off with axioms, from which he  builds a theory of geometry. Axioms are often primitive assumptions of a theory. You don't argue for them (imagine trying to argue for the existence of a point…), but that doesn't mean you get them for free. Axioms earn their keep based on how much they explain. A good theory explains whatever domain you want to explain, and is composed of axioms that show very clearly how that explanation works. Euclid describes a geometric theory, and each axiom is used to explain precisely how that theory works. There are no surprises.

Sartre's Brand of Existentialism

You might wonder why I'm talking about metaphysics in a class on existentialism. Well, today we're talking about Sartre's Existentialism is a Humanism, where Sartre is responding to three objections to existentialism in general. His main line of response is that his objectors are confused. His strategy for responding to them is to clarify existentialism as a theory. He does this by outlining the axioms of his brand of existentialism. Sartre is engaged in theory building for the sake of clarification.

We will take the axioms in turn, and see if Sartre has adequately responded to his objectors. I list the axioms here:

(A1) Existence precedes essence
(A2) The only standards of evaluation are those created by agents
(A3) There are standards of evaluation
(A4) For any agent S, action A, and context C, if S does A in C, then S creates a standard of evaluation in C, namely, that any agent S' do A in C

Consider (A1):

  • By "existence" he simply means the brute fact that something exists.

  • By "precedes" he means, I think, "explanatorily prior". To say x is explanatorily prior to y is to say that any explanation of y involves x. Suppose you and I are having a conversation. That you and I exist partially explains the conversation. We say our existences is explanatorily prior to the conversation. Similarly, the set {John} exists because of me. I am explanatorily prior to the singleton. Atoms are explanatorily prior to tables. The list goes on and on…

  • By "essence" he means function or purpose. Let me unpack these further. "Essence" is Aristotle inspired jargon. For Aristotle, we can provide four different sorts of explanation for why something exists. Consider a table. One explanation is material, i.e. the wood explains why the table exists. Another is formal, i.e. the shape of the table explains why the table exists. A third is efficient, i.e. the producer of the table or artisan. The last is the final explanation, i.e. the point of having a table. Sartre is using the word "essence" as roughly synonymous with "final cause" or purpose.

Altogether, (A1) says the brute fact of human existence is what explains whatever purpose agents have, rather than the other way around.

Consider (A2) and (A3):

  • A knife has a function and is presumably designed to satisfy that function. But in a world with no objective values, there are no objective standards of evaluation. If there are any standards, then, they must come from us, for agents impose standards. So, if a knife can be better or worse, then it must be better or worse according to some standard imposed on it by agents. Since there are values and they can't be objective, they must come from us.

  • What goes for knives goes for us too, though in a different way. Knives are material objects and can acquire functions, but we are also material objects that acquire functions. The difference here is that we create functions for ourselves.

Consider (A4):

  • This axioms bears weight in the theory, as we will see in a moment, since it's needed to respond to the more serious objection offered against existentialism.

  • Before we turn to that though, one things is worth noting…As it stands, (A4) may be either too weak or too strong. To see how, suppose I have to decide whether to save a child from drowning or not, and I'm fully able to do so without any difficulty. Suppose I do it. Then according to (A4), I'm prescribing in my action that anyone else - S' - save the child from drowning - A - in similar contexts C. But what does "similar contexts" mean?  Let's think about two extremes, trading on the distinction between types and tokens. Tokens are not repeatable; types are repeatable. In a classroom of students, there are many token students, but one student type, of which they're all instances; similarly, there are many token humans, but one human type. Let's apply this to contexts. That is, we can think of contexts as either types or tokens.

Suppose "C" in (A4) means a token context. Then it can't be repeated. Then (A4) is trivial, since I'm the only person who will ever be in that context, so of course everyone ever in that token context should do what I did; I did it!

Suppose "C" in (A4) means a type of context. Then it can be repeated, but it's not clear where to draw boundaries on contexts. Suppose I'm unable to swim and my trying to save the drowning child will ultimately kill us both. If context is understood broadly enough as a type to mean something like "a child is drowning and there's one person there who can help" then (A4) will say I should save the child in this new context. But that seems like the wrong result. Surely Sartre doesn't mean to say anyone should do the same as I or you or he does. Saying otherwise makes (A4) vacuous. Clearly, "C" needs to be spelled out in more detail.

But don't let me trick you here! It's true (A4) needs some work, but let's give Sartre whatever specification of context he needs to get his responses to objectors off the ground. This is permissible, because - remember - axioms are assumptions about theories; they earn their keep based on whether they can explain what they're designed to explain. If we want to dispute (A4), we need to think hard about whether this axiom - which I've claimed is very important in Sartre's defense - can do the work he claims it can.

Can it? Sartre considers three objections in this essay. I'm only concerned with the last, that existentialism is subjectivist about values.

(Q) Using the resources (A1)-(A4), can Sartre adequately respond to the charge that existentialism leaves us with only subjective values

My answer: No. It's a half measure at best. I think Sartre is biting the subjectivist bullet here, and trying to soften the worry by offering (A4). This is common when building a theory. We're not engaged in theory building - whether metaphysicians or empirical scientists - to provide perfect theories of the world. Perfection is too high a standard. Every theory has counterexamples; good theories provide explanations for those counterexamples, and do a good job of explaining why they're not so bad. This is just to say, simply because there is a counterexample to a theory, it doesn't mean the theory is dead. A theory may survive given its explanatory power, for instance.

This is not however to say I think Sartre's theory as characterized by (A1)-(A4) survives. Of course, you may not be moved by the preceding worry against existentialism. You may agree with Sartre that there are only subjective values. As a matter of fact, I agree with him…

Still, there are many ways to kill a theory. If you can show the axioms of a theory are inconsistent, or conflict with each other, then you can be sure that theory is false. I'm going to try and make the case that (A1)-(A4) are inconsistent, with the following argument:

The Parental Objection to Sartre's Existentialism

(1) SUPPOSE: (A1)-(A4) are true
(2) SUPPOSE: Sartre decides to and does have a daughter - Jessica - according to (A1)-(A4), who in turn raises a daughter - Sally
(3) If (1) and (2), then Sartre's action of raising Jessica according to (A1)-(A4) prescribes that Jessica raise Sally according to (A1)-(A4)
(4) Hence, Sartre's action of raising Jessica according to (A1)-(A4) prescribes that Jessica raise Sally according to (A1)-(A4)
(5) If (4), then Sartre creates a standard of evaluation on Jessica by raising her as he does
(6) Hence, Sartre creates a standard of evaluation on Jessica by raising her as he does
(7) If (6), then there is at least one agent - Jessica - whose essence precedes existence
(8) Hence, there is at least one agent - Jessica - whose essence precedes existence
(9) Hence, (A1) is false

I'll let you decide whether this is sound, i.e. whether the premises logically entail a true conclusion on line (9). Here's some advice. You might think the conclusion is true. But here I'm asking you whether the conclusion is true because of (1)-(8). That means you have to think about (1)-(8). As a general strategy, when evaluating arguments you can ignore lines that start with "SUPPOSE". Additionally, any line that starts with "Hence" follows from the preceding lines by logic. We're not going to dispute the logic in this class any further, so you can ignore those lines. That leaves lines (3), (5), and (7). If the argument fails, then at least one of those lines is false. To show a line is false, you try and provide a counterexample. As further guidance, I think (3) and (5) are plausible. If I were to dispute the argument, I'd try to undermine (7)…

Appendix

Sartre argues quickly that intuition cannot guide one's decision to do some action A over B. This is his discussion of the soldier. It’s very quick; I wanted to make sure how he’s arguing is clear. Here's the argument as I understand it:

Sartre's Objection to Intuition as a Guide to Decision

(1) SUPPOSE: Intuition guides my decision to do A rather than B
(2) If intuition P guides by decision to do A over B, then my intuition P to do A is stronger than my intuition Q to do B
(3) Hence, my intuition P to do A is stronger than my intuition Q to do B
(4) For any intuitions w, x, and actions y, z: w is stronger than x for me if and only if I actually do y rather than do z
(5) Hence, I actually do A rather than do B
(6) It is impossible to be guided by an intuition to do A and do A at the same time
(7) Hence, intuition cannot guide my decision to do A rather than B

(1) is either true or false. Sartre is supposing (1) to show this leads to contradiction. Since there are no contradictions in the world, if (1) leads to contradiction, then (1) cannot be true, so it must be false. Sartre claims (2) is true. (3) follows from (1) and (2) by logic. Sartre claims (4) is true. (5) follows from (3) and (4) by logic. (6) seems true based on the meaning of ‘guide’. It doesn’t seem plausible that intuitions can play a guidance role if they’re only useful at the time of action. That’s like saying the following is a warning: Someone yells “Watch out!” to someone else just as they’re being hit in the head by a stray basketball. That doesn’t seem much of a warning...

Textual aside: Sartre says "feeling is formed by the decisions I make" but that's not strong enough for the conclusion he draws about feelings here. For this argument to work, he needs to be saying instead that "feeling is decisions made". If he allows for temporally precedent formation, then this argument fails. This is why I believe he's making the stronger claim.

To evaluate this argument for soundness, i.e. for whether (7) follows from the premises, you need to check whether the premises are true. Ignore (1), (3), and (5), for the reasons given above. That leaves (2), (4), and (6). Can you construct counterexamples to any of these premises?

Existentialism Recitation 1

My task in this discussion is to make clear an aspect of existentialism that will motivate much of our discussion to follow, namely, the claim that there are  no objective grounds or justification for values. This might strike you as odd. Consider that the following seems true:

(T) It is wrong to torture infants solely for fun

Note, the claim in (T) concerns torturing infants solely for fun. This claim is silent over - contentious - cases where, say, such torture would be for some greater purpose. Put such cases aside. Note too, (T) is not saying said torture would be for no reason whatsoever. It's not obviously true that humans can act for no reason, so such a claim might be a non-starter. No, this claim seems defensible as it stands, i.e. (T) seems clearly true. If you doubt it, reflect for a moment. Don't you agree?

Suppose you do. Why is (T) true?

You might think it's simply obvious. But that seems an odd sort of justification. Many things that seem obviously true are in fact not. Tables seem obviously composed largely of matter, but they're largely empty space. Intuitions are notoriously susceptible to counter-evidence.

In any event, what seems obvious to you may not seem so obvious to others. Ted Bundy - the well-known serial killer - once claimed to know the difference between "right" and "wrong". He said "It's wrong to jaywalk, wrong to murder, wrong to not pay your taxes,…" Note what he's done here is lump together murder and jaywalking, among other things. He seems to not even understand the distinction between legal wrong or social wrong and moral wrong. What justification might we give him? "It seems to me obvious you're wrong, Ted" seems unhelpful. He may just as well say the same to you.

Of course, there are more of us than him, so maybe it's in his interest to play the clever knave and not murder, etc. Surely he values his own interest. Surely we might provide him that sort of justification, namely, "(T) is true because if you don't believe it we'll incarcerate you" or something like that. This amounts to morality by vote. That might work here, but it doesn't always. The slave trade was motivated by a majority who thought it permissible. That doesn't mean it was. This, moreover, applies to variations on the same theme: appeals to legal codes, cultures, family norms, etc.

Perhaps appealing to religion or some Godhead will help? Many existentialists reject such appeals, finding them just as unhelpful. We won't spend time discussing why here, but suffice it to say - for my part - I find the evidential problem of evil to provide sufficient evidence to dispute the existence of traditional Godheads.

Perhaps an appeal to human nature? This might amount to the claim that humans have a natural disposition not to torture infants for fun and so we shouldn’t. This is fallacious reasoning. Consider:

(1) If x's natural disposition is P then P is what x should do
(2) Humans have a natural disposition not to torture infants for fun
(3) Hence, humans should not torture infants for fun

The first premise encodes the Naturalistic Fallacy, that is, claiming the way something is, is the way things should be. There are many reasons to doubt this as a general rule. Humans are - arguably - naturally disposed to egoism, but it doesn't follow we should be egoistic. This - and many other examples - are reasons to think there's no royal road from dispositions and nature to morality.

It gets worse…There's also reason to think it wouldn't matter if there was such a road. The following argument cuts at the heart of the claim that there are objective moral values. Presumably, one major reason for thinking there are such things is to adjudicate disputes between those disagreeing over moral matters. Put another way, if there were such objective moral values, we'd have good grounds for saying Ted was wrong. We'd have a standard against which to assess him for failure.

Consider, however, the following Debunking Argument that suggests even if there were such objective moral values, they wouldn't be able to help us in this respect anyway:

(1) SUPPOSE: Natural selection theory is true
(2) If (1), then our evaluative (moral) attitudes have been shaped by natural selection
(3) Hence, our moral attitudes have been shaped by natural selection (from 1 and 2 by modus ponens)
(4) SUPPOSE: There are objective moral truths
(5) If (3) and (4), then there either is or isn't a relationship between our moral attitudes and objective moral truths
(6) Hence, there either is or isn't a relationship between our moral attitudes and objective moral truths (from 3, 4, and 5 by modus ponens)
(7) SUPPOSE: There is no relationship between our moral attitudes and objective moral truths
(8) If (7), then there is no reason to believe what we think are moral truths align with objective morality
(9) Hence, there is no reason to believe what we think are moral truths align with objective morality (from 7 and 8 by modus ponens)
(10) SUPPOSE: There is a relationship between our moral attitudes and objective moral truths
(11) If (10), then the best explanation for this relationship is that moral attitudes enhance fitness rather than track truth
(12) Hence, the best explanation for this relationship is that moral attitudes enhance fitness rather than track truth (from 10 and 11 by modus ponens)
(13) If (12), then we've no reason to believe what we think are moral truths aligns with objective morality
(14) Hence, we've no reason to believe what we think are moral truths aligns with objective morality (from 12 and 13 by modus ponens)
(15) Hence, if (4) then we've no reason to believe what we think are moral truths aligns with objective morality (from 4, 7-9, and 10-14 by disjunction elimination)

In other words, supposing natural selection theory is true, we're shaped by them and they're fitness-enhancing rather than truth-tracking. So, if there are objective moral truths, there's little reason to think we can track those truths, rather than track whatever enhances fitness. Moreover, there's little reason to think fitness aligns with truth. The reasoning to (15), note, follows from assuming there are moral truths. On that assumption, either our attitudes have some relation to them or not. Either way, (15) follows. The argument is valid, and there seem good reasons to think it might be sound too. Hopefully now, you see some motivation for skepticism about moral value. This is quite the worry…

Existentialists didn’t really give arguments like the one above for such claims. Even so, the preceding is a good reason to think they're right. But it gets worse. Existentialists were skeptical about objectivity all value. It applies just as well to logic. Consider an argument from Lewis Carrol, in his article What the Tortoise Said to Achilles:

Suppose you have an argument of the form:

(1) If P then Q
(2) P
(3) Hence, Q (from 1 and 2 by modus ponens)

Surely this seems valid, insofar as accepting (1) and (2) seems to commit you to (3). Rejecting (3) on those assumptions seems irrational. But consider this is all background assumption for the reasoning to go through. If we're explicit, then we should put it into the argument itself, as follows:

(1) If P then Q
(2) P
(3) If you have "If P then Q" and "P" then "Q" follows
(4) Hence, Q (from 1, 2, and 3 by modus ponens)

This seems valid, but note the initial request for justification in moving from lines (1) and (2) can be repeated for lines (1), (2), and (3). Indeed, it seems this request can be continued…forever…in other words, there is a regress.

This suggests that even in the case of logic, our justification for our rules, norms, values, etc., is ultimately ungrounded. This is a much more worrisome plight, I think, than the suggestion about moral values above. The Debunking Argument suggests moral values wouldn't be useful to us even if they existed, which is worrisome in part because we seem to lack grounds on which to justify our knowledge of such values; the above regress argument suggests there is no way to justify our logical values, even if they are useful to us.

To be fair, there are several responses one might make to each of these arguments (see my blog post “Trust Logic, Not Tortoises” for discussion of the the latter regress). Our purposes here is not to adjudicate, but rather to help you understand why some believe there is no ultimate justification for values in the world. It takes a non-negligible amount of work to mount a response to these worries, and it's contentious whether any responses are sufficient.

Do you feel existential dread yet? No? Don't worry, it gets even worse…

Put logic aside for a moment, and focus on the claim that there are no objective moral values. Suppose you believe that's true. Here's one thing I want to be able to say, and I mean I want to be able to say this literally:

(R) Our culture is better for no longer engaging in the slave trade

Presumably, you agree with this. It seems literally true to me that we've made progress in this way, i.e. we're better for no longer selling people as property. But here's the rub. If there are no objective moral values, how can I say that strictly speaking? To say we're "better" is to suppose some standard of moral evaluation. We've assumed there is no objective standard of moral evaluation. But many slave traders explicitly believed what they were doing was morally permissible, and so they wouldn't obviously think that we're better than they were. At best, our beliefs are just different rather than better. But if this is true, then we can't speak of moral progress even within a culture. That is, we can't literally say (R).

This generalizes across groups as you might expect, and is of the moment for our readings. Consider, the famous existentialist Jean-Paul Sartre wrote several important works as part of a resistance movement in a France occupied by the Nazis. Now, if there is such a thing as a just war, I think one of the best candidates for such a thing would be World War II. In fact, I believe it's true to say allied forces were right to fight the axis powers, because the axis powers were engaged in morally reprehensible behaviors. Presumably, Sartre believed this as well. But again here's the rub. If there are no objective moral values, then how can we say the Nazis were morally wrong, rather than they simply had a different set of beliefs that conflicted with ours? To be sure, they did have a different set of beliefs that conflicted with many of ours. The worry here is that's just not enough to capture the phenomenon. It seems clear the Nazis were wrong, and we were just in stopping them.

We'll see what sort of resources existentialists have to get out of this dilemma as we progress in the course. The upshot to take away here is that though the existentialists we're reading don't give arguments for thinking there are no ungrounded objective values, there are reasons to think there aren't in logic and even if there were in morality it wouldn't help us. Absent such values, however, it seems we can't make moral progress and can't justify, say, what appears to have been a just war against Nazi aggression. We'll see what Sartre has to say about some of this next week, in his Existentialism is a Humanism.

Grain of Salt

Imagine my surprise at discovering - tucked inside the cover of a first edition Alice in Wonderland – an unknown dialogue written by Lewis Carroll himself! It was scribbled on the back of a napkin, punctuated by Carroll’s tell-tale signature, and seems to have been written hastily. Carroll is known among laypersons as an absurdist, but he’s esteemed among formal thinkers as impressively logical. You can probably then imagine my further surprise at discovering various fallacies and confusions in the dialogue! I counted equivocations over use/mention, identity/predication, measurements, and lexical/material parthood, but I’m sure there are more hiding.

If you share my interest in untangling these errors, I’ve copied Carroll’s dialogue below. I’ve found the task best pursued with help, whether students, interns, sisters, tarot readers, etc. As you’ll see, I’ve divided the dialogue into five sections, of varying difficulties. I recommend dividing helpers accordingly, assigning one section per group, then directing each to identify both good and bad reasoning in the section. After some time, groups should pass their discoveries to other groups for scrutiny. For example, if group 1 examined section 1, they’d pass their discoveries to group 2 who then checks group 1’s work against section 1. Proceed until each group has examined each section and – hopefully – you’ll find all the errors. Happy hunting!

Section 1: Garbage Logic

Dee: Do you know that song by Garbage titled “I’m only happy when it rains”?

Dum: Classic.

Dee: It’s about my life.

Dum: Lucky you, it’s drizzling!

Dee: Don’t mock me!

Dum: What? You said you’re only happy when it rains. It’s raining. So, you’re happy.

Dee: No. No. “Only” is one of those words unaffected by happiness.

Dum: I see…You’re happy only if it rains…

Dee: Right, and sad more often than that; it’s a rule I adopt as a guide to life, if you can call it that.

Dum: A rule?

Dee: A life.

 

Section 2: Vulcan Logic

Dum: That seems a morbid, unwise, rule…

Dee: Morbid perhaps, but I assure you I’m nothing if not wise.

Dum: Saying so doesn’t prove it so. So…

Dee: So? You logicians are so extra. Look, if I’m not wise, then I’m nothing, and as you can see, I’m obviously something.

Dum: You’re something alright…

Dee: …then I’m wise. QED.

Dum: Is it wise to say trivial things?

Dee: Tricky fellow…If I say “good question” and it is, I’ll be unwise…

Dum: Even the wise admit it might be a good question though…

Dee: Trickier and trickier…saying that would be even more trivial!

Dum: I think you mean false, since no two trivial things are any more or less trivial than each other. You’re starting to sound like that Vulcan chap…

Dee: Spot?

Dum: Spock…always saying this or that is “highly illogical.” No need to elevate; it’s illogical or it isn’t.

Dee: I’ve struck a nerve?

Dum: Substantially. But mights and maybes aside, my question was at least probably good.

Dee: Especially since there’s no telling whether that’s a trivial thing to say or not!

Dum: Unless you’re among the wise?

Dum: Which I believe has been established in my case…

Dee: On the contrary, seems to me in your case, if you’re nothing then you’re not wise.

Dee: Just my point; watch and see, I’ll come out the wiser, since I’m still either something so wise, or wise so something.

Dum: Or something and not wise…

Dee: Only if we must consider all the options…

 

Section 3: Willy-Nilly Logic

Dum: …You can’t exclude options willy-nilly!

Dee: “Willy-nilly?!” I’m not trying to contradict myself!

Dum: Few are…

Dee: That’s what “willy-nilly” means though! Old English, old friend, from ‘will I, nill I’, which meant ‘I intend to’ and ‘I don’t intend to’ respectively.

Dum: Oh my…nidy offend, my friend.

Dee: Why yes you did.

Dum: No, I mean ‘nid I offend’ or ‘I didn’t intend to offend’.

Dee: I…okay…this conversation is not a great way to help me find my happiness.

Dum: Well, at least you know it’ll be in the last place you look…unless you stop looking…

Dee: Thanks?

Dum: It gets worse, since also at least you know if you look for happiness you won’t find it…

Dee: Just as the Sun appears; I’m now exhausted.

Dum: Tired?

Dee: Not tired, exhausted.

Dum: Speaking willy-nilly again!

Dee: A regular daredevil, aren’t you?!

Dum: If you’re not tired, then you’re not exhausted…unless you didn’t mean what you literally said. Perhaps mean to say you’re not both not tired and exhausted?

Dee: Is this necessary?

Dum: Logically so. You’re either tired or not exhausted.

Dee: But I am exhausted.

Dum: Tired and exhausted, but not tired?

Dee: Not just tired…

Dum: How unjust...

Dee: How indeed.  

Section 4: Incremental Logic

Dum: We’re far off track.

Dee: Let’s have some air, and perhaps stroll to the bakery. I’ve some shopping to do anyway.  

Dum: Not the bakery! The baker’s why I’m in this mood. You know I like to meal plan two weeks in advance and live on a diet of one scone per day.

Dee: Naturally.

Dum: So, I asked the baker for a dozen and two bakers worth of scones…

Dee: So, 14 scones.

Dum: Exactly!

Dee: What a lucky day for the baker…did he overcharge? I've heard the baker charges a pretty penny, and sometimes ugly ones too…

Dum: I wish it were that simple! He seemed not to know that 'baker' is an increment of "1."

Dee: To be fair, I think the baker's education extends only as far as pastries, so this isn't surprising…did you tell him the rhyme?

Dum: As much as I remembered:

Divide a dozen bakers
And you'll have two six in pairs
But divide a baker's dozen
For half dozen and half share
And since the time of Solomon
We've kept our loaves in wholes
Thus, now our baker’s increment
As naturally follows

As best a proof as one can offer for "baker" meaning nothing more - nor less - than "add one."

Dee: Impenetrable logic!

Dum: And yet, he then asked: "How many inches are in a pinch?"

Dee: Well that’s easy: 1. There is one "inch" in "pinch," easy as pie.

Dum: Wish I’d thought of that delicious answer…

Section 5: Baker’s Logic

Dum: Puzzles are quite tricky when set up poorly, and I’ve set you up poorly by reporting the puzzle quite backwards. The baker actually asked: "How many pinches are in an inch?"

Dee: Just as easy: 0. A “pinch” is too big to be an “inch”…

Dum: Hmmm…

Dee: Wait…that can't be right…a pinch is smaller than an inch, so there should be at least one pinch in an inch…

Dum: …and so either one inch in a pinch and one pinch in an inch…

Dee: …or some inch in a pinch and many pinches in an inch…

Dum: You’ve the better options; otherwise anytime you had a pinch you'd have an inch, but that can't be true…my grandmother is fond of cheek pinches, but I've always either more or less than an inch of cheek, depending on the cheek…

Dee: You are a pinch-able but not inch-able sort of fellow…

Dum: Compliments aside we've not progressed on the baker's puzzle…

Dee: Don't be glum Dum! Try a different flavor of the question…a concrete example perhaps?

Dum: Like an inch of salt?

Dee: My palette can't handle so much…let's start with a pinch.

Dum: Right. Take a pinch of salt and line it along the ground…

Dee: That can't be good for Earth…

Dum: …and of course a pinch is around 1000 grains of salt...

Dee: Sayeth Google…

Dum: And a grain of salt is approximately .03 mm.

Dee: Where does this Dum line lead?

Dum: More plumb than Dum…lining up 1000 grains of salt at approximately .03 mm each is 12 inches, or…

Dee: Pinch me, that's one short of a baker's dozen! I see the baker's point…

Dum: Go on…

Dee: I’m inspired by the muse of pedagogy -

A pinch of salt is a foot in a line
While a foot's 12 inches per row
And from our well-known nursery rhyme
12 bakers lined up head to toe
But then each inch is a baker,
And each baker himself is an inch
But it also follows we've a pinch per baker
And just one baker per pinch
Consequently - from the baker's query
Counting pinches out one, two, and three…
We've a dozen bakers at the end of our summing
And a puzzling patisserie!
For we've stated as true, there're no fractional bakers
Yet provided a counter-example:
"The baker above equaled to a foot
Is comprised of 12 bakers entangled"
That so-clever baker has managed to put us
In pinches tied all up in knots
Deriving confectioners lined up together
When taken, with a grain of salt

Dee: And now you see why I’m so affected!

Dum: I do, I do. I’m afraid your mood is catching.

Dee: And just as it begins to rain…

Addendum

I’ve scribbled here brief notes from my reading of the preceding dialogue, one for each section, in the event other hunters might find them useful.

Section 1:

Applying a formal translation using the material condition to the expression “I’m only happy when it rains” results in ambiguity between: (A) I’m happy only if it rains; (B) It rains only if I’m happy. Dum initially took Dee’s meaning to align with (B), and since it was raining, deduced Dee was happy. Dee, however, meant (A), which is consistent with Dee not being happy, though it’s raining, given standard material conditional truth-conditions.

Section 2:

The expression “I’m nothing if not wise” can be paraphrased as “If I’m not wise, then I’m nothing” and by contraposition (and a few other assumptions!) is equivalent to (C) “If I’m something then I’m wise.” Confusion arises in the dialogue, however, when “I’m nothing if not wise” is initially understood as “If I’m nothing then I’m not wise” which is equivalent to (D) “If I’m wise then I’m something.” Dee suggested either reading implied his wisdom, so it didn’t matter which reading was adopted. For the first, since Dee is something, if (C) is true, then Dee is wise. Trouble stems from the second. Dee suggests since he is something, (D) is always true, and deduces from this that he is wise. Dum observes this is erroneous as Dee seems to be affirming the consequent. 

Section 3:

Dee and Dum become formally tied up in by a few common colloquialisms assumed to be literally true. A little more precisely: Dee has lost his happiness; if you find something you’ve lost it’s always in the last place you look; but if you look for happiness, you won’t find it. The pair takes this consequence as dire, since it seems Dee should stop looking for happiness since he won’t find it, but they also seem to believe that as soon as Dee stops looking, happiness will be in the most recent place he looked. Of course, were Dee to go look there again, he wouldn’t find happiness. Dee and Dum are, among other things, fluctuating between reading the word “last” as meaning “most recent” or meaning “final.”

Section 4:

Dee and Dum are attempting to establish that the expression “baker” when qualifying a group of items, should be read as incrementing the group elements by one. Incrementing results in “baker’s dozen” being 13, and so a “baker’s baker’s dozen” being 14. But the force of their claim seems to depend on decrementing, as evidenced in the rhyme where they suggest “half a baker’s dozen” doesn’t make sense, since items counted in the group are assumed to be indivisible units, and rounding up or down isn’t apparently applicable. Reasoning in this section, admittedly, vexes me the most out of the dialogue. This is perhaps to be expected since evidence offered by Dee and Dum in support of reading “baker” this way, was acquired in their grade school education, which I did not have. I trust their instructors had their reasons.

Section 5:

I clarify just one of the several problematic lines of reasoning in this poem: Lining up the number of grains of salt assumed to be in a pinch, results in a line one foot in length. That implies there’s one pinch of salt per 12 inches. It was defended earlier – by use/mention confusion – that there is exactly one “inch” in a “pinch” where reference was clearly to the letters of each word. Combining these confused claims - and strategically ignoring units of measurement in parentheses here - results in exactly one inch (of salt) contained in each pinch (of salt) and yet each pinch (of salt) containing 12 inches (of salt).

Author Bio

John Beverley is student of the world – with a present emphasis on Northwestern University and the School of the Art Institute of Chicago – who enjoys trite rhymes, snark hunting, raven-inspired writing desks, and quiet seashells. John’s work ranges from formal logic and social epistemology to high church and applied metaphysics. He considers himself a member of the Graham Priesthood, which presently does not exist, as he endeavors to accomplish between 4 and 6 impossible things each morning, depending on the weather. Among John’s impossible tasks is trying desperately to make formal logic funny enough to warrant a Netflix special.

Logic Notes 11/18 - 11/22

Disambiguate Expressions with Quantifier Elimination

Consider the following sentence:

If anyone loves someone, then John is bald.

And let's fix the following dictionary for the purposes of evaluating this sentence in standard FOL:

D: {a, j}
a: Alex
j: John
L_ _: _ loves _
B_: _ is bald 

When translating into our language, note there are at least two plausible candidate translations (I will use “V” for universal quantifiers and “E” for existentials):  

(1) VxEyLxy -> Bj
(2) Vx(EyLxy -> Bj)

These are not logically equivalent. The main connective of (1) is a material conditional. The main connective of (2) is a universal quantifier. We might express the difference in English as:

(1') If anyone loves someone then John is bald
(2') Out of anyone, if that person loves someone then John is bald

These still might sound rather similar. They are nevertheless distinct, as can perhaps be shown by the fact that (1) and (2), and so presumably (1*) and (2*), have different truth-values when comparing interpretations.

For our purposes, an interpretation is a dictionary combined with a visual diagram representing elements of the domain as satisfying some, all, or none of the dictionary elements. Recall, we can show two sentences are not logically equivalent in our language with respect to a given dictionary, by providing an interpretation where one is true while the other is false. This should sound familiar, since we had a similar procedure when we didn't have quantifiers in the language. There we observed two sentences to be logically equivalent just in case they had the same truth table assignments. Indeed, interpretations are analogous to truth tables in this way, enough to make the following statements:

In propositional logic, expression A is logically equivalent to expression B if and only if A and B are true in all and only the same truth table rows

In quantifier logic, expression A is logically equivalent to expression B if and only if A and B are true in all and only the same interpretations

This is just to say that if (1) and (2) are distinct, as I claim they are, then there is at least one interpretation in which one of the pair is true and the other is false.

This, however, might not be easy to see given how similar the expressions are. At this point, it will be useful to practice an expansion  technique for evaluating the truth or falsity of quantifier expressions. To see how this works, note that in finite domains - the only sort of domain you'll be working with in this class - universal quantifiers are just conjunctions while existentials are simply disjunctions. More specifically, consider the following dictionary:

D: {a, j}
j: John
a: Alex
B_: _ is bald 

Now observe the following are true: 

"VxBx" can be replaced with "Ba & Bj"
"ExBx" can be replaced with "Ba v Bj"

This should seem intuitive. Since the domain consists only of Alex and John, if we say something about everything in the domain, that simply means we're saying something about Alex and John. Similarly, if we say something about someone in the domain, that means we're saying something about Alex or John.

To see how this helps with our motivating ambiguity, return to our initial dictionary:

D: {a, j}
a: Alex
j: John
L_ _: _ loves _
B_: _ is bald 

And expressions:

(1) VxEyLxy -> Bj
(2) Vx(EyLxy -> Bj)

Starting with (1), we replace the universal, then existential:

(1*) Ey(Lay & Ljy) -> Bj
(1**) ((Laa \/ Laj) & (Lja \/ Ljj)) -> Bj

Consider next expansion of (2):

(2*) (EyLay -> Bj) & (EyLjy -> Bj)
(2**) ((Laa \/ Laj) -> Bj) & ((Lja \/ Ljj) -> Bj)

 To see how these come apart, let the following be true in our interpretation:

~Bj & ~Laa & ~Laj & Lja & Ljj 

In (1**), since Laa and Laj are false, then the left-hand side of the conjunction in the antecedent is false, which means the antecedent is false, so (1**) is vacuously true. On the other hand, in (2**) we have a vacuously true left-hand side of the conjunction, but the right-hand side has a true antecedent and false consequent. Hence, (2**) is false.

We have, then, found an interpretation where (1) is true and (2) is false. That’s sufficient to show they're not logically equivalent. Hopefully, this has also gone some way in illustrating how (1') and (2') are distinct in natural language. It might be worth reviewing the respective sentences with the preceding interpretations in mind.

Logic Notes 11/11 - 11/15

Quantifiers, Interpretations, and Expansions

Recall in our logic with just sentence letters and connectives, we defined validity as:

An argument in is truth-functionally valid iff: if all of its premises are true then its conclusion is true

We need something more for quantificational logic.  We need the notion of truth on an interpretation:

An argument is quantificationally-valid iff: there is no interpretation on which all of its premises are true and its conclusion is false.

Consider the following sentences of our logic with predicates, relations, and quantifiers:

Mb
Wm

These sentences will have different truth values on different interpretations.  Consider the following two interpretations.

D: People
M:   is male.
W:   lives in the White House
b: Barack Obama
m: Michelle Obama

D:  Animals
M:   is a manatee
W:   is a wombat
b: Bruce Willis
m: Minnesota

Mb
Wm

On the first interpretation, both of the sentences are true, because Barack Obama is (in fact) male, and Michelle Obama lives in the White House and is not male.  On the second interpretation, both sentences are false, because Bruce Willis is not a manatee and Minnesota is not a wombat.

If you didn’t know anything about Barack, Michelle, Bruce, and Minnesota, you wouldn’t be able to tell whether these sentences are true on these interpretations.  But there are ways of providing interpretations so that anyone can tell whether the sentences are true or false in the interpretation.  Consider the following interpretation.

-------------------------------------

|           W                    MW     |

|             ☺                  ☺        |

-------------------------------------

D: The figures above
M:   has an “M” above it
W:   has a “W” above it
b: the first figure above.
m: The second figure above.

The first sentence is false on this interpretation, and the second one is true.

That said, there are some sentences that are true in absolutely all interpretations, such as:

Mb v ~Mb

No matter what object ‘b’ refers to in this interpretation, and no matter what ‘M’ means in that interpretation, that object either has the property meant by ‘W’ in that interpretation or it does not.

Consider the following argument. Mb & Wm  |= Mb

If the premise is true on an interpretation, then so is the conclusion.  There is no interpretation on which the premise is true and the conclusion is false.  Therefore, the argument is valid.

The following argument is invalid. Mb  |= Wm

We can see this by producing an interpretation on which the premise is true and the conclusion is false.

-------------------------------------

|            M                                |

|             ☺                  ☺        |

-------------------------------------

D: The figures above
M:   has an “M” above it
W:   has a “W” above it
b: the first figure above
m: The second figure above.

Consider the following small interpretation.

-------------------------------------

|           F                      FG       |

|           ☺                    ☺        |

|                                               |

------------------------------------

D: the smiley faces above
F:  has an “F” above it.
G:   has a “G” above it.

Let’s now determine whether the following sentence is true in this small domain.

VxFx

I think it is obvious that this sentence is true in this interpretation:

A sentence of the form Vvφ is true in an interpretation iff: every object in the domain of the interpretation satisfies φ.

So the above sentence will be true in this interpretation iff every object in the domain satisfies “Fx”.  We can see whether every object in the domain satisfies this open sentence by giving the stick figures names, ‘a’ and ‘b’ respectively, and then deciding whether the resulting sentences are true.

Similarly, let’s determine whether the following sentence is true in the above interpretation.

ExGx

I hope that it is obvious that it is true in the above interpretation.  Here is an official rule.

A sentence of the form Evφ is true in an interpretation iff: there is an object in the domain of the interpretation that satisfies φ.

We can see whether ‘ExGx’ is true in this interpretation by seeing whether there is a stick figure in the domain that satisfies ‘Gx’. 

You might notice that the universal is true iff both instantiations are true, while the existential is true iff either one or the other is true. When the domain of an interpretation is finite, then a universal generalization is true in that interpretation if and only if a certain conjunction is true.  And existential generalizations are true iff a certain disjunction is true.  Consider the following sentences.

VxFx.

EyFy

---------------------------

|           F                      |

|           ☺        ☺        |

-----------------------------

D: The smiley faces
F: has an “F” above it.
a: The first smiley face.
b: The second smiley face.

Notice that the first and second smiley faces are the only objects in the domain of quantification ‘a’ and ‘b’ name these objects in this interpretation.  Therefore:

“ExFx” is true in this interpretation iff  “Fa v Fb” is.

“VyFy” is true in this interpretation iff  “Fa & Fb” is.

This conjunction and disjunction are the expansions of the universal and existential in the above interpretation.  You can now use truth-table rules to discover that that the disjunction is true in this interpretation and the conjunction is false in this interpretation.  So, you can infer that the universal is false in this interpretation and the existential is true in this interpretation.

1.  To find the expansion of some quantified sentences in a finite domain, first name everything in the domain.

2.  Next, start with the leftmost quantifier.  Replace universals with conjunctions using every name to replace the variable.  Replace existentials with disjunctions.

3.  After that, work your way into further quantifiers.  Be sure to keep parentheses.

Notice that the expansion of a sentence will be different with different interpretations. Suppose that we have three objects in the domain, as in the following interpretation.

------------------------------------

|           F          G          F         |

|           ☺        ☺        ☺        |

------------------------------------

D: The smiley faces
F:  has an “F” above it.
G:  has a “G” above it.

Then:

VxFx               expands to       (Fa & Fb) & Fc
ExFx                expands to       (Fa v Fb) v Fc

The placement of parentheses makes no difference.

Now, let’s move on to checking whether arguments are valid using interpretations. Consider:

Fa \= VxFx.

Check whether we can construct an interpretation that uses a domain with just one object (We can’t; we need a domain with at least two objects).

---------------------------

|           F                      |

|           ☺        ☺        |

----------------------------

D: The smiley face above
F:   has an “F” above it
a: The smiley face above.

The premise is true in this model, but the conclusion is false.  So this argument is invalid.   We can use an expansion to check this. Here is a numerical interpretation that is structurally analogous.

D: {1, 2}
F:   is in .
a: 1

Logic Notes 11-4 to 11-8

*I’ve pulled together notes from David Braun’s symbolic logic course at UB and Gary Hardegree’s text Symbolic Logic, which can be found online*

We can describe the meanings of the quantifiers roughly as follows (I use “V” for universal and “E” for existential in what follows):

V: for all

E: for some

Recall, the meaning of connectives like “/\” is given by their truth tables.  ‘->’ means just what the truth table says.  This may not be quite what ‘if then’ means in English, but it is close enough so that we can use “->” to symbolize ‘if then’.  We can give an analogous official explanation of the official meanings of "V” and “E”.  The official explanation gives the official meaning by saying when universal generalizations and existential generalizations are true.  

(Informal) Definitions of the quantifiers

To tell whether or not a sentence of the form Vx(...x...x...) is true:

Remove the initial universal quantifier. Pretend that the variable it was binding is a name letter. If you now have a sentence that is true no matter what the pretend constant stands for, then the original sentence is true; otherwise it is false.

To tell whether or not a sentence of the form Ex(...x...x...) is true:

Remove the initial existential quantifier. Pretend that the variable it was binding is a name letter. If there is something that the pretend constant could stand for such that the sentence you now have is true, then the original sentence is true; otherwise it is false.

Now let’s work on translations into natural language.

Symbolization and Translations

Knowing how to symbolize these four basic categorical forms will get you a long way in symbolization.

All F are G                              Vx(Fx -> Gx)

Some F are G                        Ex(Fx /\ Gx)

Some F are not G                Ex(Fx /\ ~Gx)

No F are G                              ~Ex(Fx /\ Gx) or Vx(Fx -> ~Gx)

For example:

All cats are mammals.

For all x, if x is a cat, then x is a mammal.

Vx(Cx -> Mx).

Some dogs bark.

For some x, x is a dog and x barks.

Ex(Dx /\ Bx)

Some cats are not white.

For some x, x is a cat and x is not white.

Ex(Cx /\ ~Wx)

No cats are dogs.

It is not the case that there is a cat that is a dog.

It is not the case that for some x, x is a cat and x is a dog.

~Ex(Cx /\ Dx)

Every cat is a non-dog.

Vx(Cx -> ~Dx)

Variants on “all” and “every”

All Fs are Gs.

Every F is a G

Each F is a G

All of the preceding are to be translated as:

Vx(Fx -> Gx)

The Domain of Quantification and absolutely universal quantification

Sometimes the way in which we symbolize a universal sentence will depend on the domain of quantification we choose.  Consider the following sentence.

Everyone is happy.

This will depend partly on what we take our domain of quantification to be.  It seems that ‘everyone’ here is quantifying over people.  So suppose we let the domain of quantification be just people.  Then we should symbolize as follows.

D: people

Hj: j is happy

VxHx

If we change the domain to all living things, then we need to change the symbolization.

D: all living things.

Hj: j is happy

Pj: j is a person.

Vx(Px -> Hx)

Pay attention to the domain of quantification when symbolizing. 

“Not” and ambiguity

We need to be careful about negation and the universal quantifier.  First consider the following sentences.

Not every dog is brown.

Not all dogs are brown.

These are unambiguous.  It is simply the denial of “every dog is brown”.

~Vx(Dx -> Bx)          

It is not the case that all dogs are brown.

This will be true if some dogs are brown, as long as some dogs are not brown.  The next sentence, however, is ambiguous.

All dogs are not brown.

On one way of understanding it, it simply denies that all dogs are brown.  On this way of understanding it, we symbolize it in exactly the way above.  But there is another way of understanding it: as asserting that every dog is such that it is non-brown, or as asserting that no dog is brown.  We can paraphrase these two ways of understanding the sentence as follows.

It is not the case that all dogs are brown.

All dogs are non-brown (things).

We symbolize these two readings as follows.

~Vx(Dx -> Bx)           It is not the case that all dogs are brown.

Vx(Dx -> ~Bx)           All dogs are non-brown

An unambiguous way to express the latter in English is: No dog is brown.

More on Existential Sentences

There are several variants of existential generalization in English.

Some F is G.

Some Fs are Gs.

At least one F is G.               

There is an F that is G.                                

There exists an F that is G.                             

All of the preceding are to be translated as:

Ex(Fx /\ Gx)

We may simply want to assert the existence of something.

There is an F.                          

There is a cat.

These are to be translated as:

ExFx

Existentials and negations

Some sentences containing the existential also contain a negation, as does one of our basic categorical forms.

Some F is not G

There is an x such that (x is F and x is not G).

Ex(Fx /\ ~Gx)

Watch where the negation is placed.

It is not the case that some F is G.

It is not the case that there is an x such that (x is F and x is G)

~Ex(Fx /\ Gx)

We might restate this “No F is G”, which can be symbolized in two equivalent ways.

No F is G.

~Ex(Fx & Gx)

Vx(Fx -> ~Gx) 

Existentials with arrow

Notice that the main connective used in symbolizing an existential English sentence is “/\”

and not “->”.  Here’s why.  Consider the sentence:

Some cats are dogs.

This sentence is obviously false.  Now consider the following bad symbolization of it.

Ex(Cx -> Dx)

This sentence is true!  For notice that it will be true if there is just one thing that makes conditional true.  And the conditional will be true when the antecedent false.  So if there is just one thing that is not a cat, then this symbolization will be true.  But there is: Fido, for example, is not a cat.

Another way to see this: notice that the conditional inside the formula is equivalent to a disjunction.

Ex(Cx -> Dx)

Ex(~Cx v Dx)

Now this last sentence is true iff there is something that is either not a cat or is a dog.  But that’s true! 

Only

Consider the sentence

Only mammals are dogs.

It seems to be true.  How should it be symbolized?  An existential would be true even if some dogs are not mammals.

Ex(Mx /\ Dx)

We need to use a universal.  Which of the following should we use?

Vx(Mx -> Dx)            “All mammals are dogs”

Vx(Dx -> Mx)            “All dogs are mammals”

The first is false, and the second is true.  So the second seems to be the way to go.  Generalizing:

Only Fs are Gs                                                 

Vx(Gx -> Fx)

Notice that ‘only’ introduces the predicate that will appear in the consequent of your

symbolization.  This is like ‘only if’ and conditionals.

All Fs and Gs

The rules of thumb for basic categorical sentences usually give one the right symbolization, but they can lead one astray in certain cases.  Consider:

All juniors and seniors are upperclassmen.

This seems to be a universal.  But the following symbolization is problematic.

Vx([Jx & Sx] -> Ux).

It is problematic because nothing is both a junior and a senior.

We could instead use a conjunction of two universals.

Vx(Jx -> Ux)  /\ Vx(Sx -> Ux)

Or we could use a single universal with disjunctive antecedent.

Vx([Jx v Sx] -> Ux).

Or we could use a single universalization of a conjunction.

Vx([Jx -> Ux] /\ [Sx -> Ux])

Both

A similar issue arises with ‘both’.  Consider the sentence:

Both juniors and seniors are upper-classmen.

This seems to be a universal.  We might be tempted to symbolize with

Vx([Jx /\ Sx] -> Ux)

But this is wrong, because nothing is both a junior and a senior.  We could use two universals.

Vx(Jx  -> Ux) /\ Vx(Sx -> Ux).

Or we could use a single universal with a disjunctive antecedent.

Vx([Jx v Sx] -> Ux)

Vacuous Universal Generalizations

Consider the following sentence.

Every purple cow moos.

Is this sentence true or false?  It may be hard to say.  However, our symbolization of this sentence is definitely true.

Vx([Px /\ Cx] -> Mx)

To figure out whether this sentence is true, first drop the universal quantifier phrase.  Then ask whether the result would be true no matter what object is assigned to some object in the domain.  Since there are no purple cows, the antecedent is false no matter what is assigned to.  Therefore, the whole conditional is true.  Therefore, the universal is true.

Think of it this way: all purple cows moo, all none of them. When a sentence of the form

Vx(Fx -> Gx)

We say that it is vacuously true.

Logic Notes, Week 10/28 - 10/31

I will walk you through the three general proof strategies - the only strategies you'll need in this class - using proofs as examples.  

Proof Strategies 

There are three strategies you'll need in this class for proofs: Direct, Conditional, Indirect.  

Direct Proof: In many cases to prove something you need only apply one or more rules without making any assumptions. For example, I might want to prove "P v Q" follows from "P". That's simple:

  1. P

  2. P v Q vI, 1

We just introduce a disjunct and we're done. The absence of the need to make additional assumptions is a hallmark of Direct Proof.

Of course, were that the only sort of proof strategy, we'd not be able to prove much. Fortunately, we have others.

Conditional Proof: Sometimes you're asked to prove something of the form: "P -> Q", i.e. something that has "->" as the main connective. This might be simple, as is the example I just gave, or it could be complex, like: "(P /\ R) -> ~(S v T). In either case, if the main connective is a conditional then you will be using the Conditional Proof Strategy. You have a basic rule that reflects this already, namely, "->I". But let's make sure you know when to use it.

Pro-Tip - This is a common stumbling point for students, so pay attention to what I say here even if you feel confident about using "->I". Students often feel confident about logical steps when they see them, but then have trouble proving things on their own. That's likely because every step we make in this class should seem obviously true on reflection. You make inferences like this in your daily life all the time. Of course you can follow a proof; we're not trying to teach you that skill. Rather, we're teaching you how to prove things on your own, intentionally.

Anytime you need to prove a statement that has a conditional as its main connective, you will always assume the antecedent. This is important to keep in mind for at least one good reason. In our logic, you can assume anything you want. Literally, anything, e.g. "P /\ ~P". That's fine, you won't break the logic. That might seem overwhelming. You might feel you have too much freedom to assume things, and so you might find it difficult to know where to start making assumptions. That's a reasonable thing to worry about given the freedom we have in this logic. But note when employing Conditional Proof, you only ever assume the antecedent. That sharply narrows down the scope of things you might assume. Moreover, assuming the antecedent is - we logicians have learned over time - one of the most efficient ways to prove conditional statements. Put another way, you can strictly speaking assume anything you want, but not everything will be useful to you when you're trying to prove something. If you're proving a conditional, just restrict your attention to the assuming the antecedent.

Get into that habit. Whenever you're asked to prove an expression with a conditional as the main connective, assume the antecedent. This should be the first thing that comes to mind.

After you've assumed, then you'll prove the consequent follows. You may need to use Direct Proof steps to get you there. For example (recall, I include "SHOW" lines to remind you - in the proof - of your goal; you can remove them if you prefer):

1. SHOW P -> (Q -> P)

Here I've to prove a conditional expression. There are two connectives. Both are conditionals. The first is the main connective. So I employ the Conditional Proof Strategy (recall, I include "SUPPOSE" in proofs instead of drawing vertical bars, to illustrate sub-proofs):

2. SUPPOSE P
3. SHOW (Q -> P)

Now, we've broken our proof down to the consequent, which we must prove. We can apply the same reasoning as above, and note the main connective here is also a conditional. That means we should apply the Conditional Proof Strategy again:

4. SUPPOSE Q
5. SHOW P

At this point, we've only to show P follows from lines 2 and 4 to finish. This is perhaps a good point to observe that when you assume something you get to use it as a premise in your argument. Put another way: assuming something gets you more to work with.

It's at this point we apply the Direct Proof Strategy. This one is rather simple. We use the "R" - Repetition - derived rule to bring "P" down under the scope of our assumed "Q".

6. P

From here we can discharge our assumption of Q with "->I", resulting in:

7. Q -> P ->I, 4-6

Which was what we were trying to prove on the assumption that "P", so we can discharge with "->I" again, resulting in:

8. P -> (Q -> P) ->I, 2-7

And that's the end of the proof. We used Conditional Proof twice, and Direct Proof once. It should be clear then how these proof strategies play together.

That said, sometimes you must prove something you can't prove directly and which is not in the form of a conditional. For that, we use the last proof strategy:

Indirect Proof: Anything that can be proven in our logic can be proven using Indirect Proof. You can always convert a proof using the Direct Proof or Conditional Proof Strategy into one using the Indirect Proof Strategy. The respective converses are not true. Some expressions can only be proved with the Indirect Strategy.

This strategy is codified in our rule "-I". Namely, if you assume something and get a contradiction on that assumption, then you take that assumption back. Since every sentence in our language is either true or false, and no sentence is both, you know, say, if you get a contradiction from assuming "A", then it has to be the case that "~A".

Pro-Tip - If you can't figure out how to apply a rule to prove something without making an assumption and you aren't being asked to prove something with a conditional as its main connective, then use the Indirect Proof Strategy. Put another way, if the other two strategies aren't obviously helpful, then just assume the opposite of what you need to prove. In fact, I wouldn't spend much time trying to figure out if one of the other proof strategies will be helpful. If it's not obvious, just assume the opposite of your goal and try to derive a contradiction.

Note again, we can assume anything we want in our logic. But, it will be most efficient to simply assume the opposite of what you want to prove. This sharply constrains what you might practically want to assume. Coupled with the Conditional Proof Strategy, and noting that these are the only three strategies you will be using in this course, it should be clear that though you can assume whatever you like in a proof, you should only be assuming things that take one of two forms: (i) The antecedent of a conditional; (ii) The negation of what you want to prove.

I said some things can only be proven with Indirect Proof. I'll give you an example:

1. SHOW (P v ~P)

Observe: this is not in the form of a conditional proof, and it's not obvious how to apply rules without making an assumption to prove it (of course, you can derive rules, e.g. De Morgan's, to help, but you often use Indirect Proof to establish those derived rules are true, so…). With that in mind, we'll apply the Indirect Proof Strategy:

2. SUPPOSE ~(P v ~P)

Here, we still don't have an obvious way to use Direct Proof or Conditional Proof. We'll have to be creative. Observe, we have proven the following in previous lectures:

De Morgan's: ~(P v Q) -> (~P /\ ~Q)

Let's rehearse:

1. SHOW ~(P v Q) -> (~P /\ ~Q)
2. SUPPOSE ~(P v Q)
3. SHOW (~P /\ ~Q)

We pause here to note we are again at a loss for how to apply Direct or Conditional Proof to show line 3. So, we go Indirect:

4. SUPPOSE P
5. P v Q vI, 4
6. ! Contradiction, 2, 5
7. ~P

Note, we have to prove a conjunction, so we need to show each side independently. We continue:

8. SUPPOSE Q
9. P v Q vI, 8
10. ! Contradiction, 2, 9
11. ~Q
12. ~P /\ ~Q /\I, 7, 11

Okay, back to the other proof, we had:

1. SHOW (P v ~P)
2. SUPPOSE ~(P v ~P)
3. ~P /\ ~~P De Morgan's, 2
4. ~P /\E, 3
5. ~~P /\E, 3
6. ! Contradiction, 4, 5
7. (P v ~P)

And that's it. We have proven this, note, from no premises. That means it's a logical truth, i.e. it's always true in our logic. In many cases, proving logical truths that don't have conditional main connectives requires Indirect Proof.

To sum up:

(1) There are only three proof strategies you need to remember: Direct, Conditional, Indirect

(2) Direct Proofs do not need you to provide assumptions

(3) Conditional Proofs are used when you need to prove an expression where the main connective is a conditional; you always assume the antecedent, then derive the consequent

(4) Everything else is Indirect Proof, where you assume the negation of what you want to prove

(5) There is no need to assume anything other than what I've noted in (3) and (4), and anything you can prove in this logic you can prove using (2)-(4)

Logic Notes, Week 10-21 - 10-25

In section this week we largely proved things. I'll give you an example (note, I use a derivation system that is slightly different from Sean's. The difference between Sean's and mine is that mine is more explicit about the reasoning involved. For that reason it includes a few more steps. You can easily translate my derivations into Sean's by removing those extra steps. I like to include them for elementary logic so students can see all of the reasoning that goes on clearly. I've found once that's explicit, students start seeing that derivations are like arithmetic calculations in that they're very mechanical and rather easy):

1. A -> C
2. B -> (A v C)
3. SHOW (A v B) -> C

Note line 3 is something you've not seen. It's the thing you're being asked to prove. I like to include this in the proof directly so you can keep in mind your goal. Specifically, you know in line 3 you need to prove a conditional. You know that conditionals are only false if the antecedent is true and the consequent false. We're trying to show line 3 follows from lines 1 and 2. That means we're trying to show that if 1 and 2 are true, then so is 3. So we're trying to show 3 is true. To show line 3 is true, we essentially need to show it's not false. For that reason, we are warranted in assuming the antecedent is true in our proof. To do this, I like to add the following line:

4. SUPPOSE (A v B)
5. SHOW C

That is, I'm assuming the antecedent of line 3 is true. If I can show the consequent is derivable from 1, 2, and 4, then I'll have shown line 3 is entailed by lines 1 and 2. I've added a new SHOW line with "C" as our new target to make this clearer. You can think of this as a divide and conquer strategy. You assume some things to narrow down parts of the proof you need to apply rules to derive. At this point we've narrowed down our task to just having to prove "C" from lines 1, 2 and 4.

To be clear, it's not always the case that something of a conditional form is provable from premises. Just because we've assumed the antecedent of a conditional it doesn't mean we can derive a consequent. Put another way, in logic "assuming makes an ass out of you and me" doesn't apply. You can assume whatever you like, but it doesn't mean you can prove whatever you like. To this, just think about this attempt at a proof that won't work:

1* ~A
2* (B v C)
3* SHOW B -> C
4* SUPPOSE B
5* SHOW C
6* ?

There's no way to prove 3* follows from 1* and 2*, because there's no way to prove 5* follows from 1*, 2*, and 4*.

Again, this is just to say it's okay to assume the antecedent of a conditional when you're trying to prove it's true. If the antecedent is true and the consequent is false, you won't be able to prove it. If the antecedent is either false, or true and so is the consequent, then you'll be able to prove it. Hence, it's okay to assume it's true and focus on the consequent in derivations. Okay, now back to the other proof. We made it to:

1. A -> C
2. B -> (A v C)
3. SHOW (A v B) -> C
4. SUPPOSE (A v B)
5. SHOW C

Now we need to show "C". It might not seem obvious how. But note that we have line 4 available now. Moreover, it should be intuitive that the following holds:

(METHOD OF CASES): (A -> C) /\ (B -> C) |= (A v B) -> C

Consider: "If John goes to Home Depot then he buys batteries and if John goes to Target then he buys batteries, so it must be the case that if John goes to Home Depot or Target then he buys batteries." I hope that strikes you as true. But if not, let me prove it for you:

1** (A -> C)
2** (B -> C)
3**. SHOW (A v B) -> C
4**. SUPPOSE (A v B)
5**. SHOW C

There are many ways to show this, but I will show you how to do it by assuming the negation of "C" is true. Recall, everything in our language is either true or false. So, if "C" is true then "~C" is false, and vice versa. Moreover, in our language there are no contradictions. That means there is nothing of the form "C /\ ~C" outside a SUPPOSE line. Strictly speaking, we can suppose contradictions if we want. But - importantly - that's the only place a contradiction can live in our proof. In other words, we assume our language is consistent. All of this means that if I assume "~C" is true and get a contradiction, then it has to be the case that "C" is true. So:

6**. SUPPOSE ~C

But now look at line 1**. Recall, we have this rule:

(MODUS TOLLENS) (A -> B) /\ ~B |= ~A

We can apply that to lines 1** and 6** to get line 7**. We can do it again with lines 2** and 6** to get line 8**.

7**. ~A
8**. ~B

Now we can use line 4** and line 7** with the following rule:

(DISJUNCTION ELIMINATION) (A v B) /\ ~A |= B

That gives us line 9**.

9**. B

But lines 8** and 9** contradict each other. I like to write "!" to indicate that. Strictly speaking, "!" just means "B /\ ~B".

10**. !

Since I've a contradiction on the assumption of "~C" I must take back that assumption. That means I know "C" is true. The proof altogether is:

1** (A -> C)
2** (B -> C)
3**. SHOW (A v B) -> C
4**. SUPPOSE (A v B)
5**. SHOW C
6**. SUPPOSE ~C
7**. ~A
8**. ~B
9**. B
10**. !

Since my goal was to show line 3** followed from lines 1** and 2**, and I broke that down into me just having to show line 5** followed from 1**, 2**, and 4**, and since I just showed line 5** does follow from these premises, then I'm done. We now know the (METHOD OF CASES) works in our logic. Hence, we can use it whenever we want. We don't need to run through the proof again. We'll just label it and that'll be an abbreviation in our future proofs for the proof just above this paragraph.

Okay, so now we can finally return to our initial proof. Recall again where we left off, and let's apply (METHOD OF CASES). To do that, note we need to prove two things for this to apply, namely (A ->C) and (B -> C). Let's break that into two parts. starting with the first. I'm going to move a little faster now since we've covered all the tools we need to prove this:

1. A -> C
2. B -> (A v C)
3. SHOW (A v B) -> C
4. SUPPOSE (A v B)
5. SHOW C
6. SHOW A -> C
7. SUPPOSE A
8. SHOW C
9. C Modus Ponens, 1, 7
10. SHOW B -> C
11. SUPPOSE B
12. SHOW C
13. (A v C) Modus Ponens, 2, 11

Note at this point we need to show "C" follows from lines 1, 2, 4, 11, and 13. Importantly, we can't use line 7 anymore. This is because we already proved the thing we were trying to prove when we assumed "A" was true. We've "closed" that assumption off from the rest of the proof, when we derived "C" under it. This is analogous to moving from one nested line in Sean's proof system to a line just to the left of it. In any event, note in line 13 we have another disjunction and need to show "C" follows. We can apply (METHOD OF CASES) again:

14. SHOW (A -> C)
15. SUPPOSE A
16. SHOW C
17. C Modus Ponens, 1, 15
18. SHOW (C -> C)
19. SUPPOSE C
20. SHOW C
21. C Repetition, 20
22. (A v C) -> C Method of Cases, 14, 18
23. C Modus Ponens, 13, 22
24. (A v B) -> C Method of Cases, 6, 10
25. C Modus Ponens, 4, 24

And we're done. Here's the full proof altogether:

1. A -> C
2. B -> (A v C)
3. SHOW (A v B) -> C
4. SUPPOSE (A v B)
5. SHOW C
6. SHOW A -> C
7. SUPPOSE A
8. SHOW C
9. C Modus Ponens, 1, 7
10. SHOW B -> C
11. SUPPOSE B
12. SHOW C
13. (A v C) Modus Ponens, 2, 11
14. SHOW (A -> C)
15. SUPPOSE A
16. SHOW C
17. C Modus Ponens, 1, 15
18. SHOW (C -> C)
19. SUPPOSE C
20. SHOW C
21. C Repetition, 20
22. (A v C) -> C Method of Cases, 14, 18
23. C Modus Ponens, 13, 22
24. (A v B) -> C Method of Cases, 6, 10
25. C Modus Ponens, 4, 24

Next time we'll walk through the details of the justifications on the side of the proof more carefully. I'll also show you how to extract Sean's proof style from that above. If you prefer using Sean's proof system that's okay, it's equivalent to mine. Again, the only difference is mine makes every assumption and target in the proof explicit so you can understand the reasoning involved more easily. Once you've got the reasoning down, you won't need to see all those extra lines.

Logic Quiz 1 Study Guide

Logic Quiz Study Guide for Quiz 1

I will walk through some of the exercises in detail to illustrate and remind you of important concepts.

Symbolization

If Z remembered to do his chores then things are clean but not neat. If he forgets, then things are neat but not clean. Therefore, things are either neat or clean, but not both.

I find it helpful to put this in the form of a premise-conclusion argument while translating:

(1)   If Z then C and not-N

(2)   If not-Z, then N and not-C

(3)   Therefore, N or C and not N and C

Note I’ve left some scope ambiguities, e.g. “not N and C” in line (3) could be read as either “not-(N and C) or “not-N and C.” The former is the correct reading, but I wanted to walk you through these ambiguities explicitly. Consider next, where I use “~” for negation:

(1)   Z -> (C /\ ~N)

(2)   ~Z -> (N /\ ~C)

(3)   (N \/ C) /\ ~(N /\C)

You can see whether (3) follows by examining the premises. We know either Z is true or ~Z is true. If Z is true then C is, from which it follows that (N \/ C) is. If ~Z is true, then N is, from which it follows that (N \/ C) is. Hence, in either case (N \/ C) is true. Hence, we have the left side. Similarly, if Z is true, then ~N is, from which it follows that ~N \/ ~C is, from which it follows ~(N /\C) is. If ~Z is true, then ~C is, from which it follows that ~N \/ ~C is, from which it follows ~(N /\ C) is. Hence, in either case ~(N /\ C) is true. Hence, we have the right side of (3).

Note too that line (2) could be translated as (N /\ ~C) unless Z, i.e. “Things are neat but not clean unless Z remembered to do his chores.” This is because:

P unless Q =

P, if not Q =

If not Q, then P

Speaking of conditionals, remember that “if” not preceded by “only” introduces the antecedent of a material conditional. The antecedent of the preceding unless statement is complex, since it has a negation inside it. You can read that as: P, if [not-Q], where the antecedent is everything in the brackets.

This is distinct from “only if” which introduces the consequent of an expression. That is:

P only if Q =

If P then Q

Putting these observations about “if” and “only if” together, we can define “if and only if” as, where I bracket each side of the conjunction for clarity:

P if and only if Q =

[P, if Q] and [P only if Q]

Which is to say – and this is important – that conjunction comes first in priority here. That is, you bracket the conditionals after you separate the conjunction sides. The above is equivalent to:

[Q -> P] /\ [P -> Q]

 Semantic Concepts

Suppose A and B are logically equivalent. That means they always have the same truth-table values. For example:

P->Q:          T F T T

~Q -> ~P:   T F T T

 Suppose then you have:

(P -> Q) <-> (~Q -> ~P)

This is equivalent to:

[(P -> Q) -> (~Q -> ~P)] /\ [(~Q -> ~P) -> (P -> Q)]

Look at just the left side:

[(P -> Q) -> (~Q -> ~P)]

This claims that whenever (P->Q) is true then so is (~Q->~P). This must be the case since they always have the same truth value assignment. Hence, the left side must be true. Similarly for the right. But then both sides of the biconditional are always true when the sides are logically equivalent. Hence, we’ve a tautology. A simpler example is:

P <-> P

Clearly this is always true. When P is true so is P, hence P<->P is true. When P is false, so is P, hence P<->P is (biconditionals are true just in case both sides have the same truth value). Hence, P<->P is a tautology.

Suppose next that we have:

(1)   R /\ S

(2)   T

(3)   P <->P

We know the conclusion is a tautology. We are examining whether (3) follow from (1) and (2). We check validity by examining whether there are any cases in which the premises are all true and the conclusion false. But note here, the conclusion is a tautology, and so is never false.

Now let’s return to our logically equivalent A and B. Let’s consider two arguments:

(1)   A

(2)   Therefore, B

And:

(1)   B

(2)   Therefore, A

And examine the validity of each. Note, if A and B are logically equivalent, then they have the same truth assignments. So, whenever A is true/false, so is B. Recall to the definition of validity:

            An argument R is valid if and only if when all R’s premises are true, so is R’s conclusion

As stated, this is a biconditional. That means if R is a valid argument, then when all R’s premises are true then so is R’s conclusion. Similarly, when all R’s premises are true then so is R’s conclusion, R is valid.

We have some options with respect to our pair of arguments above. Suppose A is true. Then so is B. Then it’s true that if A is true then so is B. Hence, we’ve found no counterexample to the validity of the first argument. We have more work to do of course. A is either true or false. Suppose A is false. Well then it doesn’t matter what B is (B is false of course) for the sake of validity. You can only have a counterexample to validity (and so an invalid argument) when all premises are true. Since A is false, we count this first argument as valid. I’ll let you make the similar observations about the second argument.

Partial Truth Tables

(1)   A -> B:       T F T T

(2)   B:               T F T F

(3)   A:               T T F F

 We’re checking if (3) follows by constructing truth tables. I find it somewhat clearer to write the truth tables in the preceding way, since it illustrates it’s an argument we’re considering. To check whether (3) follow we look for counterexamples to validity, i.e. cases where all the premises are true and the conclusion is false. Observe there are two rows where both premises are true. In the second, we see that A is false. Hence, this is not a valid argument.

Now, let’s check whether ~(A /\ ~B), B -> ~A, and ~B are jointly satisfiable. Consider:

~(A /\ ~B):    T F T T   

B -> ~A:         F T T T

~B:                 F T F T

Since there is one row in which all assignments are true, this set is jointly satisfiable.

*********************************************************************************

[What follows is priming for later in the quarter, so you don’t to worry about it now if you’d prefer to focus for the quiz]

You can make the preceding easier by observing the first expression is equivalent to: A -> B, so you have:

A -> B

B -> ~A

~B

From the first two you can argue:

(1)   A -> B

(2)   B -> ~A

(3)   Therefore, A -> ~A (contradiction!)

But, if we assume both A and B are false, then what we have expressions of the form:

~A -> ~B

~B -> A

B

From which we might argue:

(1)   ~A -> ~B

(2)   B

(3)   Therefore, ~~B

(4)   Therefore, ~~A

(5)   Therefore, A

But nothing much else follows of interest, and certainly no contradiction.

*************************************************************************************

 

Logic Notes

Notes

In recitations you will be expected to work in groups to solve challenging problems illustrating the course content covered by Sean in the preceding Wednesday, Thursday, Monday classes where applicable. I will provide different ways to approach the same content that will challenge you to think creatively about it, and so improve your understanding. You should expect to think hard during recitation. I typically walk around and provide guidance, a joke to lighten the mood, some formal strategy, some strategy for solving problems under pressure, etc. 

 Disjunctions should be rather familiar by now. Let’s remind ourselves of some examples. Consider the following:

John is bald or John is a man

Now, we know that only one side has to be true for this to be evaluated as true. Both sides are true. What about the following:

John has hair or John is a man

Again, this should evaluate to true since at least one side of the disjunction is true. We would translate the first sentence as:

BvM

And we would translate the second sentence as:

HvM

What if we translated the first sentence in the following manner:

MvH

Do you think this changes the meaning of the sentence? No, this does not.  Disjunctions, like conjunctions, are commutative. We can also build them up as we have done with the conjunctions. That is, we can build longer disjunctions in the following manner:

HvFvN

This might capture the meaning of some sentence like the following:

John either has hair or is funny or is neat

We can also combine the disjunction and conjunction in various ways. Consider the following;

John is either going to the beach and swimming or laying around at home

We might translate this sentence in the following way:

(B&S)vL

This may lead to more complex sentences such as the following:

John is a bald instructor or a bald student

Which could be captured as:

(B&I)v(B&S)

Not both

Now that we have covered conjunctions and negations, and introduced a disjunction into the truth table, now let’s look at disjunction in more depth. More specifically, let’s look at the negations of disjunctions. That is, let’s look at sentences like the following:

It is not the case that either John has hair or John is a woman.

Now, this is true. This should be straightforward for our symbolization from English into the connectives. We will symbolize this in the following manner:

~(HvW)

Is this previous statement equivalent to:

~Hv~W

What do you think? This sentence says that it is not the case that John has hair or it is not the case that John is a woman.

I think they are not equivalent. The first translation above is much stronger than the second. I do not want to leave open the possibility that one of these is true. I am making a claim that both of the disjuncts is false. That is, 

~H&~W

Now, in many circumstances you won’t hear the sentence as we have prepared it here. Our English is a little stilted. I have used the locution ‘it is not the case that John has hair or is a woman’. Instead, you will hear something like the following:

John is neither bald nor a woman

We will translate sentences using neither nor as the negation of disjunctions. Since this locution is the logical equivalent of saying either of the following two sentences:

(1) John does not have hair and John is not a woman

(2) It is not the case that John has hair and it is not the case that John is a woman

Then we will translate these sentences all as the negation of disjunction. Thus, all of these sentences are logically equivalent for our purposes.

Conditional

With our conditional we have an antecedent and a consequent. The antecedent recall comes first and the consequent second. There are many ways you will see this written in English. Think about translations of the following conditional sentences:

(1) If John goes to the store John will buy candy

(2) John buys candy if John goes to the store

 (3) In case John goes to the store, John buys candy

(4) Provided that John goes to the store, John buys candy

We would translate all of these in the following manner:

(1) S -> C

This is because they all have the same form. The ‘if’ you will note, when it is apparent, will always introduce the antecedent while the ‘then’ will always introduce the consequent. Provided, on the condition that, in case, etc., are all equivalent for our purposes to ‘if’. So when you see them, be sure to translate them as the antecedent. Let’s see how well you have mastered this concept:

Translate the following sentence into our symbolic language using the material conditional:

If John went to the store, then either John bought candy or John bought mints and John did not buy both candy and mints

The following would be an acceptable translation:

S -> [(CvM)&~(C&M)]

Do you think this captures the meaning of the sentence. I hope you recall the meaning of the second portion of the sentence. We have an exclusive sense of or going on in the consequent of the material conditional. Now, what is the main connective of the sentence? Exactly, this is the conditional. Now, let’s look at a few more examples of English translations with the material conditional.

Only If

Consider the following sentences:

(1) John will buy candy only if John goes to the store

(2) John will buy candy if John goes to the store

Should they be translated as the following:

(1) C -> S

That is, should we translate both of these sentences in the same way? What about the other direction? Should we translate these sentences in the following direction?

(2) S -> C

What do you think?

I should point out that it is not necessary that we have to translate them both into the same form. Indeed, one will be translated in one direction and the other in the other direction. Recall that if sentences always introduce the antecedent. That suggests that the second sentence should be translated as above. What about the other sentence? It has only if rather than simply the if. Don’t let this fool you though! When you see only if, this is different from simply the if. When you see ‘only if’ you will need to note that this introduces the consequent. That is, the first translation will be translated in the first manner.

Now, consider the following:

(1) If John goes to the store then John buys candy

(2) If it is not the case that John buys candy then it is not the case that John goes to the store

How might we symbolize these? Get together and provide a solution:

(1) S -> C

(2) ~C -> ~S

These are logically equivalent. That suggests that a comparable way to translate sentences such as ‘only if’ would be as (2) above. That is, sentences like the following:

(1) If John doesn’t go to the store then John doesn’t buy candy

Can be translated in the following:

(2) If John buys candy then John goes to the store

(3) John buys candy only if John goes to the store

(4) ~S -> ~C

(5) C -> S

What about the following:

John’s tree will grow only if it receives enough light

 T -> L

This is misleading though. This says that if the tree grows then it will have enough light. Yet, this is incorrect. This direction suggests that there is a causal relation between the tree growing because it has enough light in the sense that growing comes first or precedes the acquisition of light. The problem is the tense involved. The material conditional when combined with tense may lead us astray. We will avoid many of these constructions. We will not try to capture tense with this logic. There are more advanced logics that can handle them though. We have to stop somewhere! Note, you probably remember a similar argument provided when we discussed certain conjunction sentences. I repeat here, we won’t be able to translate such sentences in our logic.

If and Only If

We can introduce another derived connective today. This will be what we call the biconditional. The name should be suggestive since it is simply two conditionals. One will go one direction and the other in the other. Consider the following:

John goes to the store if and only if John buys candy

We will learn to translate this in the following manner:

S <- -> C

You can surely see that the conditionals go both ways. Now consider the following:

If John goes to the store then John buys candy and if John buys candy then John goes to the store

This reveals the structure of the bi-conditional. Try to formalize this without the two arrows. Just use the other connectives that we have.

Hopefully, your construction looks like the following:

(C -> S) & (S -> C)

Our bi-conditional is the abbreviation of this. Anytime you have a bi-conditional you will have the opportunity to replace it with this as they are logically equivalent..

Unless

One final translation will be considered today. Consider the following:

John goes to the store unless John buys candy

This will be tricky. I want you to think about unless in the following manner. When you see unless between two sentences, I want you to translate what follows as ‘if not’. So, the above sentence will be translated as:

~C -> S

Now, I want you to think with me for a moment about this sentence as compared to the following:

John goes to the store or John buys candy

How do you think we would translate this sentence?

CvS

Note, that they are logically equivalent! That suggests that when you translate unless sentences, you may translate them as disjunctions. For instance,

John goes to the store unless John buys candy

Is readily translated as:

SvC

Or even as:

~C -> S

That ends our discussion for today.

Santorio's Counterfactual Triviality Result

I recently presented a manuscript of Paolo Santorio's where he extends Lewis's well-known triviality results to counterfactual conditionals. Similar material was covered in Paolo and Justin Khoo's NASSLI course Probabilities of Conditionals and Conditional Probabilities. I essentially walk through the details in my presentation. If you're inclined to work through the details of proofs - to make sure they work - then you might enjoy this excursion here

Speak No Evil: Hermeneutical (In)justice and Extreme Abuse

Speak No Evil: Understanding Hermeneutical Injustice in Cases of Extreme Trauma

Gaps in collective hermeneutical resources[1] stemming from prejudice may result in members of marginalized groups being unable to render harmful experiences intelligible to themselves or others. Miranda Fricker identifies such situations as instances of Hermeneutical Injustice (HI). For example, prior to the introduction of the term “sexual harassment,” there was a gap[2] in the relevant collective understanding – the intersection of hermeneutical resources among groups that just about anyone can be expected to draw upon and be understood by anyone else. This lacuna hindered attempts by, say, women harassed in the workplace, from fully understanding these harmful experiences.

Fricker’s original presentation of (HI) left open several theoretical choice points leading to criticisms[3],[4] and subsequent – needed - clarifications.[5] Yet, there remain aspects of (HI) in need of further explication the overlooking of which may lead to, among other things, verbal disputes. In what follows, I carefully extract principles governing Fricker’s characterization of (HI). I first show (HI) must be the manifestation of a background hermeneutical marginalization, and argue this feature precludes certain cases of extreme abuse from being counted as (HI). Rather than considering this a cost of Fricker’s proposal, I observe how this clarification allows Fricker to avoid otherwise substantial objections. Second, I show (HI) entails hermeneutical marginalization, hermeneutical marginalization entails hermeneutical disadvantage, and neither converse holds. Third, I argue the best way to make sense of hermeneutical marginalization is via a threshold where agents have been coerced into situations involving an imbalance of disadvantages to advantages. I then use these principles to construct a sufficient condition for (HI) that captures cases intuitively exhibiting the phenomenon, while distinguishing distinct nearby phenomena.

Hermeneutical Injustice Entails Marginalization, but Not Conversely

Consider:

CASE 1a: Sue lived in a psychologically and physically abusive home from birth to age 16. Sue internalized coping mechanisms to survive. Sue never learned to reflect on these harmful experiences or on her internalized coping mechanisms.[7]

The sort of coping mechanisms intended in CASE 1a consist of habits of ignoring psychological/physical pain, a tendency to dissociate,[8] fusion with thoughts, and other avoidant cognitive behavior. Suppose, moreover, in Sue’s community there were no collective resources adequate for understanding what we would characterize as child abuse, and that this absence owes to structural prejudice concerning women and children. If granted, CASE 1a exhibits many features of (HI). Sue lives through harmful experiences which she is unable to render intelligible to herself or others and relevant collective hermeneutical resources are lacking owing to prejudice.[9] Contrast:

CASE 1b: Sue from CASE 1a, as an adult, realizes her psychological development and dispositions differ significantly from many acquaintances. Sue eventually acquires cognitive dispositions that incline her to reflect on and attempt to render experiences in her abusive past and present intelligible.

Again, we might suppose Sue’s environment lacks the relevant hermeneutical resources she needs to render her experiences intelligible. If granted, CASE 1b also exhibits many features of (HI); in fact, CASE 1b seems paradigmatic. To be fair, one potentially salient difference between CASE 1a and CASE 1b is the absence in the former of cognitive capacities present in the latter. But it is unclear why that should preclude CASE 1a from counting as an instance of (HI). Presumably, lacking capacities to render experiences intelligible is just one way of being unable to render experiences intelligible. If CASE 1b is a paradigmatic example of (HI) – and absent capacities is a difference that makes no difference – then CASE 1a should count too.

And yet CASE 1a does not count as (HI). Fricker insists (HI) arises only when an agent struggles to make sense of an experience.[10], [11] The when and where of (HI) is tethered to those affected who try and fail to render their experiences intelligible. This implies if an agent is not attempting to render their harmful experience intelligible, there is no (HI). Generally speaking, Fricker seems to accept what I will call the Manifestation Condition (MC): (MC) Case C involving agent S exhibits (HI) at time t only if S attempts to render a relevant harmful experience intelligible in C at t

If (MC) is true, CASE 1a is not (HI). This seems problematic for at least three reasons:

·         First, CASE 1a exhibits a prejudicial gap in hermeneutical resources undermining any attempt Sue might have at rendering her experience intelligible. Surely Sue lives under something like “…holes in the ozone…”[12] hermeneutically speaking. Whether or not Sue struggles to render her experience intelligible seems incidental to whether she is “…burned.” Intuitively then, CASE 1a seems an instance of (HI).[13]

·         Second, there seem good reasons to reject (MC) as too strong. Consider Sue in CASE 1b, busy at work or momentarily distracted or sleeping, and so not attempting to make sense of her harmful experiences. If (MC) is true, at these moments it seems we must say Sue is not subjected to an injustice that undermines her abilities to render her experiences intelligible. That seems false. Similarly, for CASE 1a. Hence, (MC) should be rejected.

·         Third, consider the primary harm of (HI): “…the subject’s being unfairly disadvantaged…in the construction of selfhood.”[14] Sue operates against a background hermeneutical deficit that may undermine “construction of selfhood” regardless of whether she struggles to make sense of her harmful experiences or not. But if (MC) is true then the presence of the primary harm of (HI) is not sufficient for (HI). This may not seem initially problematic since - generally speaking - the primary harm of (HI) is not sufficient for (HI). For example, agents may experience unfair epistemic disadvantaged without this being (HI), as evidenced by epistemic bad luck, e.g. patients with undiagnosed illnesses.[15] Nevertheless, granting the primary harm of (HI) need not generally be sufficient for (HI), surely we should expect the primary harm to be sufficient for (HI) in some class of cases. CASE 1a does not exhibit an incorrect assessment of otherwise reliable evidence based on bad luck,[16] and seems just the sort of scenario in which to expect the primary harm sufficient for (HI). But if (MC) is true, then CASE 1a is not (HI). Hence, (MC) should be rejected.

Altogether, CASE 1a is plausibly (HI), but is ruled out by (MC) which divorces (HI) from its primary harm. Consequently, it seems Fricker should reject (MC) and accept CASE 1a as (HI).  

            This, however, is too quick.[17] Though CASE 1a does not exhibit (HI), the scenario exhibits Hermeneutical Marginalization (HM): a state of affairs exhibiting non-accidental inequality between individuals or groups that provides the background condition against which instances of (HI) manifest.[18] An analogy makes the point clear: Salt is disposed to initiate a dissolving process, if placed in background conditions.[19] But salt being so disposed does not entail it ever will; dispositions and associated processes are only correlated.[20] Analogously, Fricker seems to hold: agents are to salt as (HM) is to water and as manifesting (HI) is to dissolving. This analogy makes sense of CASE 1b, which exhibits (HM), dispositions to manifest (HI), and manifestation of (HI). Hence, this counts as an instance of (HI). And it also makes sense of why CASE 1a does not count as an instance of (HI), as it exhibits (HM), but neither disposition to manifest (HI) nor manifestation of (HI). CASE 1a is more like iron, rather than salt, in a cup of water. And neither (HI) nor dissolving manifests in such respective setups. Importantly, CASE 1a exhibiting (HM) makes all the difference when responding to the preceding objections. Working backwards:

·         It is true the primary harm of (HI) is not sufficient for (HI) even in CASE 1a. But this is no surprise if in “…a subject’s being unfairly disadvantaged…in the construction of selfhood” we understand “unfairly disadvantaged” as denoting the background conditions against which the subject operates, and we locate the primary harm of (HI) in this background condition, i.e. (HM). Moreover, we might transpose in this manner and still speak of this being the primary harm of (HI), since Fricker seems committed to the following claim:

(HI-HM) If case C exhibits (HI) at time t, then C exhibits (HM) at t[21]

Any instance of hermeneutical injustice entails hermeneutical marginalization. Hence, the primary harm of (HM) will, in any instance of (HI), be present, but since there may be (HM) without (HI), there may be the primary harm of (HM) without (HI). That is, Fricker seems committed to, where “(PH)” denotes the primary harm of (HM):

(HI-PH) If case C exhibits (HI) at t, then C exhibits (PH) at t

Which with (HI-HM) entails:

(HI-HM&PH) If C exhibits (HI) at t, then C exhibits (HM) & (PH) at t

And that seems a general enough relationship to satisfy our objector, even if it was not in the direction anticipated. Our objector may retrench and inquire into the relationship between (HM) and (PH). But here it is plausible for Fricker to claim (PH) is necessary for (HM):

(HM-PH) If case C exhibits (HM) at t then C exhibits (PH) at t

So that in any case of (HM), a subject is unfairly disadvantaged in construction of selfhood.[22] If so, there is a connection between (HM) and (PH), even with (MC) accepted.

·         Above it was claimed if (MC) is true, it seems we must say Sue in CASE 1b is not subjected to an injustice that undermines her abilities to render her experiences intelligible when she is, say, busy doing other things. Emphasizing (HM) reveals this worry to be largely verbal. True, in CASE 1a Sue is not subjected to (HI), but there is nevertheless (HM). We might then say while Sue is not struggling to render her harmful experiences intelligible to herself or others, she still operates against this background condition which would undermine her attempts at doing so, and in that way Sue is marginalized. Our objector may be unmoved, and insist Sue be treated as subjected to an injustice. I am sympathetic, but it is not clear what is gained. This leads naturally to the next objection…

·         …namely, that CASE 1a is intuitively (HI). But whatever pull this intuition has trades on whether it is sufficient to claim Sue is subjected to mere marginalization, or if we must also claim Sue is subjected to hermeneutical injustice. To be fair, reading Fricker as treating CASE 1a as (HI) is not incoherent. Rather than Sue being to salt as (HM) is to water as (HI) is to dissolving, an alternative reading might result in Fricker holding: Sue is to salt as (HI) is to water as manifesting (HI) is to dissolving. Then (HI) would be the background condition, but distinct from manifesting (HI). CASE 1a would exhibit (HI) given the gap in the collective hermeneutical resources, and this would be independent of whether Sue manifests (HI). Note, however, this reading suggests either (HM) is (HI)[23] or is superfluous, as it is unclear what role it would play in Fricker’s theory. If this alternative reading were better motivated, it may be right to identify (HM) and (HI) or drop (HM) altogether. But coherence alone is insufficient motivation, and being able to say Sue is subjected to an injustice rather than mere marginalization is not obviously compelling. 

Altogether, CASE 1a is not overlooked in Fricker’s account, as it is an instance of (HM) though not (HI). This may initially seem problematic, but the counter-intuitiveness fades once (HM) is clearly distinguished from (HI). It is, moreover, unclear what is gained by adjusting Fricker’s theory to accommodate that initial intuition. Additionally, there seems a clear connection between (HI), on the one hand, and (HM) and (PH), on the other, reflected in Fricker’s various commitments, all of which are consistent with accepting (MC) and rejecting CASE 1a as (HI).

Hermeneutical Marginalization Entails Disadvantage, but Not Conversely

Consider next:

CASE 2: Sally became pregnant at 15, dropped out of school, married at 16, had more children with her husband Mike, and was a “house wife” who relied on Mike for support. Mike was psychologically and physically abusive. Sally eventually came to believe attempting to render her harmful experiences was a waste of effort. Sally instead focuses on avoiding Mike’s anger. Over time, Sally internalized coping mechanisms preventing her from attempting to make sense of her experiences.[24]  

Let us further suppose there is no gap in the collective hermeneutical resources, but that Sally is unable to access those resources owing to coping mechanisms. As before, Sally is not struggling to render her experience intelligible, so CASE 2 is not an instance of (HI).[25] However, since both Sue and Sally lack relevant capacities for rendering their respective harmful experiences intelligible, and since CASE 1a exhibits (HM), it is plausible CASE 2 exhibits (HM) too. Moreover, there is a positive reason for treating CASE 2 as at least exhibiting (HM). Since Sally self-imposed coping mechanisms, rejecting CASE 2 as exhibiting (HM) seems close to victim blaming,[26] i.e. claiming Sally is not hermeneutically marginalized, but perhaps inappropriately self-imposes coping mechanisms making her epistemically culpable. Of course, rejecting CASE 2 as (HM) does not entail characterization of Sally in a way that supports victim-blaming. Still, it seems plausible if there is an alternative characterization of CASE 2 that does not so easily lend itself to such a reading, then we should prefer that alternative. I will thus assume our task in what follows is to discover how to classify CASE 2 as exhibiting at least (HM) while remaining consistent with Fricker’s commitments.

Yet, there may be reasons to think CASE 2 does not exhibit (HM). Fricker claims one cannot simply “opt in”[27] to (HM), e.g. become a hermit. Sally self-imposing coping mechanisms seems rather close to opting in. Hence, it seems CASE 2 might not exhibit (HM). But this quick argument deserves a quick response: Sally is not simply opting in to (HM). Sally is coerced into developing coping mechanisms. That said, we cannot infer simply from the presence of coercion to the existence of (HM), since in general coercion is insufficient for (HM). Fricker’s recent discussion[28] of the potential overlap between (HI) and the phenomenon of White Ignorance[29] illustrates why. Fricker examines two scenarios relevant to our discussion. First:

IGNORE 1: Non-culpably[30] ignorant white people in environment where hermeneutical resources have been suppressed and knowledge, e.g. black efforts during WWII, has been forgotten or never learned.   

And second:

IGNORE 2: Non-culpably[31] ignorant white people in environment where hermeneutical resources have been suppressed and knowledge cannot be accessed as population lacks needed concepts for acquiring this knowledge.

Fricker claims both cases exhibit white ignorance, but claims only the second exhibits (HI). Specifically with respect to (HI), members of the relevant non-white population attempting to render their harmful experiences intelligible to ignorant members of the white population in IGNORE 1 are not subjected to (HI) since the inability of the white individuals to make sense of these harmful experiences stems from epistemically culpable behaviors, e.g. failing to infer from existing concepts needed conceptual resources to understand. In contrast, IGNORE 2 exhibits (HI) when members of the relevant non-white population fail to render their experiences intelligible to white individuals since the inability of the latter individuals to make sense of these experiences stems from the complete absence of needed concepts from collective resources. Put another way, whether (HI) is exhibited in these cases trades on whether communication breaks down due to needed concepts for comprehension being hidden or being absent. If the former, there is not (HI); if the latter, there is (HI). But note, if coercion alone were sufficient for (HM), then it is plausible members of the relevant white population might also be subjected to (HM), since it is not difficult to imagine, say, the suppression of relevant concepts and knowledge needed to understand the experiences of marginalized individuals is coerced, say, through education, parents, peer groups, etc.[32] Even under such conditions, however, it seems incorrect to say the ignorant white population is subject to (HM). Hence, the presence of coercion alone seems insufficient for (HM).

Exploring in more detail why ignorant white individuals in IGNORE 1 and IGNORE 2 are not subject to (HM) will, moreover, bring us closer to seeing precisely why CASE 2 exhibits (HM). Observe first: Fricker urges members of the ignorant white population in IGNORE 1 and IGNORE 2 do not exhibit (HI) - since they are not disadvantaged – though she suggests members of the ignorant white population do exhibit Epistemic Disadvantage (ED).[33] Fricker does not elaborate on (ED), but plausibly this is any disadvantage an agent experiences with respect to acquiring or sustaining knowledge. Observe second: Fricker distinguishes (HM) from Hermeneutical Disadvantage (HD), i.e. a deficit in subjects’ abilities to contribute to collective epistemic resources.[34] (HD) seems necessary for (HM), but is distinct as evidenced by cases of epistemic bad luck[35] in which individuals experience disadvantage but not necessarily marginalization,[36] i.e. Fricker maintains:

(HM-HD) If case C at t exhibits (HM), then C at t exhibits (HD)

And plausibly exhibiting (HD) is just one way to exhibit (ED), suggesting Fricker also maintains:

(HD-ED) If case C at t exhibits (HD), then C at t exhibits (ED)

Now, if members of the relevant white population with respect to IGNORE 1 and IGNORE 2 exhibited (ED) but not (HD), then by (HM-HD) they would not exhibit (HM). It seems clear Fricker believes these cases exhibit (ED). But it also seems there are good reasons to think these cases exhibit (HD) as well. Simply put, there is at least a local marshalling of forces against attempts to render intelligible harmful experiences expressed by marginalized groups, i.e. the absence of resources needed for mutual understanding is not accidental.[37] But if whites in these cases exhibit (HD), there seems no easy path to conclude they do not exhibit (HM).

            Fortunately, there are commitments we have not yet employed, namely, that ignorant white individuals in these cases also exhibit Hermeneutical Advantage (HA), i.e. a surplus in subjects’ abilities to contribute to collective epistemic resources.  Of course, simply being subject to (HA) alone is insufficient to show a case does not exhibit (HM).[38] Marginalized groups can exhibit both (HA) and (HD) and still exhibit (HM). What seems crucial to determining whether (HM) is exhibited is the ratio of quantity/quality of (HA) to (HD). We need not attempt to make this precise.[39] Let P denote a quantitative and qualitative combination of (HA); let Q denote a quantitative and qualitative combination of (HD); let T denote a sequential range of positive real numbers, e.g. (4 - 6). It suffices to say a case counts as (HM) with respect (HA) and (HD) if T < P/Q, and a case does not count as (HM) if T > P/Q. In other words, in a given context, a case counts as (HM) if the hermeneutical advantages weighed against disadvantages results in a number greater than a certain threshold which – perhaps – allows for indeterminate borderline cases. With this in mind, it is clear ignorant white individuals in IGNORE 1 and IGNORE 2 do not exhibit (HM), since the ratio of advantages to disadvantages is plausibly greater than any reasonable specification of T. On the other hand, non-white individuals in these cases are plausibly more disadvantaged than they are advantaged. Hence, there is (HM) with respect to these communities.

            These resources, moreover, illustrate why coercion alone is insufficient for (HM). For coercion must play to the disadvantage of the relevant marginalized group. Ignorant white individuals can be coerced into ignorance, but since they are nevertheless hermeneutically advantaged, they are not subjected to (HM). Additionally, Fricker’s insistence that one cannot simply opt in to (HM) suggests (HD) alone is insufficient for (HM), since one can surely opt in to (HD). This suggests coercion is needed for (HM). We can combine these observations into what seems a plausible further commitment Fricker makes concerning a sufficient condition for (HM):

(C&T-HM) If case C at time t exhibits coercion resulting in T < P/Q, then C exhibits (HM) at t

And with (C&T-HM) we can finally explain why CASE 2 exhibits (HM), since Sally is coerced resulting in a proportion of (HA) to (HD) below some reasonable specification of T.

This explication aligns with results one should expect from Fricker’s characterization of (HM) and (HI), generally.[40] And provides a precise way to distinguish (HI) and associated concepts from nearby phenomena. Consider: 

CASE 3: Sam’s childhood resembles that of Sue’s in CASE 1a. Sam acknowledges his experiences are harmful, but considers himself a martyr, and believes his experiences are for some greater purpose.

Additionally, suppose there is a gap in the relevant collective hermeneutical resources. One might expect CASE 3 to exhibit (HI), but this is not so. Sam does not struggle and fail to render his admittedly harmful experiences intelligible because Sam is not struggling to render his experiences intelligible; he thinks he has rendered them intelligible. Whereas reflecting on CASE 1a emphasizes what it means to render an experience intelligible, CASE 3 emphasizes what it means to render an experience intelligible. But whatever the answer to that admittedly difficult latter question, Fricker can maintain CASE 3 exhibits (HM) by (C&T-HM).[41]  Similarly, we can bring into dialogue cases like CASE 1a and CASE 2, to determine what sort of harms or injustices might be exhibited:

CASE 4a: 12 year old Mary – who has experienced much abuse in her home life - attempts to communicate to her mother Sally – from CASE 2 - a harmful experience she had involving her father – and Sally’s husband – Mike. Sally responds “Mike would never do such a thing,” as Sally – in the process of developing coping mechanisms – is strongly disinclined to understand Mike’s harmful behavior as such.  

Suppose there is no gap in the collective hermeneutical resources, but Sally is again unable to access them due to firmly entrenched coping mechanisms, and Mary is blocked from accessing them by Sally. In CASE 4a, both Sally and Mary plausibly satisfy the antecedent of (C&T-HM), since both seem coerced and sufficiently disadvantaged. Hence, by (C&T-HM) it follows that CASE 4a exhibits (HM). It does not, however, exhibit (HI) since the Mary’s failure to communicate her harmful experiences stems from Sally’s epistemically culpable behavior, i.e. uptake failure stems from failure at the level of beliefs. As before when examining IGNORE 1 and IGNORE 2, Fricker maintains that communicative failures stemming from such behavior are not (HI), but some other phenomenon. On the other hand, consider: 

CASE 4b: Same as CASE 4a, but Sally has developed coping mechanisms preventing her from recognizing Mike’s behavior as harmful. 

Given this slight adjustment, so that Sally plausibly lacks “requisite concepts”[42] to make sense of her daughter’s harmful experiences, we have a case of (HI). These last observations suggest we can state a sufficient condition Fricker seems committed to for (HI):

(SF-HI) If case C at t involving agents S and S’ is such that:

(1) S is coerced leading to (HM)[43] at t, and

(2) S struggles to render a harmful experience intelligible to S’ at t, and

(3) S’ fails to understand S due to S’ lacking conceptual resources and not due to epistemically culpable behaviors by S’, then

C exhibits (HI) at t

Where S and S’ may be the same individual, e.g. Carmita Woods, Sally in CASE 2.

            We have the following results with respect to cases: (HM) is a background condition for (HI). Sue in CASE 1a and Sally in CASE 2 exhibit (HM), (PH), and (HD) but not (HI), since neither struggles to render their respective experiences intelligible. Hence, neither CASE 1a nor CASE 2 satisfies (MC), and so neither satisfies clause (2) of (SF-HI). On the other hand, CASE 1b exhibits (HM), (HD), (PH), and (HI), as evidenced by each clause of (SF-HI) being satisfied in this case. With respect to IGNORE 1 and IGNORE 2, marginalized individuals in the former are not subjected to (HI), as evidenced by clause (3) of (SF-HI) not being satisfied – though they are subjected to (HM) by (C&T-HM), while marginalized individuals in the latter are subjected to (HI) by (SF-HI).[44] Ignorant white individual in neither case are subjected to (HI) or (HM), though they plausibly are subject to (ED). It is unclear whether they are subject to (HD), i.e. exhibiting epistemic bad luck. CASE 3 arguably does not exhibit (HI) as evidenced by failure to satisfy clause (2), since the individual in this case does not appear to be struggling to make sense of his experiences. CASE 4a and CASE 4b come apart on condition (3) of (SF-HI) with the latter, but not the former exhibiting (HI).

Works Cited

Anderson, E. (2012). Epistemic Justice as a Virtue of Social Institutions. Social Epistemology. 26(2): 163-73.

Beverley, J. (2016). The Ties that Undermine. Bioethics. 30(5)

Beverley J. & Beebe, J. (2017). Judgments of Moral Responsibility in Tissue Donation Cases. Bioethics. 32(2).

Dotson, K. (2011). Tracking Epistemic Violence, Tracking Practices of Silencing. Hypatia: A Journal of Feminist Philosophy. 26(2): 237-57.

Futa, K.T. et. al. (2003). Adult Survivors of Childhood Abuse: An Analysis of Coping Mechanisms used for Stressful Childhood Memories and Current Stressors. Journal of Family Violence. 18(4). 227-39.

Fricker, M. & Jenkins, K.T. (2017). Epistemic Injustice, Ignorance, and Trans Experience. The Routledge Companion to Feminist Philosophy.

Fricker, M. (2016). Epistemic Injustice and the Preservation of Ignorance. In The Epistemic Dimensions of Ignorance (eds.) Peels, R. & Blaauw, M. 160-77.

Fricker, M. (2012). An Interview with Miranda Fricker. Social Epistemology. 26(2): 253-63.

Fricker, M. (2009). Can There Be Institutional Virtues?  Oxford Readings in Epistemology (Special Theme: Social Epistemology).

Fricker, M. (2007). Epistemic Injustice: Power and the Ethics of Knowing. Oxford and New York: Oxford University Press.

Goetze, T. (2018). Hermeneutical Dissent and the Species of Hermeneutical Injustice. Hypatia: A Journal of Feminist Philosophy. 33(1).

Hanel, H. C. (2018). What is Rape? Social Theory and Conceptual Analysis. Bielfeld, Deutschland.

Jenkins, K. (2017). Rape Myths and Domestic Abuse Myths as Hermeneutical Injustices. Journal of Applied Philosophy. 34(2): 191-206.

Lowe. E.J. (2006). The Four-Category Ontology: A Metaphysical Foundation for Natural Science. Oxford: Clarendon Press.

Mason, R. (2011). Two Kinds of Unknowing. Hypatia: A Journal of Feminist Philosophy. 26(2): 294-307.

McMahan, J. (2002). Ethics of Killing: Problems at the Margins of Life. Oxford University Press.

Medina, J. (2017a). Epistemic Injustice and Epistemologies of Ignorance. The Routledge Companion to the Philosophy of Race.

Medina, J. (2017b). Varieties of Hermeneutical Injustice. The Routledge Handbook of Epistemic Injustice.

Medina, J. (2013). The Epistemology of Resistance: Gender and Racial Oppression, Epistemic Injustice, and Resistance Imagination. New York: Oxford University Press.

Mills, C. (2007). White Ignorance. In Race and Epistemologies, (ed.) Tuana, S. S. N.

Nguyen, C.I. (2019). Echo Chambers and Epistemic Bubbles. Episteme. 2-21.

Nozick, R. (1969). Coercion. In Philosophy, Science, and Method: Essays in Honor of Ernest Nagel. St. Martin’s Press. 440-472.

Polhaus, Jr. G. (2012). Relational Knowing and Epistemic Injustice: Toward a Theory of Willful Hermeneutical Ignorance. Hypatia: A Journal of Feminist Philosophy. 27(4): 715-35.

Tremain, S. (2016). Knowing Disability, Differently. The Routledge Handbook on Epistemic Injustice.

Romdenh-Romluc, K. (2016). Hermeneutical Injustice: Blood-Sports and the English Defense League. Social Epistemology.

Simion, M. (2018). Hermeneutical Injustice as Basing Failure. In Well-Founded Belief: New Essays on the Epistemic Basing Relation. (eds.) Carter, J.A. & Bondy, P.

Smith, B. & Spear, A. & Ceusters, W. (2016). Functions in Basic Formal Ontology. Applied Ontology. 11. 103-128.

Van Loon, et. al. (2005). Reclaiming Myself after Child Sexual Abuse. Glenside, St. Augustine Research Unit.

Ward, C. (1988). Stress, Coping, and Adjustment in Victims of Sexual Assault: The Role of Psychological Defense Mechanisms. Couns. Psych. Q. 1:165-78.

Williams, N.E.W. (2019). The Powers Metaphysic. Oxford University Press.

 

[1](Fricker, 2007, pg. 1), (Fricker, 2016, pg. 166), among other places. 

[2]Not all “gaps” result in (HI). First, it is plausible collective hermeneutical resources contain a confounding surplus resulting in, say, suspension of belief. But since this “gap” operates at the level of belief it will not result in (HI) (Fricker, 2016). Second, agents who have not inferred implicit resources from explicit hermeneutical resources exhibit a “gap” but this operates at the level of belief. Corollary: generating new hermeneutical resources must sometimes arise ex nihilo. Suppose otherwise. Presumably, a conceptual definition corresponding to the phrase “sexual harassment” could have been constructed by Woods prior to introducing the term based on available conceptual resources, e.g. this or that behavior with this or that intention. But that suggests “sexual harassment” was implicit in the existing resources and Woods simply failed to identify it. Hence, this is not (HI). But this is (HI). So, the concept arose ex nihilo.

[3]E.g. (Dotson, 2012) and (Mason, 2013) independently argued (HI) precluded members of marginalized groups from developing local resources. Each appears to have interpreted the “collective hermeneutical resource” as the union of hermeneutical resources of various groups (Goetze, 2018), which implies marginalized groups lack local hermeneutical resources. (Fricker, 2016) clarified the intent was the intersection of resources, which blunts these objections.

[4]E.g. (Medina, 2013) worried Fricker was unable to accommodate marginalized groups with local resources experiencing (HI) when attempting to communicate with groups having different resources. (Fricker, 2016) extended (HI) to maximal (HI) – global gap in collective resources – and minimal (HI) – a local gap – species of (HI), with Joe from the novel Enduring Love illustrating the latter, since the hermeneutical gap is just between Joe and the police.

[5]Fricker claims “…a commitment to the existence of localized interpretive practices…is present…in the…original account of hermeneutical injustice.” (Fricker, 2016, pg. 167). I am skeptical. First, extending the original theory to maximal/minimal (HI) hardly shows they were implicit; theory extensions are cheap. One can consistently extend a minimal linear order of time to either a dense or discrete order. Similarly, Fricker’s original account could be consistently extended in ways inconsistent with maximal/minimal (HI). Second, appealing to Joe (Fricker, 2016, pg. 2016) as hermeneutically marginalized as evidence of minimal (HI) is questionable (Romdenh-Romluc, 2016).

[7]I suspect this sort of case falls under what (Medina, 2017a; 2017b) has usefully identified as epistemic death.  

[8](van Loon & Kralik, 2005) and (Ward, 1988) illustrate childhood coping strategies manifesting in adulthood, e.g. repression, emotional insulation, dissociation. These “avoidant strategies” (Futa, Nash, Hansen, & Garbin, 2003) help create a sense of control through avoiding emotions.

[9]Objection: The reason there is a gap in resources is not the same as the reason Sue lacks the capacity to render her experiences intelligible, so it is questionable whether CASE 1a exhibits (HI). The former may be due to prejudice while the latter to, say, fear. Response: These reasons dovetail, i.e. Sue’s fear of abuse stems from abuse caused by prejudice.

[10]“…hermeneutical injustice comes only when the background condition is realized in a more or less doomed attempt…to render an experience intelligible...” (Fricker, 2007, pg. 159); “…hermeneutical marginalization…leaves practitioners susceptible to hermeneutical injustice whenever they should attempt to render the experience intelligible…” (Fricker, 2016, pg. 166)

[11](Goetze, 2018)’s revised definition of hermeneutical injustice reflects (MC) as well: “…primary harm of hermeneutical injustice is that the subject has some…social experience that at some crucial moment lacks intelligibility.” As does (Hanel, 2017, pg. 2010) “As long as the subject of hermeneutical disadvantage undertakes no attempt to understand her experience…there is no hermeneutical injustice…”

[12](Fricker, 2006, pg. 161).

[13](Simion, 2018) suggests arguments to this effect.

[14]“…hermeneutical injustice can mean…someone is…constituted as…something they are not...” (Fricker 2007, pg. 168).

[15](Fricker, 2007, pg. 152). We return to this below.

[16]E.g. while rejecting Carmita Woods exhibited mere epistemic bad luck: “…it was no accident that their experience had been falling down the hermeneutical cracks…the whole engine of collective social meaning was effectively geared to keeping these obscured experiences out of sight.” (Fricker, 2007, pg. 153) This seems equally applicable to CASE 1a.

[17]But not uncharitable: “A hermeneutical injustice is done when a collective hermeneutical gap impinges so as to…disadvantage some group(s)…which…is effectively discriminatory.” (Fricker, 2007, pg. 162) “…the conceptual lacuna which handicaps her as an interpreter of her experience entails a hermeneutical injustice. (Fricker, 2012)

[18]“…the conditions of hermeneutical injustice (namely, hermeneutical marginalization)…” (Fricker, 2006, pg. 174) “The hermeneutical inequality that exists, dormant, in a situation of hermeneutical marginalization erupts in injustice only when some actual attempt at intelligibility is handicapped...” (Fricker, pg. 159) “…hermeneutical injustice and its precondition, hermeneutical marginalization.” (Jenkins & Fricker, 2017, pg. 268) “…the primary harm of hermeneutical injustice consists in situated hermeneutical inequality…” (Fricker, 2007, pg. 162). See too (Goetze, 2018, pg. 81).

[19](Williams, 2019).

[20](Smith, 2016), (Lowe, 2006).

[21]Fricker must reject the converse of (HI-HM), since it entails CASE 1a is (HI), which is a rejection of (MC).

[22]As noted above, Fricker rejects the converse, e.g. epistemic bad luck. 

[23]This reading avoids commitment to (MC). Fricker might adopt instead the weaker:

(MC*) Case C involving agent S – who has requisite cognitive dispositions - exhibits (HI) at time t only if S is disposed to render a relevant harmful experience intelligible in C at t

   (MC*) bridges (HI) and attempts to render experiences intelligible, but is silent when agents lack dispositions.

[24]CASE 2 likely involves testimonial smothering (Dotson, 2012), but more besides since Sally eventually does not reflexively silence based on assessment of her audience. We might refer to this phenomena as hermeneutical smothering, identifying testimonial smothering carried to the point of unreflective habit as one route to this injustice.

[25]Objection: Sally initially attempted to render experiences intelligible; that is sufficient for CASE 2 to later exhibit (HI). Response: (HI) is asymmetrical. Woods experienced (HI) before coining “sexual harassment” but was not subject to (HI) with respect to sexual harassment after. If exhibiting (HI) prior entails exhibiting later, then Woods did exhibit (HI) later. The objector must motivate Woods exhibiting (HI) later, or explain why Woods did not, but Sally does.

[26](Jenkins, 2016, pg. 10) makes a similar point involving rape/abuse myths as confounding hermeneutical resources.

[27](Fricker, 2006, pg. 153).

[28](Fricker, 2016).

[29](Mills, 2007).

[30](Fricker, 2016, pg. 173).

[31](Fricker, 2016, pg. 174-5).

[32]By “coercion” I mean something along the lines of (Nozick, 1969, pg. 441-5): Agent S coerces S’ just in case: (1) S aims to prevent S’ from performing action A; (2) S’ is at least implicitly aware of (1); (3) S’ is at least implicitly aware if S’ performs A then S will bring about some consequence that makes A-ing less desirable to S’ than not A-ing; (4) S’ does not perform A; (5) Part of why S’ does not perform A is to decrease chances that S will bring about consequences in (3). Adjustments include allowing S’ to be implicitly – rather than explicitly – aware of S’s intentions. There is more to say, of course, but this rough characterization suffices for our purposes. 

[33](Fricker, 2016, pgs. 173-5).

[34](Fricker, 2007, pgs. 151-2).

[35](Fricker, 2007, pg. 152).

[36]See (Tremain, 2017, pg. 177) for good reasons to doubt Fricker’s example illustrating epistemic bad luck is tenable.

[37]This conclusion stems from (Fricker, 2007, pg. 153)’s rejection of Woods as epistemic bad luck.

[38]Fricker approvingly cites (Medina, 2012, pg. 108) who argues convincingly that members of dominant groups are in some ways epistemically disadvantaged, even though they are clearly advantaged. Similarly, members of marginalized groups may have epistemic advantages, though they are clearly disadvantaged too. This strongly suggests (HA) does not undermine (HM) since otherwise marginalized groups would not exhibit the latter if they exhibit the former. 

[39]I agree with Aristotle that one should only seek precision to the extent one’s domain permits. Here we find a limit.

[40]Not all is satisfactory, however. Fricker claims a patient with a disease yet to be diagnosed – who is subject to (HD) – is not subject to (HM). We capture that by claiming T<P/Q for some reasonable specification of T. So far, so good. Trouble arises when we note Fricker maintains Joe from Enduring Love exhibits (HM). It is unclear why Joe is more disadvantaged than advantaged, while an undiagnosed patient is more advantaged than disadvantaged. It seems if one exhibits (HM) they both do, or if one does not, neither do. I suspect this is a tension in Fricker’s theory, rather than a fault in the principles defended here, but this issue deserves further reflection.

[41]A related scenario we can distinguish from (HI) might be, say, James is raised in a psychologically and physically abusive cult and does not attempt to render these harmful experiences intelligible because he does not perceive them as harmful. This scenario is distinct from CASE 3 since in that case Sam does recognize the abuse as harmful. As before, this would not count as (HI) but plausibly exhibits (HM) by (C&T-HM).

[42](Fricker, 2016, pg. 175).

[43]Because T > P/Q.

[44]For all that has been said, there may be other ways in which marginalized individuals in IGNORE 1 count as exhibiting (HI), but Fricker does not appear forced to say so given her commitments.

Al-Farabi's First Existent

In Chapter 1 of The Perfect State, Al-Farabi (AF) presents the First Existent (FE) as having several properties:

(i) Unity
(ii) Thinking
(iii) Power
(iv) Eternal
(v) Immaterial

However, AF also claims that any entity that has at least two properties is divisible. This implies the FE is divisible. But if the FE is divisible, then (i) is false. AF seems to be caught in a puzzle.

One strategy to resolve this puzzle is by showing (i)-(v) are just one property. This may initially seem implausible, i.e. to say Power = Thinking. We should remember we're doing metaphysics. Intuition is a good starting point, but only gets us so far. Consider, there is more space in your desk than matter. That's unintuitive; it's true all the same. This truth earns its place in our scientific theories in part by playing a key role in explaining physical phenomenon. A good explanation can override our intuitions. We should give AF the benefit of the doubt with respect to what his theory of the FE - with (i)-(v) each denoting a single property - can explain. If it can do the work he says it can do, it earns its place in a theory; if it can't, it doesn’t. But this is orthogonal to whether his claims are intuitive or not.

We nevertheless must make sense of how (i)-(v) might each denote a single property. We divide our task into examining (i) and examining (ii)-(v).

Consider (i) first: I don't even think it's accurate to say this is a property worthy of entry on the list. This is not to say (i) isn’t a property. Rather, this seems to be a property that is reducible to other properties on the list. I think this is what is called a supervenient feature of the FE. This is what you get when you have all the other properties, which are themselves just one thing, together. Suppose you buy a sandwich and the clerk tells you to pay for the sandwich, the bread, the meat, etc. all separately. Surely you’d balk; buying the sandwich just is buying the bread, meat, etc. Similarly, the FE exhibiting (ii)-(v) just is exhibiting (i), and it is nothing over and above. This brings us to…

Consider (ii)-(v) next: Observe some properties come in degrees, e.g. x being taller than y. Others properties don’t admit of degrees, e.g. x being 6 feet tall. Properties of degree are comparative. I claim properties (ii)-(v) are properties of degree. One can think more or less than another. One can be more powerful, or exist longer, than another. Moreover, there are plausibly some respective maximal degrees of such properties, e.g. some x that thinks the most, or is the most powerful, etc. It seems plausible each of (ii)-(v) are maximal properties of degree, and when understood as reflecting maximal degrees, each dovetails into the same property.

I will only defend (v) as exhibiting maximal degree in what follows; feel free to explore the others on your own. With respect to (v), it seems plausible that something can be more immaterial than another. This trades in part, of course, on whether you think there are immaterial things. I think there are. e.g. numbers are immaterial. You won't find these things one day while looking for your keys. You may be fine with numbers being immaterial, but if you’re astute you’ll notice you can accept the existence of immaterial entities like numbers, without thereby accepting the existence of immateriality being a property of degree. Clever you.

But the world is full of holes. Holes seem like things, not merely absences of things, but they are not obviously material things, e.g. tables, chairs, etc. Holes are plausibly immaterial and they can be parts of material things. You might balk. You might think holes are just perforations of material objects. So that, say, the side of a building doesn't really have two immaterial things - holes, or windows - as parts, but rather perforations of the material that is the building, i.e. just one thing. But things can be perforated in several ways. A building may have two perforations, while a cup only has one. But here we are counting things! What are we counting? We're counting holes! And if we’re counting holes, then we ought to treat them as things in their own right, rather than perforations of things, and if they’re things in their own right they seem sometimes parts of material things.

You might not be impressed. You might think what we're counting are something like hole-linings, i.e. the surfaces of the interiors of holes. So, we don't need to count holes as things, just surfaces. But this sort of commitment is odd. We usually think the surface in which we find holes surrounds the hole, but if holes are just hole-linings, this means we think holes surround themselves. But that's absurd. Nothing surrounds itself. Also, this commitment entails holes are made of their interiors, i.e. the window holes are made of the interior of the building. But this is odd, since it's the absence of the building that we seem to refer to when talking about holes. We could go on to discuss, say, ways to paraphrase away these puzzles, but it suffices for my point here to put on the table that's it's plausible to treat holes as legitimate immaterial things, and it's legitimate to treat them as parts of material things. And with that, we return to whether immateriality is a property of degree.

If there are holes which are immaterial entities, and material things can have more or fewer of them as parts, then material things can have more or fewer immaterial parts. But then it seems immateriality comes in degrees, since we can compare counts of immaterial parts. Moreover, the maximal degree of immateriality would be some entity lacking any matter as part. And the maximal degree of immateriality is what AF seems to think the FE has; the FE has no material entity as part.

Now, it remains to show maximal immateriality is equivalent to each of (ii)-(iv). I’ll sketch how some of the equivalencies might go:

  • Matter impedes power, so absent matter there is no impediment, and so power is exhibited in the maximal degree by purely immaterial entities. (v) -> (iii)

  • Nothing can prevent a maximally powerful entity from existing, so they’re eternal. (iii) -> (iv)

Try your hand at showing (iv) -> (ii) and then complete the equivalencies by showing (ii) -> (v). This is known as a round robin proof.

Assuming the above equivalencies hold, I think the initial puzzle can be resolved by reducing (i) to (ii)-(v) and observing each property in the latter collection comes in degrees which, when understood as exhibiting maximal degree dovetail into a single property. If this is correct, then FE may be said to exhibit (i)-(v) consistently, since there is but one fundamental property exhibited by the entity, just as AF requires.

That said, I think there are other worries not so easily avoided.

  • First, AF treats properties like they're parts. I think this is confused. My hand is part of my arm, but it's not a property of my arm. It's a part, and parts aren't properties. This is important because divisibility concerns parthood, not properties. To say something cannot be divided means it can't be divided into parts. But an indivisible thing can have many properties. An atom - a true atom - can be red and have a shape. If this is correct, then AF's insistence on the FE being indivisible is just to say it has no parts. But it might have all these properties nonetheless without there being a problem.

    • Response: But you have the property of having an arm.

    • Rejoinder: This seems just a way of speaking. It's not the case that just because you can use a predicate - a piece of language that applies to a subject - that you have a property that corresponds to it. Properties aren't so easy to come by. The predicate being the set of all sets that are not members of themselves does not, for example, pick out a property. Moreover, being red is a property, it seems, since being red is a quality objects have that they share with other objects. Suppose there are two red apples before us. Then there are two instances of red. Properties are repeatable across instances. Having an arm isn't, since plausibly if you had your arm and I had your arm, then my arm would be attached to you. Still, we have both have distinct and yet identical properties of redness. The objection stands.

  • Second, AF is committed to the following:

(CON) If S can clearly and distinctly conceive that x is P, then x has P

For example, if I can clearly and distinctly conceive that a triangle has three sides, then it has three sides. If I can clearly and distinctly conceive God exists, then God exists. In fact, we can construct an ontological argument from AF for the existence of God based on this:

  1. If S can clearly and distinctly conceive of x with property P, then x has property P

  2. S can clearly and distinctly conceive of FE with necessary existence

  3. Hence, FE has the property of necessary existence

  4. If x has the property of necessary existence, then x exists

  5. Hence, FE exists

Indeed, AF seems to argue in just this way. Note: Necessary existence is just eternal existence. It simply means that in any way the world could have turned out, God exists. Put another way, God couldn't fail to have existed. That holds both for the future and past.

But (2) is questionable. It's not because I think it's false though. It's because I don't think I can know if it's true with respect to certain things. And AF agrees with this. He admits we're fallible creatures with limited minds. How can we be sure that we clearly and distinctly conceive of something? I might believe - be convinced - that a number I'm considering at a time is prime, but be entirely mistaken. If this is true, then it seems - whether or not this argument is sound - it's useless to us. To me, that's as bad as being unsound. I'll take known sound arguments over unknown sound arguments any time. To make this useful to us, we'd need a principle like the following:

(CON-CON) If S clearly and distinctly conceives that x has P, then S clearly and distinctly conceives that S clearly and distinctly conceives that x has P

 Put another way, if you know, then you know you know. But is (CON-CON) true? Come up with a counterexample.

It's for this reason that I'm not too interested in exploring AF's various arguments for whatever properties he thinks the FE has. This seems a crux of his metaphysical picture, and I have no reason to accept it and several reasons to reject it. Let this be an illustration of a way of thinking I've found valuable. Sometimes philosophical views are very detailed, and can take much time to work out. There are so many of them too, that it's daunting. There's no way you'll understand them all. But that's okay, since you only want to understand the true ones anyway. If you can examine a philosophical proposal and find a core thesis - a thesis the picture cannot do without - that there are good reasons to reject, then you can put that picture aside and move on to a more worthy project. That's what I'm doing here with AF.

White Ignorance and Musical Manipulation

Consider the notion of a web of belief. There are peripheral beliefs, e.g. John is bald, and central beliefs, e.g. 2+2=4. How far a belief is near the center indicates how many other beliefs depend on it. Believing I have hair won't change many other beliefs; believing 2+2=5 will. Consider complementary hierarchy of concepts. We all have a store of concepts, e.g. tables, chairs, dogs, mammals, humans, etc. They're likely arranged in an unsurprising hierarchy. If you see a dog, then you see a mammal, because all dogs are mammals. There are dependencies here too. What's important for us is noting that concepts are inputs to beliefs we have. You each have a hierarchy of concepts. You receive information from the world through your sense organs. But in every case what you receive is mediated by these concepts. You never just see the world, you see the world through concepts. That's what it means to perceive something. It should be clear how these concepts then frame how we see the world, and so determine what we believe about the world.

Charles Mills classifies both false beliefs and the absence of beliefs as ignorance in his article White Ignorance. Does that remind you of another scholar we read? David Walker in his Appeal pointed to slaves holding both false beliefs and no beliefs as ignorance. In pursuit of reminding yourself of some of Mills' very dense paper, consider:

(Q1) Suppose we each have a hierarchy of concepts that inform our perceptions and so inform our web of beliefs. On this model, how do we understand ignorance as:

(i) the absence of beliefs?
(ii) the presence of false beliefs?  

The mechanism is straightforward. You might acquire concepts in your hierarchy that are inaccurate and so you will have inaccurate input into your beliefs. This will lead to false beliefs. On the other hand, you might not acquire certain concepts, and this might lead to a gap in beliefs about a certain domain. On the former, if we think of this blue circle as the way the world is, or should be, and your hierarchy of concepts with red, the presence of false beliefs might look something like this X while the absence of beliefs might look something like this Y. This is very crude, of course, and just to illustrate the difference between there being a gap and there being wrong information.

There's another axis along which we might analyze ignorance of these sorts. You might have an accurate hierarchy of concepts, but you might nevertheless make incorrect judgments about it, leading to false beliefs or no beliefs. For example, if someone learns their lover has been unfaithful, they might refuse to believe it for many reasons. I don't think that would conflict with their hierarchy of concepts. Their concepts remain the same, it's just that they refuse to place their lover under the concept 'wrong' or something like that. Similarly, if someone learned of a parent's racist beliefs, they might refuse to believe their parent is racist, but instead claim they must not know what they believe is wrong. Here again, the relevant agent might have the right hierarchy of concepts, but still not have the right beliefs about the world. These examples illustrate how the simple mechanism of a hierarchy of concepts informing beliefs is not straightforward. You might have accurate concepts, but be motivated to make poor judgments and so have false beliefs about them. This suggests another important feature of the model we should make clear: desires.

I have a concept of a chair, so when presented with a certain pattern of electromagnetic stimulation through my optical nerves I perceive a chair. This leads to me either voluntarily or involuntarily forming the belief that there is a chair. You know what happens next. I sit down, and I roll around the room like a child. Jokes aside, this is important. My beliefs inform my actions. But beliefs alone aren't enough. I roll around in the chair because I want to roll around in the chair. I want this because it's fun, or to lighten the mood, or something like that. But importantly, note just like my hierarchy of concepts informs my web of beliefs, it also informs what I desire. Presumably, I can't desire something I have no concept of. Moreover, my beliefs and desires interplay. I have beliefs about the world and they're informed and inform my desires. We have then, a straightforward plausible picture of human action. Concepts inform perceptions which inform beliefs and desires which inform behaviors. It's not just about what I believe; it's also about what I want. This is a sort of commonsense picture of the relationship between concepts/perceptions and beliefs.

Now we might ask how come to have the concepts we have, which leads us back to Mills on White Ignorance. Broadly speaking, we acquire concepts in two ways: Intentionally and Unintentionally.

Intentional - An example of intentionally acquiring concepts would hopefully be you attending college. When we intentionally learn concepts, we're often on guard to avoid inaccurate concepts, or concepts that seem to conflict with deeper concepts we hold. If someone tried to teach you in class that members of same racial group weren't part of the human species, you'd likely reject that concept. For one thing, it would likely require significant revision to your hierarchy of concepts. I think we can intentionally learn inaccurate concepts and avoid acquiring new concepts about some domain. That's what echo chambers seem to be about.

Unintentional - An example of unintentionally acquiring concepts might be, say, you acquiring the concept of 'chair'. I don't remember ever learning the concept 'chair'. I also don't ever remember ever learning the various pejorative concepts I know about women, minorities, etc. I likely picked them up as a matter of acculturation, and they likely gained credibility out of sheer habit. Familiarity doesn't necessarily breed contempt. Often, it just breeds more familiarity.

Following Mills, lets focus on concepts and beliefs of the unintentional sort:

(Q2) How might a privileged white individual of the sort Mills described unintentionally acquire inaccurate concepts or unintentionally avoid acquiring concepts about some domain?

Presumably, when we're intentionally picking up new concepts, we're ready to spot red flags and reject concepts that don’t align with other concepts we hold. But if our hierarchy of concepts is acquired unintentionally, we'll likely be unable to spot red flags, and notice signs that such concepts aren't tracking anything true in the world, or anything that should be true. But then if faulty concepts are unintentionally adopted in our hierarchy, they will invariably inform our beliefs. Then we get false beliefs. This seems a plausible explanation for how, say, many people I grew up with believed negative stereotypes about black people, though when pressed for why they held such beliefs it became clear they'd never really thought about it before. Similarly, when you're growing up and acquiring concepts you might not get everything you need. You're sort of a sponge, but you need nutrients to absorb. If you lack a certain set of concepts you'd need to perceive a certain phenomenon, say, like racial discrimination, then it's likely you won't be able to understand the phenomenon, and surely unlikely you'll have beliefs about it. Now:

(Q3) How might a privileged white individual of the sort Mills described who has unintentionally acquired inaccurate concepts or unintentionally avoid acquiring concepts about some domain, then maintain false beliefs or a lack of true beliefs about that domain?

I think Du Bois in the opening of The Souls of Black Folk is illuminating here. Recall, we concluded the existence of the veil by an argument to the best explanation. Du Bois had expectations about how he'd be treated, likely based on observing how other people were treated, and these expectations were undermined. The best explanation was the existence of some mediation between white and black experiences. There was a color line. But whites don't see the color line or notice the veil, because they don't experience similar friction. Glibly put, the world makes sense to privileged white people. And this might go some way to explain why privileged whites who unintentionally lack concepts might maintain their ignorance.

(Q4) Does this seem a plausible explanation? Is white privileged sustained because unintentionally acquired concepts don't meet with friction or call for revision in white life?

Let's not get carried away; this should strike you as an odd way to describe things. Is it really the case that the world simply makes sense to white privileged people? Is it really the case they don't experience social friction and undermined expectations? Surely not. There seems to be ample evidence available of the mistreatment of marginalized groups. And this is not a novel phenomenon. In this course we've seen protests, marches, court cases, riots, etc. It seems to me privileged white people have a lot of evidence - and have had a lot of evidence - indicating they hold racist false beliefs, right?  

White ignorance is motivated ignorance, and resistant ignorance. White privilege is a privilege. Whites stand to gain from keeping it in place, materially, psychologically, etc. I think it would be naïve to overlook - what seems to me a clear possibility - that white privileged individuals not only have a conflict between implicit and explicit beliefs, but between explicit and implicit desires. Informed, well-meaning white allies might explicitly desire equal consideration of interests, equality, the absence of discrimination, but surely they also at least implicitly desire to remain privileged. That's reflected in behavior. White privileged individuals have inaccurate concepts perhaps acquired unintentionally, and these inform implicit and explicit beliefs and desires, which inform behaviors, e.g. they might outwardly want to diversify the neighborhood but inwardly not want some people to live near them. I take this to be one reason why privileged white people who have plenty of evidence that they've racist beliefs, don't correct their behaviors. They have implicit desires to maintain their status.

This is, of course, not the only motivation privileged white individuals might have to maintain the status quo. I think we can pull from our discussion of Baldwin to uncover another potential sources of resistance. We distinguished guilt from shame, and noted the latter seems to concern the individual, i.e. they're broken. Consider:

(Q5) Recall the difference between guilt and shame. How might guilt and shame lead to privileged white resistance to evidence that they hold racist concepts and beliefs?

Someone who has acquired racist concepts acculturation, like the child Fanon mentions who says "Look, A Negro!" and isn't corrected, likely wouldn't feel guilty for having these concepts, if they were made aware of them. You feel guilty for things you've done. But they may nevertheless feel shame for the conceptual hierarchy they sustain. Recall, Baldwin suggested developing integrity was needed to unearth inconsistent values. We can easily transpose this into the key of the conceptual hierarchy. Integrity might also involve exploring your own concepts in detail, and seeking consistency. This is a tough task to engage in psychologically, intellectually, and physically.

Psychologically, it's easy to think through your conceptual repertoire and just get confused. This is doubly problematic if you've just learned that you hold many problematic concepts about people that are inconsistent with values you hold. It might make you skeptical of your ability to explore your own conceptual hierarchy. It's difficult intellectually, because you'll need to uncover deeply held concepts that you likely don't know you have. It's tough physically because of the pain and discomfort of changing your mind. I suspect this is the largest barrier. Few people want to feel shame. We're all likely aware of this explicitly, but we're also likely on the same page implicitly. When I'm talking to my counselor about shame I feel about my childhood, it hurts. Over time you can will yourself to face it directly. But even then, I've come to see how tricky the mind can be when it wants to avoid discomfort. I'll begin to talk about shame I feel and before I know it I'm talking around the issue, or bringing up something else. I have to catch myself, over and over, because - it seems - my brain just doesn't want to deal with it. Shame hides, and you want it to hide, even when you don't.

These factors make it difficult to develop integrity. These factors motivate resistance. It's my hope that identifying these factors might help us construct ways to address these forms of resistance. If the issue is desire for sustaining the status quo, we might identify how this conflicts with other values. If the issue is shame, we might do something else…but before moving on to signals of resistance, let me ask:

(Q6) What other motivations might privileged white individuals have for resisting evidence they hold inaccurate concepts and so exhibit ignorance we haven't covered that you'd like to discuss? Take a moment and see if you can come up with something. 

We can also look at the ways in which this motivated resistance emerges in practice. As a practical matter, I suspect you've experienced or heard of something like the following:

Evasion - When presented with evidence of racist beliefs or concepts, some simply avoid the topic. My grandfather would prefer not to talk, than to talk about race. They might change the subject, or claim the topic is inappropriate for the present discussion. I think in some cases this is correct. If I'm trying to literally put out a fire, it's probably not the best time to discuss race relations in the U.S. But this is an extreme example. In many cases, like at a relaxed dinner with friends, this seems an appropriate topic. In these contexts, I suspect evasion is reflecting motivated resistance.

I think it's useful to name these tactics so they can be referred to in the wild.

(Q7) Can you think of a time in which an interlocutor evaded engaging in discussion of white privilege, or race, where it seemed the evasion was motivated by resistance of the sort described above.

Consider next:

Different Cause - Insistence that issues stemming from white ignorance are not about race, but about, say, class or economic disparities. In conversation after conversation, people question  whether race is a cause of marginalization.

Now:

(Q8) Can you think of a time in which an interlocutor employed what I'm calling the Different Cause strategy to avoid engaging in discussion of white privilege, or race, where it seemed the this seemed motivated by resistance of the sort described above.

It seems unlikely to me that you can explain all the vast marginalization we see across racial groups, without appealing to race as playing a causal role. Imagine Du Bois trying to make sense of his mistreatment without appealing to race. Moreover, even if you could explain current disparities without appealing to race, doing so would overlook the vast history of marginalization that likely informs class and economic privilege. Not looking at race as playing a historical role in present disparities suggests closure of the sort Davis warned us against, as if we're done with race and can claim victory.

Consider too:

Moral Purity - People who exhibit racist beliefs or concepts are viewed as not blameworthy because they simply don't know any better. No morally good person would mistreat others this way. The conclusion of this sort of reasoning is that privileged whites aren't blameworthy and aren't responsible.

 And answer:

(Q9) Can you think of a time in which an interlocutor claimed moral purity rather than engaging in discussion of white privilege, or race, where it seemed the claim was motivated by resistance of the sort described above.

We've gone down a single thread of Mills deep article, but before we end, I'm curious about remedying the situation. We have a few signals we can identify to determine forms resistance might take. We might use this in pursuance of correcting the problem when we see it. But it's a deep problem. One strategy for solving the problem might be identifying the root cause. This seems complicated. Acquired concepts is part of it, for sure. But so are desires and beliefs, judgments about concepts, etc. This suggests we should start early.

What about existing white ignorance? I suggested last session that manipulation might be warranted, and appealed to art and music in particular as a means to instill knowledge into people's conceptual repertoire without them knowing it. Note the parallel here with Mills on acquired concepts. The idea is that people were raised - were manipulated - into having the hierarchy of concepts they have, and so they can be counter-manipulated. Music seems a way to achieve this to some extent. Privileged whites may realize they know more marginalized individuals and their plights, and can empathize with them more, than they previously believed. This would be like having concepts of a chair without yet forming beliefs about chairs. This raises, of course, a moral question, which will be our last for the day:

(Q10) Is it morally justifiable to manipulate the conceptual hierarchy, and thereby influence the web of beliefs and desires of, privileged whites?

More Things Change; More Things Stay the Same

Section 0: Introduction

Change at least involves gain or loss of properties.[1] Gain or loss of properties requires difference in time.[2] Hence, change at least involves difference in time.[3] Intuitively, gain or loss of properties involves some property bearer,[4] i.e. an object.[5] A leaf, for example, might gain a color property – yellow – and lose another – green – in concert with the seasons. Moreover, it seems plausible objects involved in change remain the same through change, at least in some respects. A green leaf that becomes yellow likely retains other properties, e.g. shape, mass, etc. Hence, change appears to involve objects which gain or lose properties over time while often[6] retaining others.

A long-standing debate in contemporary analytic metaphysics is how to make sense of intuitions about the persistence of changing objects over time. Endurantism maintains – roughly – that objects are numerically identical across time and through property gain or loss.[7] The green leaf at t1 is numerically identical to the yellow leaf at t2. David Lewis[8] shaped contemporary discussion by posing the problem of temporary intrinsics for naïve versions of Endurantism. Lewis claimed objects bear intrinsic properties[9] – which do not depend on anything other than their bearer – such as shape and mass, and observed if Endurantism is true, it seems numerically identical objects may bear incompatible intrinsic properties at different times. But since it is plausible to maintain[10] that for any object(s) x and y, and any intrinsic property P, if x=y then x has P just in case y has P, it follows that incompatible properties at distinct times undermine numerical identity over time. This consequence of naïve Endurantism motivated Lewis’s alternative account of persistence – Perdurantism – which maintains an ontology of temporal parts each of which bear intrinsic properties. Characterizing a leaf changing shape over time, for example, involves a temporal part at t1 bearing a certain shape property and a temporal part at t2 bearing a distinct temporal property. Since these temporal parts are distinct objects bearing incompatible intrinsic properties, the problem of temporary intrinsics is no problem at all.

Advocates of Endurantism typically claim it is the commonsense view of persistence. This is both questionable and of unclear value in this metaphysics dispute. Fortunately, this is not the only motivation for accepting Endurantism. For this view of persistence has a native answer to what we might call the tracing problem, i.e. how objects are tracked over time.  According to Endurantism, tracking a given object from t1 to distinct time t2 is a matter of the numerical identity of the object at these distinct times. In contrast, while Perdurantism was designed to avoid the problem of temporary intrinsics, the mere existence of temporal parts bearing (in)compatible intrinsic properties at distinct times provides no answer to how to track a given object over time. For this reason, Perdurantism is often supplemented by claiming temporal parts are proper mereological parts of larger wholes, often characterized as worms stretching through space and time.[11] For Perdurantism thus supplemented, tracking an object over time amounts to tracking temporal parts through space and time. The leaf changing from green to yellow is, strictly speaking, a series of temporal parts – separated like a deck of playing cards viewed from the side – each bearing intrinsic properties. That is, the leaf is an entity extended in both space and time with proper parts appearing in series. Thus far, it seems then that Perdurantism[12] gains the upper hand in characterizing persistence, since it is designed to avoid the problem of temporary intrinsics, and can be straightforwardly supplemented to answer the tracing problem. But Endurantism can be supplemented just as easily to avoid the problem of temporary intrinsics, e.g. eschewing intrinsic properties and relativizing properties to times.[13] The leaf at t1 and t2 are numerically identical, though it bears, say, one shape-at-t1 property at t1 and another shape-at-t2 property at t2. Supplementing Endurantism in this manner results in a plausible contender in the dispute over the nature of persistence.[14]

We could say much more about which of these theories of persistence is preferable in this dispute, but our task here is not arbitration between these rival theories. Rather, we introduce a problem neither Endurantism nor Perdurantism is able to adequately address, even when supplemented as standardly done. In what follows, we examine to what extent Perdurantism and Endurantism can explain how objects generate other objects or sustain themselves over time through property gain and loss. Specifically in Section 1, we motivate the problem of generation, argue it is distinct from both the problem of temporary intrinsics and the tracing problem, and rebut reasons for thinking it is an insubstantial metaphysical problem. We examine prima facie answers to the problem of generation available to Perdurantism and Endurantism, noting the former can ultimately provide no answer to the problem while the latter provides at best inadequate answers. We then examine Endurantism supplemented with causally robust laws of nature in an attempt to address the problem of generation. Noting this version of Endurantism comes close to adequately addressing the problem of generation, we observe it still falls short. In Section 2, we provide a novel solution to the problem of generation based on dispositional properties, which explains how objects generate other objects and sustain themselves through property change over time. We examine how this solution differs from varieties of Endurantism, in particular the version supplemented with robust laws of nature, and argue dispositional properties succeed where robust laws of nature failed.

Section 1: The Problem of Generation

Change appears to involve objects which gain or lose properties over time while – in many cases - retaining other properties. Understood loosely, either Perdurantism or Endurantism might fit this gloss on change.[15] But change is not obviously exhausted by our initial observations. For example, persisting objects appear to generate later associated objects or sustain themselves over time.[16] An oak tree at t1 stands tall in a forest, but is reduced to ash by t2; a home constructed at t3 is given a new coat of paint at t4. A plausible explanation for the generation of ash from oak would seem to involve the existence of the oak being relevant to the existence of the ash; a plausible explanation for the home remaining the same through painting would seem to involve the existence of the home at the former time being relevant to the existence of the home at the latter time. Still, mere relevance is insufficient. That an arsonist remembered to set fire to the oak tree is relevant to the explanation of the existence of ash at t2; that an arsonist forgets to burn down the home at t3 is relevant to the explanation of why the home exists at t4. However, the arsonist’s memory does not seem to explain how the oak tree generates ash or how the home sustains its existence over time. Mere relevance is not enough. Intuitively, the existence of the oak at t1 is causally relevant to the generation of the existence of the ash at t2 and the existence of the home at t3 is causally relevant to sustaining the home at t4. Even so, mere causal relevance is insufficient to characterize generation. That there presumably was a Big Bang is causally relevant to the oak tree generating ash; the existence of construction workers who built the home is causally relevant to the home sustaining itself. But again, neither the Big Bang nor the existence of the construction workers explains respective generations.[17] An explanation of object generation seems to involve matters more local to the object than mere causal relevance captures, i.e. intrinsic properties. This suggests change involves in some cases objects generating other objects or sustaining themselves over time through causally relevant intrinsic properties. Call the task of adequately explaining this additional ‘generation’ aspect of change, the problem of generation.

Identifying a problem is one thing, but showing it is a problem worth pursuing another. To be worth pursuing an answer for, it must be shown the problem of generation is a distinct substantive metaphysical question and a distinct substantive metaphysical question. If the problem is not distinct from, say, the problem of temporary intrinsics or the tracing problem, then we should expect Perdurantism and Endurantism to provide an answer to the problem of generation since each provides respective answers to the other two. Supposing the problem is distinct, if the problem of generation is not a substantive metaphysical question, then it should not be viewed as a cost if a given theory of persistence does not provide an adequate answer. The appearance of object generation might be maintained as nothing more than an appearance. We will explore whether the problem of generation is distinct and substantive within the contexts of Perdurantism and Endurantism, arguing neither theory provides an adequate solution to the problem, and there seem few reasons to think the problem of generation is insubstantial.  

Perdurantism and Generation

Failure to adequately address the problem of generation is easiest to see with respect to Perdurantism. Strictly speaking, a temporal part at t1 is only related to another temporal part at t2 in virtue of being parts of the same whole. But proper parthood does not amount to generation. My index finger and thumb are also proper parts of the same whole, but either generates the other. This is mere difference, and mere difference is not change, any more than a fire poker being hot at one end and cold at another at the same time is. This is not a novel observation. Thomson, for example, famously criticized Perdurantism as “crazy metaphysics” on similar grounds, i.e. since it seems to involve the creation of objects ex nihilo.[18] Defenders of Perdurantism sometimes rebut such criticism by claiming temporal parts of the same mereological whole do generate other temporal parts.[19] For temporal parts bear causal relations to other temporal parts that are part of the same spacetime worm. However, this answer is misleading.[20] Causal links between temporal parts - as understood by defenders of Perdurantism – typically lack any sort of robust connection. Defenders of Perdurantism often understand this theory of persistence against a background commitment to Neo-Humeanism,[21] i.e. the thesis that there are no necessary connections joining events over time, rather, there is just “one thing after another.” As a consequence, there are only regularities through spacetime, though defenders of Neo-Humeanism claim some regularities are better than others, namely, those important to scientific investigation.[22] On this view, temporal parts over time are causally linked, and some of these regularities are more important than others, e.g. a series of temporal parts of a leaf is more important than a series of randomly selected temporal parts. But despite the legwork, it should be clear why this provides no answer to the problem of generation. Generation is more involved than merely identifying useful regularities. A temporal part p1 of a home at t1 generating a temporal part p2 of the same home at t2 is less a matter of whether we find this regularity important, and more a matter of the house. Perdurantism cannot accommodate the needed sort of robust causal connections to adequately answer the problem of generation. But if Perdurantism thus construed provides an answer to both the problem of temporary intrinsics and tracing, then since the theory does not provide an answer to the problem of generation, it seems the latter problem is distinct from the other two.

Defenders of Perdurantism might claim, however, not answering the problem of generation is not a cost, since generation is at best a confused concept. If what is meant by this response is that the pre-theoretic concept of generation is confused, I am willing to concede this may be true. But it seems no more or less confused than many other metaphysical pre-theoretic concepts were or are, e.g. modality, composition. Like these other concepts, intuitions about generation plausibly track something in reality. But this observation, combined with granting the pre-theoretic concept of generation is presently unclear, suggests we need further examination of generation, say, within the context of a systematic metaphysical theory, rather than that we should ignore generation and remain ignorant of it. On the other hand, if advocates of Perdurantism mean instead that generation seems confused within the context of Perdurantism, I concede the point. But Perdurantism is not the only lens through which we might view generation, so this response is hardly compelling.

More forcefully, proponents of Perdurantism may claim this theory of persistence is precisely the lens by which we should view generation, and any other persistence related topics. Such a response seems best understood as conceding that not answering the problem of generation is a cost, but simultaneously contending it is one worth paying. This, moreover, can be motivated by observing Perdurantism fits naturally within a broader systematic metaphysic that provides answers to various linguistic, ethical, and logical[23] problems, as well as answers the problem of temporary intrinsics and tracing. This broader systematic metaphysic is, additionally, parsimonious, well-confirmed, and perspicuous. Since this broader picture answers so many questions, and seems to accommodate many other intuitions, it seems worthwhile to reject other – perhaps less well understood – intuitions, such as that underwriting the problem of generation. This is common enough method in scientific investigations. Tables, apples, etc., are largely comprised of empty space, but our perceptions of these objects suggest otherwise. As we become more sophisticated investigators, we put aside some intuitions that conflict our otherwise well-confirmed, parsimonious, general, perspicuous theory of the world. So too for a broader systematic metaphysical picture that includes Perdurantism as a sub-theory.[24] Hence, advocates of Perdurantism might claim, giving up on the appearance of generation – whatever that appearance amounts to – is an acceptable cost. These are fair points in favor of pushing aside the problem of generation, but note while the Neo-Humean picture is impressive, it is not obviously the end of systematic metaphysical inquiry. Much recent work outside the Neo-Humean status quo has precisely sought to introduce robust causal connections between events, states of affairs, objects, etc., providing grounds on which an adequate answer to the problem of generation might be offered rather than ignored.[25] Insofar as one is moved by the intuition that generation is more robust than mere difference between temporal parts, one should at least be motivated to engage in construction of alternative systematic metaphysical theories amenable to theories of persistence other than Perdurantism. So while defenders of Perdurantism might admit the cost of not answering the problem of generation and claim Perdurantism is worth the price, negotiations are not yet over, and other theories of persistence will likely prove more amenable to generation.

Our tentative conclusions thus far then are that if it is granted that Perdurantism addresses the problem of temporary intrinsics and the tracing problem, it nevertheless does not address the problem of generation, which is plausibly worth addressing. The former conclusion strongly suggests the problem of generation is a distinct metaphysical problem from the other two; the latter conclusion suggests we have as of yet little reason to suspect the problem of generation is not a substantive metaphysical problem worth addressing. We turn next to Endurantism and explore whether this theory of persistence answers the problem of generation, or provides reasons to think this is not a substantive metaphysical problem worth our time.

Endurantism and Generation 

Supposing Endurantism provides an answer the problems of generation and tracing, one might think Endurantism provides an answer to the problem of generation. Not so. To see why, first note that Endurantism has a native explanation for how objects remain the same through the gain or loss of properties: numerical identity. Numerical identity is simple - an equivalence relation over its relata – and primitive – an indefinable commitment of the view. Note second, Endurantism is committed to whatever exists being a brute, unexplained, fact. This should be unsurprising; commitment to such a simple view of existence is something Endurantism shares with Perdurantism. Sure, once something is presumed to exist, both Endurantism and Perdurantism may provide explanations for why later objects exist. But neither theory of persistence is in the business of trying to explain existence proper, or explain – ultimately – why objects exist. Of course, when it comes to persistence, since Endurantism is committed to objects persisting as a matter of numerical identity, these theories sharply come apart. For since the existence of a given object is a brute fact for Endurantism, and objects persist according to a primitive notion of numerical identity, then persistence is ultimately explained by brute facts related by a primitive. This is – roughly – why Endurantism cannot adequately address the problem of generation. But this point is worth belaboring.

The issue the preceding observations raise for addressing the problem of generation in the context of Endurantism is easiest to illustrate by focusing on explaining how a given object sustains itself over time without property gain or loss. If Endurantism cannot adequately answer this aspect of the problem of generation, then it plausibly cannot adequately answer the more general problem of how a given object generates other objects or sustains itself through property loss or gain over time. Now, Endurantism claims numerical identity explains why object o at t1 sustains itself at t2. This is admittedly a more robust causal connection than anything Perdurantism allows. In this respect, Endurantism at least provides an answer to the problem of generation. But this answer is inadequate to explain the corollary problem of generation. For the explanation for why o1 at t1 generates o2 at t2 is because o1=o2, and since numerical identity is primitive and existence brute, this amounts to saying o1 generating o2 is a brute fact primitively related to itself. But asserting that objects sustain themselves is a brute fact bearing a primitive relation to itself seems more a description of the problem than an explanation. And if the Endurantism answer to the corollary problem to the problem of generation is inadequate then it seems transposing this answer to the general problem of generation will be equally unsatisfying. Since Endurantism provides answers to the problems of temporary intrinsics and tracing, but fails to provide a satisfying answer to the problem of tracing, it seems the problem of generation is distinct from the other two problems.  

Defenders of Endurantism might be unhappy with the sparse version of Endurantism employed in the preceding discussion. For Endurantism clearly needs to be supplemented to answer the broader problem of generation, even if we suppose numerical identity is an inadequate explanation of the generation of an object from itself over time. Objects gain and lose intrinsic properties over time, and presumably Endurantism must be supplemented with some machinery to explain how properties are gained and lost. Defenders of Endurantism might claim that whatever explains the gain and loss of intrinsic properties generally, will provide an answer to why objects generate later objects. Nevertheless, it is worth noting that standardly understood, Endurantism is also committed to whether an object having or not having a property at a given time being a matter of brute fact. Strictly speaking, according to Endurantism what explains why object o is a given shape at t1 and another shape at t2 is simply that o is the first shape at t1 and the second at t2. This explanation seems no better than appealing to numerical identity over time. More promising, however,[26] is supplementing Endurantism with commitment to laws of nature as governing the gain and loss of properties over time. For example, there may be a law of nature to the effect that necessarily, for any leaf at t1 with a certain shape in context C1, at t2 in context C2 that numerically identical leaf will have a distinct shape. Causal connections between property instantiation on such a view would be robust. And since these causal links are governed by necessary laws, this seems a better explanation of property gain and loss than simply assuming brute facts about property instantiation, existence, and numerical identity.[27] Moreover, this proposal appears to provide a straightforward answer to the corollary problem of generation: necessarily for any o1 at t1 in context C1, o2 at t2 in context C2 is such that o1=o2, where each context is spelled out appropriately. It seems then, we have discovered a supplement to Endurantism that provides an adequate answer to the problem of generation.

Putting aside worries one might have with laws of nature governing property gain and loss generally speaking,[28] there seems a significant worry worth raising to Endurantism thus supplemented. Simply put, on this proposal whatever was intrinsic about generation vanishes. An object numerically identical to itself over time is not due to the object sustaining itself over time, but rather an extrinsic law of nature generating numerical identity. Similarly, a leaf changing shape is understood, on this proposal, as extrinsic laws of nature governing transitions from one shape to the other. The intrinsic properties of the leaf at best play a role in generation insofar as they satisfy conditions for being governed by a particular law. But an object bearing intrinsic properties that satisfy being governed by an extrinsic law of nature through a process of generation to another set of intrinsic properties, is generation by an indirect route. The object itself plays an ancillary role in generation, and this seems to fall short of our motivating intuition that earlier objects generate later objects or sustain themselves over time.

If the preceding is correct, then it seems the answers provided by Endurantism to the problem of temporary intrinsics and the tracing problem do not adequately answer the problem of generation. Moreover, if the preceding is correct, then supplementing Endurantism with necessary causal laws of nature also falls short of answering the problem of generation, though it gets much closer than other varieties of Endurantism considered. However, at this stage advocates of Endurantism might simply reject anything more must be said to address the problem of generation. They might maintain the answers provided to the problem of generation – either generation being primitive or robust laws of nature - are adequate, since the problem itself deserves no better sort of answer. On the former view, an object o at t1 being numerically identical to t2 despite changing properties is an intrinsic matter to the object o, and numerical identity over time is at least a robust causal connection, even if property instantiation is brute. On the latter view, an object o at t1 being numerically identical at t2 despite changing properties is an extrinsic matter, due to governance by robust laws of nature, and property instantiation is explained by these laws. In either case, the respective advocate might claim, we have as adequate an answer to the problem of generation as we need. In response, I grant advocates of Endurantism of the second stripe make a good case for leaving the problem of generation without a full answer. In light of this second answer, however, I find answering the problem by appealing to primitive identity unsatisfying, so I am much less compelled to consider Endurantism of the first stripe as providing an adequate answer to the problem. Still, part of the difficulty in adjudicating any answer to the problem provided stems from not clearly seeing what an adequate answer to the problem of generation would be. It is thus worth examining what a full answer might be, in route to determining whether we should be satisfied with, say, this second form of Endurantism.   

Section 2: A Third Turn betwixt Them

Dispositional Generation

Neither Perdurantism nor Endurantism of any variety described above permits the existence of irreducible dispositional properties had by objects. Insofar as either countenances the existence of such properties, they are considered reducible, or supervenient, or grounded on other so-called categorical properties had by objects. It is not difficult to see why metaphysical theories have preferred reducing dispositional properties to others in most cases, since dispositional properties are not extensional. Adequately characterizing the shape, mass, electronegativity – that is, categorical properties – of a sample of table salt is something that can be done at a single time and place. In contrast, adequately characterizing the disposition table salt has to dissolving when placed in unsaturated water cannot obviously be done at a single time and place. Had no sample of table salt ever contacted water, it seems table salt would have still had the disposition to dissolve. Characterizing dispositional properties, it is commonly thought, requires extending beyond what happens at a time and place, into what could – but may never – happen. Suffice it to say, systematic metaphysics are much cleaner when dispositional properties can be entirely explained in terms of non-dispositional properties.[29] Otherwise, it seems one must introduce irreducible modal properties into one’s systematic metaphysic.

And yet many recent metaphysicians who advocate various powers-based theories of causation, laws of nature, and persistence, seem to prefer messiness to the neat standard options one finds in contemporary analytic metaphysics.[30] This recent movement suggests the last option we will consider for addressing the problem of generation: objects generate other objects or sustain themselves over time due to irreducible dispositional properties.[31] To illustrate, consider first an object o1 at t1 in context C1 generating the existence of a distinct object o2 at t2 in C2. The dispositional proposal on offer is committed to o1 having dispositional properties that act in concert with other dispositional properties in C1 and together bring about the existence of o2 in C2 at t2. Moreover, leaning further on the notion of dispositional properties acting in concert, we might say that the dispositional properties of o2 in C2 at t2 also act in concert with those properties of the preceding context, object, and time. More cleanly, the first object manifests a disposition to generate the second, and the second manifests a disposition to be generated by the first. On this proposal, moreover, the relevant dispositional properties are intrinsic to the respective objects. Object o1 generating o2 stems from an intrinsic dispositional property had by o1, and o2 permitting – as it were – generation by o1 stems from an intrinsic dispositional property had by o2. Moreover, on this proposal the relevant dispositional properties are causally robust. That is, we can say necessarily, if object o1 exists at t1 in C1, then o2 exists at t2 in C2.[32] We have then, an answer to the problem of generation that permits robust causal connections between generated objects and captures generation as an intrinsic affair. This proposal also answers the corollary problem of generation: necessarily, if object o1 exists at t1 in C1 then o2 exists at t2 in C2 and o1=o2, when the respective contexts are appropriately spelled out. Altogether then, this dispositional proposal provides robust causal connections and intrinsic properties in answering the problem of generation.

Dispositional answer to the problem of generation in hand, we can return to the answer offered by Endurantism supplemented with robust laws of nature. Recall, the latter answer solved the problem by introducing necessary laws of nature that governed objects generating other objects and sustaining themselves over time. While this variety of Endurantism allowed for robust causal connections in generation, we noted it seemed inadequate since the stated robust causal connections were extrinsic to object generation. The dispositional proposal, in contrast, ties robust causal connections to intrinsic properties of the relevant objects involved in generation. Glibly put, the dispositional proposal simply converts laws of nature into intrinsic properties, thereby satisfying the plausible constraint on an adequate answer to the problem of generation that generation be an intrinsic affair between the relevant objects. To that extent, the dispositional view provides a more satisfying answer to the problem than Endurantism supplemented with laws of nature.

That said, one may worry the dispositional proposal shares too much in common with the first Endurantism answer we considered to the problem of generation. There, existence and property instantiation was assumed a brute fact and numerical identity a primitive, which led to the explanation of persistence being brute and primitive. Similarly, one might argue that the dispositional view – thus far described – treats existence as brute, and both persistence and property instantiation as primitive. Hence, insofar as one found the former unsatisfying, one should also find the latter. In response, it is true that on this proposal existence is brute – just as it is on any of the other theories considered – and property instantiation is primitive just as on this rival version of Endurantism. Nevertheless, the properties instantiated on the dispositional proposal are not of the same kind as those one would have on the Endurantism proposal. That a given object instantiates a set of properties may be a primitive unexplainable fact, but if those properties are irreducibly dispositional, there are available explanations for why that object has or loses those properties later, namely, because dispositional properties are directed at other arrangements of properties in the world. Indeed, once the world is peppered with objects instantiating dispositional properties, which is admittedly a brute fact, gain and loss of properties over time is explained by these initial conditions. The same cannot be said for Endurantism of the first stripe, which lacks intrinsic irreducible dispositional properties. Given a world peppered with objects not instantiating irreducible dispositional properties, all properties on such a view will be reducible to some, say, categorical base. But then there is no obvious explanation for how the fact that an object has one set of categorical properties at one time is related to the fact that the same object has another – or the same set of – categorical properties later, other than numerical identity. In short, what distinguishes Endurantism of the first stripe from the dispositional proposal offered here is precisely that the latter provides an adequate answer to the problem of generation. So, even if these theories of persistence are similar, they can be distinguished based on how they address this problem.

Of course, much more must be developed for dispositional accounts of persistence to be considered legitimate contenders.[33] Still, some progress has been made on that front here. We have argued the little remarked on problem of generation finds no adequate answer among varieties of Perdurantism and Endurantism found in the extant literature on persistence. We have observed a novel dispositional solution seems to provide an adequate solution to the problem, while respecting intuitions about what features an answer to this problem should have. Generation, it seems, requires dispositional properties. And that is, perhaps, a surprising change to the standard picture of contemporary analytic metaphysics worth exploring in more detail.

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[1]There are nearby notions of change, e.g. mereological change. Gain or loss of parts may result in a gain or loss of some properties while retaining others, e.g. a red sphere is divided into two red hemispheres. I focus on property change as the more general notion.  
[2]We suppose time is a linear order of discrete temporal points (Benthem, 1983), though not much depends on this here.
[3]The converse does not seem to hold; time may proceed without change, e.g. two cards stacked against each other in equilibrium (Williams, 2019). (Shoemaker, 1969) argued for this claim, but the soundness of his argument is unclear. That does not mean the conclusion is false, however. See (Warmbrod, 2017).
[4]Trope theories of a certain stripe (van Cleve, 1985) might deny there are objects, but countenance change. We put such options aside for what follows.
[5]I intend to remain neutral over whether, say, objects are states of affairs, bare particulars, composites of tropes, etc.
[6]Change may involve complete loss of properties via destruction, e.g. a vase destroyed by a supernatural force.
[7]This is a standard gloss as found in (Sider, 2001), (Williams, 2019), among others.
[8](Lewis, 1986).
[9]The notion of intrinsic properties is notoriously difficult to characterize. The intuitive gloss suffices for our purposes, but see (Bird, 2007) and (Lewis, 1999), for discussion.
[10]This is, of course, a version of Leibniz’s Law restricted to intrinsic properties. (Ayer, 1954).
[11](Lewis, 1986). I put aside considering Stage Theory varieties of Perdurantism (Sider, 2001), in what follows.
[12]In the remainder, I will use “Perdurantism” to refer to the version of this theory of persistence supplemented with spacetime worms.
[13]E.g. (Haslanger, 2003).
[14]In the remainder, I will use “Endurantism” to refer to the version of this theory of persistence supplemented with relativized temporal properties. Admittedly, this restricts the scope of my conclusion, there is not enough space for a full treatment of varieties of Endurantism here.
[15]Perdurantism has the trickier time, since in most cases of change for this theory of persistence objects either always retain all their properties – if viewed as a spacetime worm – or never retain any – if viewed as temporal parts. 
[16](Armstrong, 1997, pg. 74) observes the “actual bringing into existence” of later temporal parts by earlier temporal parts is a necessary feature of persistence.
[17]Pace what (Lewis, 1986b) says about how we should understand causation. There, Lewis motivates thinking of explanation in purely causal – regularities we find important – terms. For x to explain y, all that is needed is that x exist in the causal history of y, e.g. the Big Bang is an explanation, in some sense, for me writing this paper. This would allow – at the risk of a verbal dispute - advocates of Perdurantism to say causal relations provide all the explanation one needs.
[18](Thomson, 1983).
[19](Sider, 2011).
[20]Some (Williams, 2019), say it is confused. I doubt Sider is confused about his commitments. I take him as providing damage control in the cited passage.
[21]See (Schrenk, 2010), (Jackson, 1998), (Lewis, 1986), and many others for evidence.
[22](Lewis, 1986), (Sider, 2011).
[23](Lewis, 1973; 1986; 1999), (Sider, 2001; 2011).
[24](Lewis, 1986).
[25]See (Martin, 1997; 2007), (Williams, 2019), (Mumford & Anjum, 1998), (Mumford, 2004), (Bird, 2007), (Armstrong, 1987; 1997), (Lowe, 1994), (Tugby, 2013; 2013b) among others.
[26]What follows is inspired by (Armstrong, 1983; 1997)’s characterization of nomic necessitation.
[27]One might worry there are nevertheless brute necessary laws of nature which need further explanation. This is outside the scope of our discussion. That said, even if this is a problematic feature of the variety of Endurantism under discussion here, it seems less problematic than simply brute facts and identity explaining generation.
[28]And there are many. See (Bird, 2007), (Bird, 2016), (Mumford, 2004), (Lewis, 1986) among others.
[29](Bird, 2003), (Jackson, 1998), (Sider, 2011).
[30](McKitrick, 2009; 2016), (Bird, 2003; 2007), (Williams, 2019), (Tugby, 2013, 2013b).
[31]Though I do not have the space to defend this here, I have a preference for fundamental irreducible intrinsic dispositional properties as constituents in states of affairs, i.e. particulars bearing properties. Higher level dispositional properties may be reducible to lower level dispositional properties, but ultimately everything is dispositional, and properties are dispositional all the way down. See (Williams, 2019), (Tubgy, 2013, 2013b), and (Bird, 2007) for similar versions of powers.
[32]One might wonder what it means for, say, o2 to have the dispositional property to be generated at t2 in C2 by o1 at t1 in C1, if at t1 in C1 o2 does not exist. I presume but do not have the space to defend, that the relevant dispositional properties are abstract objects realized in concrete objects when certain conditions obtain. The dispositional properties of o1 at t1 in C1 are realized, then generate C2 at t2 which realizes other dispositional properties, namely, those which act in concert to generate o2 at this time and context.
[33]For example, dispositional theories of persistence must also answer the problem of temporary intrinsics and the tracing problem. Concerning the latter, it seems plausible dispositional properties in concert with other dispositional properties constrain possible processes, e.g. lives, in which an object might participate, providing grounds on which to trace objects. Concerning the former, it seems open to advocates of dispositional theories of persistence to claim, say, an object of a certain shape at a given time may have the power to take on another shape at a later time. In the limiting case, this ‘other’ shape will in fact be the same shape. In more interesting cases, distinct shapes. John at t1 might manifest sitting while it being true of John at t1 that he has the power to stand though it is not manifesting, while John at t2 might manifest standing while it being true of John at t2 that he has the power to sit, though it is not manifesting.