This Week in Virology

I cannot recommend Vincent Racaniello’s This Week in Virology enough. If you’re interested in listening to experts discuss cutting-edge, published and preprint articles covering the pandemic, with (often) minimal jargon and a healthy balance between skepticism and optimism, check TWIV out.

It will forever be the place where I first heard the quote: “If you’re going through hell…keep going.” Delightful.

While I’m plugging, you might as well check out Vincent Racaniello’s Columbia Virology Lectures course, currently free to watch.

Leveraging Ontology to Fight COVID-19

Barry discusses our work alongside Lindsay Cowell, Shane Babcock, Alex Diehl, Oliver He, and many others in the fight against COVID-19, in an interview here in MedicalX.

CIDO: The Community-based Infectious Disease Ontology

CIDO: The Community-based Infectious Disease Ontology, with Oliver He, Asiyah Lin, Barry Smith, et. al.
(Published in Science Data)

Current COVID-19 pandemic and previous SARS/MERS outbreaks have caused a series of major crises to global public health. We must integrate the large and exponentially growing amount of heterogeneous coronavirus data to better understand coronaviruses and associated disease mechanisms, in the interest of developing effective and safe vaccines and drugs. Ontology has emerged to play an important role in standard knowledge and data representation, integration, sharing, and analysis. We have initiated the development of the community-based Coronavirus Infectious Disease Ontology (CIDO). As an Open Biomedical Ontology (OBO) library ontology, CIDO is an open source and interoperable with other existing OBO ontologies. In this article, the general architecture and the design patterns of the CIDO are introduced, CIDO representation of coronaviruses, phenotypes, anti-coronavirus drugs and medical devices (e.g. ventilators) are illustrated, and an application of CIDO implemented to identify repurposable drug candidates for effective and safe COVID-19 treatment is presented.

Infectious Disease, Viruses, COVID-19, and Ontology

Barry Smith provides an overview of the scope of and updates to the Infectious Disease Ontology, and outlines recent work on extensions pertaining to viruses, and in particular COVID-19.

Check out the video here!

Fair Allocation of Philosophers in the Age of COVID-19

We philosophers are often trained to identify, refine, and illuminate difficult issues with a range of techniques. I would like to direct attention towards opportunities where philosophical skills might contribute to healthcare efforts during the present pandemic.

The first involves contributing to important ethics discussions held not in philosophy journals, but in journals like The Lancet and the New England Journal of Medicine. For example, on March 23rd the latter published an article advocating guidelines for allocating scarce resources, prioritizing predicted quality of life and mortality of patients in allocating resources for patients infected with SARS-CoV-2. The article has already been cited 230 times in peer-reviewed journals such as The Lancet, Nature, has been viewed nearly half a million times, and ranks in the 99th percentile of articles mentioned in social media across all medical articles. Notably, this journal has also published four “Letters to the Editor” each objecting to the advocated guidelines. One letter worried such guidelines would sharply disadvantage members of marginalized communities. Authors of the original article responded to each, in this case suggesting discrimination could be avoided by “guidelines and triage committees to preclude the arbitrariness and bias endemic to improvised, bedside rationing.” As of today, that is the end of this discussion in this widely-read, highly influential, medical journal. There was no follow-up discussion of, say, how guidelines not designed to preclude discrimination have a tendency to lead to discriminatory practices when implemented. I suspect readers of this blog already recognized this as an issue worth discussing. Many of us spend our time reflecting on, teaching about, and arguing over such ethical issues. The authors of the above article and associated letters, however, specialize elsewhere. The first opportunity I see then is just this: Direct our philosophical training towards widely-read medical journals via letters to the editor, commentaries, or even articles, in the interest of helping medical researchers think through touch ethical issues.

The second involves contributing to research at the intersection of philosophy, computer science, and medicine focused on making existing medical data more accessible to researchers who need it. Data collected, say, in hospitals is often annotated in ways that make it only locally accessible. Researchers in the growing field of Applied Ontology have been developing ontologies, functioning as dictionaries which allow translations among such datasets. Because medical research generates so much data, these ontologies must be computer-readable; because researchers in the same domain working at different institutions may carve up their domain differently, ontologists are needed to ensure the coherence of translations. And these needs are why philosophers have been a staple in the creation and development of the most widely-used ontologies. To be computer-readable, ontologies are built on a decidable fragment of first-order logic; to ensure coherence, ontologists work with domain experts, e.g. immunologists, virologists, etc., using conceptual analysis. This is expertise in the toolkit of most philosophers, and can be used to contribute to the current development of ontologies being designed to unify data concerning the Covid-19 pandemic, e.g. Virus Infectious Disease Ontology (VIDO), the Coronavirus Infectious Disease Ontology (CIDO). Even under development, these ontologies have already been used to facilitate re-purposing of drugs likely useful in treating Covid-19. Philosophers have been working alongside immunologists, microbiologists, and other relevant researchers in development of these ontologies, and given the state of development, there is plenty of space for those interested in helping researchers explore datasets as they work to address the pandemic. In short, the second opportunity I see is this: Direct philosophers trained as described above towards developing coherent, consistent, structure vocabularies for medical research. For more information about the details of this opportunity, feel free to contact me directly, or explore the National Center for Ontological Research.

In the midst of the present crisis, it may not be clear how our expertise can be useful. I hope the above opportunities illustrates how useful we can be, and I encourage readers to seek out and share other opportunities where our specific skillsets might be useful during these dire times.

Bioethics Week 5 Question 1 Answer

Question 1:  Thompson claims abortion is morally permissible independent of evaluations of moral status. This conclusion is approached by employing a thought experiment, involving the society of music lovers and life-saving treatment. One way of understanding Thompson’s argument is:

1.      Pulling the plug in the Music Lovers case is morally permissible
2.      Pulling the plug in the Music Lovers case is morally analogous to cases of abortion
3.      Hence, cases of abortion are morally permissible

It seems plausible that (1) is true. You might wonder whether (2) is true. This rests in part on the meaning of “morally analogous”…

A heuristic for testing if a situation A is morally analogous to situation B, is to examine whether the explanation for moral judgments about A are of the same type as those for B. For example, compare John stealing candy from a baby to John stealing medication from a pharmacist. Presumably, the explanation for judgments that the former is wrong are of the same type as those for the latter, namely, stealing is wrong. If so, these situations may be morally analogous. On the other hand, though John stealing from a baby and John murdering Sally are both morally wrong, the explanations of judgments differ in each case, suggesting these cases aren’t morally analogous. Similarly, if we add that John murders Sally by stealing medication she needs to survive, these situations aren’t obviously morally analogous, since the explanation for moral judgments about John stealing candy from a baby seems just a part of explanations for moral judgments about John murdering Sally by stealing her medication. That’s sufficient to make these explanations of different types, at least for our discussion here.

Initial Post: I’d like you to identify various morally relevant* differences between these cases that make the claimed morally analogy suspect. Once you’ve identified differences, adjust the Music Lovers case so it is morally analogous to typical cases of abortion. Call your adjusted case “Music Lovers 2”.

Response Posts: I’d like you to examine whether the proposed Music Lovers 2 cases of your peers affects the soundness of Thompson’s original argument. For Thompson’s argument to be valid - which is required for soundness, since only valid arguments can be sound - changing “Music Lovers” in premise (2) to “Music Lovers 2” requires changing premise (1) also, that is:

4. Pulling the plug in the Music Lovers 2 case is morally permissible
5. Pulling the plug in the Music Lovers 2 case is morally analogous to cases of abortion
6. Hence, cases of abortion are morally permissible

Premise (1) of the original argument seemed true, but not premise (2). I think you’ll find replacement with “Music Lovers 2” will make premise (5) true, but make premise (4) false.

*Note: Some differences will be relevant to judgments about the permissibility of the situations, e.g. intention, kidnapping, others won’t, e.g. the presence of certain medical equipment.

Answer: We can make progress on this question by first observing – simply due to the respective structures of the situations compared – that Music Lovers is at best analogous to a rather specific subset of abortion cases. Cases of abortion arise for many reasons, are conducted in a variety of ways, and consequences are frequently much different than analogous consequences in Music Lovers. Of course, we’re interested in morally relevant differences, so this structural observation alone is insufficient to put (2) in question. To see why, observe the following argument:

1.      Murdering Steve with arsenic is morally wrong
2.      Murdering Steve with arsenic is morally analogous to murdering Steve
3.      Hence, murdering Steve is morally wrong

Murdering Steve with arsenic is – structurally speaking – analogous only to a subset of ways to murder Steve. Nevertheless, these situations both involve the same morally relevant features, namely, murdering, i.e. unjustified killing. In arguments involving claims of moral analogy, morally relevant features are most important to keep in mind.

That said, it isn’t too difficult to identify morally relevant differences between Music Lovers and cases of abortion. For example, typically cases of abortion do not involve an individual taken involuntarily and hooked up to anyone. This seems a clear violation of autonomy, and so clearly morally relevant. Such a difference suggests, however, that Thompson’s argument as presented above isn’t sound, since premise (2) is false. That is, it’s not true that pulling the plug in Music Lovers is morally analogous to cases of abortion, since many cases of abortion differ from Music Lovers in this rather important way.

We can attempt to repair the argument, however, by expanding Music Lovers so that it’s also morally analogous to cases of abortion that do not involve being kidnapped and involuntarily hooked up to someone. Suppose, for instance, you enter a lottery knowing that one person who enters will be selected and expected to be hooked up to the musician in Thompson’s case, in the interest of saving that musician’s life. As it turns out, you’re selected, and then you are hooked up to the musician. Call this Music Lovers 2. The argument now runs:

4. Pulling the plug in the Music Lovers 2 case is morally permissible
5. Pulling the plug in the Music Lovers 2 case is morally analogous to cases of abortion
6. Hence, cases of abortion are morally permissible

We questioned premise (2) in the original argument, since there seem important differences between Music Lovers and cases of abortion. We’ve now attempted to repair premise (2), resulting in premise (5) above. A few observations are in order though. First, note that while we have surely made progress on making premise (5) true, there are other morally relevant differences which might undermine the truth of this premise. For example, in most cases of abortion the developing entity is dependent on the mother because of the mother’s actions. This is not so in Music Lovers 2. As described, you entering the lottery is not why the musician needs your help. This is simply to say to make premise (5) fully general we’d need to continue adjusting morally relevant variables, and there are many more to adjust. Putting that aside, second, we can already see trouble on the horizon for Thompson’s argument as described above. To ensure this argument is valid, if we adjust Music Lovers to Music Lovers 2 in premise (5), then we must adjust it similarly in premise (4). Recall, in the original argument premise (1) seemed true, and if you share my intuitions, it seemed obviously true. Note, however, that premise (4) is at least not so obviously true. That is, it’s not obviously morally permissible for you to unplug given that you’d entered the lottery knowing the consequences. This suggests adjusting the Music Lovers case so it aligns more with cases of abortion runs the risk of making the first premise of Thompson’s argument false at the expense of making the second premise true.

Bioethics Week 2 Question 1 Answer

Question 1: The following seems true:

(GOOD) If agent S is reasonably confident that agent T’s life will be worse if S performs action A, then S has a prima facie responsibility to not perform A

For example, if I’m reasonably confident – i.e. I’ve sufficient evidence to believe, I’ve not made any logical errors evaluating that evidence, I’m not intoxicated, etc. – that Mauricio’s life will be worse if I steal his cat then I’ve a responsibility to leave his cat alone. This could be overridden given different details, e.g. if Mauricio had stolen ‘his’ cat from me. That’s what it means to say prima facie; the responsibility in (GOOD) might be overridden. With that qualification, (GOOD) seems defensible, and is perhaps what underwrites physician oaths to ‘do no harm’. Of course, (GOOD) is more general than medicine; it hold for all of us. That suggests there must be more underwriting physician responsibilities than (GOOD). Relevant here is that physicians sometimes must cause significant suffering in the interest of avoiding future suffering. That suggests:

(BETTER) If a physician is reasonably confident that agent T’s life will be better if the physician performs action A, then the physician has a prima facie responsibility to perform A

If this were general, it might generate, say, a responsibility to help people change tires, clean up parks, take out your neighbor’s garbage, etc. These might be contentious. Restricted to physicians, however, (BETTER) seems defensible…assuming they’ve the relevant training needed to help. A neurologist confident that a patient’s life will be better if they’ve surgery but who themselves is not a surgeon, does not seem to have a responsibility to conduct surgery. In fact, it’d seem wrong if they tried to conduct surgery. And that seems underwritten by our old friend (GOOD), since it’s likely they’d make things worse.

Now, consider the following arguments:

(1)   (BETTER) is true
(2)   If (1), then physicians have a prima facie responsibility to try to convince patients to accept treatments they believe will make the patient’s life better
(3)   Hence, physicians have a prima facie responsibility to try to convince patients to accept treatments they believe will make the patient’s life better
(4)   Physicians engaging in empathetic discussion with patients concerning recommended treatments is an effective and respectful way to convince patients to accept those treatments
(5)   If (3) and (4), then physicians have a prima facie responsibility to engage in empathetic discussion with patients concerning recommended treatments
(6)   Hence, physicians have a prima facie responsibility to engage in empathetic discussion with patients concerning recommended treatments

So far, so good. Consider next:

(1)   Physicians are not trained to engage in empathetic discussion with patients concerning recommended treatments
(2)   If (1), then physicians can reasonably expect to make the lives of patients worse by attempting empathetic discussion with patients concerning treatments
(3)   Hence, physicians can reasonably expect to make the lives of patients worse by attempting empathetic discussion with patients concerning treatments
(4)   (GOOD) is true
(5)   If (3) and (4), then physicians have a prima facie responsibility to not attempt empathetic discussion with patients concerning treatments
(6)   Hence, physicians have a prima facie responsibility to not attempt empathetic discussion with patients concerning treatments

Both arguments are valid, i.e. if the premises are true then the conclusions are true. But these arguments cannot both be sound given their conclusions are in tension.

Select one of the arguments and - in under 200 words - provide a counterexample for one of the lines of that argument. For your responses, in under 50 words, attempt to counter the counterexamples provided by at least two other students.

Solution 1: We’ll examine each argument line-by-line. Start with the first line of the first argument, which says that the following is true:

(BETTER) If a physician is reasonably confident that agent T’s life will be better if the physician performs action A, then the physician has a prima facie responsibility to perform A

Recall that a prima facie responsibility is a responsibility that can be overridden but is a plausibly a default responsibility. For example, you have a prima facie responsibility to tell the truth, but if doing so would lead to your best friend’s death, then you better not tell the truth! This is because you also have a prima facie responsibility to not let your best friend die if you can help it, and that trumps your prima facie responsibility to tell the truth. This is to say that line (1) claims if a physician can be reasonably confident that a patient’s life will be better if they do something, then the physician has a prima facie responsibility to do it. I think this is true largely due to the role physicians occupy. That said, we could nitpick and note that BETTER seems to suggest that physicians have prima facie responsibilities outside their field of expertise. For example, as stated BETTER implies a physician who is reasonably confident a patient’s marriage is harmful and that breaking up the marriage would make the patient’s life better, has a prima facie responsibility to break up the marriage. Yet, marriage counseling and advice is likely outside the scope of the physician’s expertise. That seems the wrong result.

Whether this is forceful depends, however, on how “reasonably confident” is understood. I’ve left it underspecified on purpose. Suffice it to say that the stronger this constraint, the more plausible it begins to sound that a physician does have a prima facie responsibility to perhaps break up the marriage, i.e. knowledge is power and power brings responsibility. On the other hand, if “reasonably confident” is understood as a weaker constraint, then it seems less likely the physician has a prima facie responsibility to break up the marriage. To avoid the counterexample, it seems the weaker reading should be adopted, and this informs discussion of the remaining next argument. But before we get there…

Consider next lines (2) and (3). If we assume line (1) is true, then note that line (2) is simply a specification of the part between the “if” and the “then” of line (1), to a given action. The logic from (1), (2), and (3) is:

i. If a physician is reasonably confident that agent T’s life will be better if the physician performs action A, then the physician has a prima facie responsibility to perform A
ii. If [if a physician is reasonably confident that agent T’s life will be better if the physician performs action A, then the physician has a prima facie responsibility to perform A] then physicians have a prima facie responsibility to try to convince patients to accept treatments they believe will make the patient’s life better
iii. Hence, physicians have a prima facie responsibility to try to convince patients to accept treatments they believe will make the patient’s life better

We can spell it out further though:

i.  If a physician is reasonably confident that agent T’s life will be better if the physician performs action A, then the physician has a prima facie responsibility to perform A
ii. If a physician is reasonably confident that agent T’s life will be better if the physician tries to convince T to accept treatments they believe will make the T’s life better, then the physician has a prima facie responsibility to try to convince T to accept treatments they believe will make the T’s life better
iii.  Suppose a physician is reasonably confident that agent T’s life will be better if the physician tries to convince T to accept treatments they believe will make the T’s life better
iv.  Hence, the physician has a prima facie responsibility to try to convince T to accept treatments they believe will make the T’s life better

The move from (i) to (ii) in this second expansion of the argument reveals the specification of line (1) to a given action. Line (iii) of this second expansion supposes – as is plausible – that a physician is reasonably confident such an action will be helpful for T. This is all to say that we should grant (2) and (3) since they’re points of logic, though they needed unpacking to see that.

Next is line (4), which I repeat here:

Physicians engaging in empathetic discussion with patients concerning recommended treatments is an effective and respectful way to convince patients to accept those treatments

This seems true, and borne out by briefly expanding on what it means to have an empathetic discussion. I think Gawande provides an excellent example of this sort of discussion, for reference. But you can see intuitively – I’m sure – how this works. Patients often receive bad news from physicians or treatments that alter their lives. Physicians who are able to help patient’s feel heard, validated in their concerns, and encouraged through the perhaps difficult near future the patient can expect, create an environment of dialogue so that patients are themselves more likely to listen, validate, and encourage physicians in their recommendations. As my mother used to say: “You catch more flies with honey.” (Ignore that I used to say back: “Why do I want flies? My honey is ruined.”)

Lastly, consider line (5), repeated here and unpacked:

If physicians have a prima facie responsibility to try to convince patients to accept treatments they believe will make the patient’s life better and physicians engaging in empathetic discussion with patients concerning recommended treatments is an effective and respectful way to convince patients to accept those treatments, then physicians have a prima facie responsibility to engage in empathetic discussion with patients concerning recommended treatments

This also seems true, given that the assumed prima facie responsibility from (3) plausibly transfers through the effective and respectful means of convincing patients mentioned in (4). One might attempt to object here that (5) implies the only way for physicians to make patient lives better is by empathetic discussion, and they believe that. That, however, is incorrect. All this argument says is that empathetic discussion is a way to achieve that end; there are surely others.

Let’s consider the second argument next, starting with line (1):

Physicians are not trained to engage in empathetic discussion with patients concerning recommended treatments

As stated, this seems true. Physicians are trained to treat patients as – simply put – presenting problems to be solved with certain diagnostic tools. But physicians are not often trained to supplement those tools with empathetic discussion of the sort described here. This is, of course, something that could be added to physician training, and – as Rebecca suggests – seems in the current era something medical students are sensitive to, which fills me with optimism about the future.

Consider next line (2):

If (1), then physicians can reasonably expect to make the lives of patients worse by attempting empathetic discussion with patients concerning treatments

Here is where our earlier discussion of “reasonably confident” enters again. Recall, to avoid obvious counterexamples to line (1) in the first argument, we must read this as restricted in some manner. Earlier we didn’t want physicians to become impromptu marriage counselors simply because they’re reasonably confident someone’s life would be better if they weren’t married. We could avoid this counterexample by restricting the scope of “reasonably confident” to physician area of expertise. Restricted thus, and since (1) is true, then it seems plausible empathetic discussion is outside the scope of physician expertise.

That said, there is still a leap from physicians not having such training to being reasonably confident that patient lives will be worse if they try. At this point, it’s worth thinking about context in more depth. Consider first, a physician might convince an individual to receive a life-saving blood transfusion though doing so violates deeply held religious convictions by the patient. If done empathetically, this is more likely to result in the patient feeling heard, and accepting that the decision is largely theirs to make. If done poorly, however, say, by offering a battery of arguments and reasons to the patient until they relent, without attempting empathy, that's likely to result in later feelings by the patient that the decision was somewhat forced on them, as if it wasn't really theirs to make. That in turn may lead to psychological harm, distrust in physicians, etc., all of which would plausibly make the patient's life worse. These are salient possibilities a physician might be reasonably confident in arising if the situation is not approached carefully. Of course, untrained physicians might approach such scenarios carefully, but this would be at best accidental virtue. But accidental virtue is like a toy soldier, it’s a toy, but not a soldier. Better to have intentional virtue, and that requires training.

That said, one might object that simply offering options doesn't make a patient's life worse off, and that’s all that physicians need here to undermine (2). But this is not obviously true. Physicians don't simply ever offer treatment options; the options come with a presumption that the physician thinks they're worth considering. That has force. Why else would we be listening going to the physician. In contrast, if I said to you "Hey, here's a treatment option" you'd be more likely to interpret me as offering merely an option. But if there's presumptive force behind physicians providing options, then the empathy worry arises again. Specifically, if done without empathy, this may come off as physicians simply telling patients what to do, which runs the risk of patients not feeling listened to, and so not feeling they have much of a say in the decision making process. These consequences are less likely if physicians provide options empathetically.

There is of course much more to say about line (2). It is underspecified on purpose, but hopefully thinking through scenarios helps illustrate that plausible specifications of it tend to be true. And if it is, then (3) follows.

So let’s consider (4):  

If agent S is reasonably confident that agent T’s life will be worse if S performs action A, then S has a prima facie responsibility to not perform A

I think this hardly requires defending. If you’d like a defense though, please see my Ties that Undermine and Judgments of Moral Responsibility (with James Beebe) in the journal Bioethics.

That brings us to (5), unpacked, pruned, and with “A” replaced with the relevant action:

If a physician is reasonably confident that a patient’s life will be worse if the physician attempts empathetic discussion with the patient concerning treatments, then the physician has a prima facie responsibility to not attempt empathetic discussion with the patient concerning treatments

A move which again strikes me as true. This is motivated by reflecting on the occupational role physicians have, requiring beneficence and non-malfeasance. Simply put, physicians shouldn’t try to do what they don’t know how to do so well, especially if the consequences of trying are so dire. This sort of justification is already common in the medical field. Physicians who aren’t surgeons don’t often attempt surgery, since others can help and the consequences are dire.

But here we reach the dilemma. It can’t be that both arguments are sound, since they generate conflicting conclusions. I think this dilemma can be resolved by observing that the conclusion of the first argument, though it seems the more plausible of the two arguments given, is actually misguided for the reasons given by the second argument. That said, there’s a nearby conclusion that emerges from an argument similar to the first, namely, that physicians should either learn empathic discussion skills or consult empathetic discussion specialists, i.e. therapists. This resolves the conflict. That argument is (changes in bold):

(1)    (BETTER) is true
(2)   If (1), then physicians have a prima facie responsibility to try to convince patients to accept treatments they believe will make the patient’s life better
(3)   Hence, physicians have a prima facie responsibility to try to convince patients to accept treatments they believe will make the patient’s life better
(4)   Physicians trained to engage or who seek relevant consults in empathetic discussion with patients concerning recommended treatments provide an effective and respectful way to convince patients to accept those treatments
(5)   If (3) and (4), then physicians have a prima facie responsibility to train to engage in or consult with experts about empathetic discussion with patients concerning recommended treatments
(6)   Hence, physicians have a prima facie responsibility to train to engage in or consult with experts about empathetic discussion with patients concerning recommended treatments

And that seems true.

Bioethics Week 1 Question 1 Answer

Question 1: There seem cases in which it is permissible for physicians to deceive and perhaps outright lie to patients. For example, rather than prescribe pharmaceutical drugs which have various side effects, physicians sometimes prescribe placebos (sugar pills). Placebos are sometimes effective treatment options, and they lack serious side effects. Note, however, it also seems plausible that for a given patient to consent to a treatment, providers should at least honestly convey information about that treatment to the patient. It is further plausible though that the efficacy of placebos is tied to patient ignorance about their being prescribed. These plausible commitments seem in tension. We can formulate this into an argument:

(1)   It is permissible for physicians to prescribe placebos as treatment for patients in some cases

(2)   If (1), then it is permissible for physicians to deceive or outright lie to patients in some cases

(3)   Hence, it is permissible for physicians to deceive or outright lie to patients in some cases

(4)   In acquiring patient consent for a treatment, it is impermissible for a physician to deceive or outright lie to a patient

(5)   All treatments prescribed by physicians require patient consent

(6)   If (4) and (5), then it is impermissible for a physician to deceive or outright lie to a patient about a given treatment

(7)   Hence, it is impermissible for a physician to deceive or outright lie to a patient about a given treatment

(8)   Hence, it is both permissible and impermissible for physicians to deceive or outright lie to patients about a given treatment

This argument is valid. That means that if the premises (1)-(7) are true, then the conclusion (8) must be true. Validity is a matter of form, or logic. This isn’t a logic course though. In this course, we’re more interested in whether the above argument is sound. A sound argument is a valid argument with true premises. Your task here is to determine whether this argument is sound. In under 200 words, identify a line you think is false, and provide a counterexample. If you’re correct, then that line is false. If at least one of the remaining lines is false, then the argument is unsound. For your responses, in under 50 words object to counterexamples raised to lines you did not write about, i.e. attempt to counter the counterexamples of other students.

*Hint: Lines (3), (7), and (8) – all of which begin with “Hence” – follow from preceding lines by logic. We won’t be questioning logic in this course, so you can ignore these lines. Focus on the remaining lines.

Response: We might question, (1), (2), (4), (5), or (6). You were only required to object to one, but I’ll take each in turn. Start with (1). To reject this is to assert that:

(NO) It is impermissible for physicians to prescribe placebos as treatment for patients in some cases

That is, it is never ethically ok. This sort of position might be justified by relying on a strong notion of patient autonomy, since such autonomy might require that patients be as informed as is reasonable when making decisions about treatment options. If you think patients must be as informed as possible, then (NO) would follow. That is, one might pose the following objection to line (1):

(i)                 Autonomy requires that patients be as informed as is reasonable when making decisions about a treatment option

(ii)               If (i), then it is impermissible for physicians to prescribe placebos as treatment for patients in some cases

(iii)             Hence, it is impermissible for physicians to prescribe placebos as treatment for patients in some cases

Observe, (i) requires some unpacking, specifically, with respect to what is meant by “reasonable.” You might think, for instance, that it is reasonable for physicians to deceive patients by prescribing them placebos since telling them of the placebos would undermine the purpose of prescribing them. If that’s the case, then (ii) in the above argument would be false. We should strive to be charitable to those we’re arguing against, so let’s for the moment assume the notion of “reasonable” at play rules out physicians prescribing placebos, so that (ii) is true. It nevertheless might count lots of other “reasonable” practices, e.g. autonomy requires patients understand the dangers of a given surgery. Of course, even charitably understood, there are objections to offer to (i). For it’s not clear that autonomy does require patients be as informed as is reasonable, however you spell out “reasonable”. Indeed, in some cases, it seems patients should not be informed at all when making autonomous decisions about treatment options.

Turning to (2), note how difficult this premise is to deny. That premise unpacked is:

If it is permissible for physicians to prescribe placebos as treatment for patients in some cases, then it is permissible for physicians to deceive or outright lie to patients in some cases

Note that (2) has the form "if...then", and it acts like a bridge linking (1) and (3). Objecting to lines that have the form "if...then" is typically approached in two steps. First, you assume the statement between the "if" and the "then" is true. Second, you pose a counterexample to the statement after "then". More specifically, objecting to line (2) involves first assuming it's true that it's permissible for physicians to prescribe placebos to patients for some treatments, then posing a counterexample to show that it's nevertheless impermissible for physicians to deceive or outright lie to patients in some cases.

One might try counterexamples such as the following:

(LATER) Patients who have been lied to may experience psychological/physical harm later if they find out

(LAWSUIT) Physicians may be liable to lawsuits in the event prescribed placebos don't work

With this in mind, claims (LATER) and (LAWSUIT) above can be understood as the following argument against (2): 

(i) Patients who have been lied to may experience psychological/physical harm later if they find out
(ii) Physicians may be liable to lawsuits in the event prescribed placebos don't work
(iii) If (i) and (ii), then it is impermissible for physicians to deceive or outright lie to patients in some cases
(iv) Hence, it is impermissible for physicians to deceive or outright lie to patients in some cases

But so far this in incomplete, since we must add in that we’re assuming (1) is true. That is, the argument in full is:

(i) Patients who have been lied to may experience psychological/physical harm later if they find out
(ii) Physicians may be liable to lawsuits in the event prescribed placebos don't work
(iii) If (i) and (ii), then it is impermissible for physicians to deceive or outright lie to patients in some cases
(iv) Hence, it is impermissible for physicians to deceive or outright lie to patients in some cases
(v) It is permissible for physicians to prescribe placebos as treatment for patients in some cases
(vi) If a physician prescribes placebos as treatment for a patient (in the way typically practiced) then they deceive or outright lie to patients
(vii) Hence, it is permissible for physicians to deceive or outright lie to patients in some cases

Hopefully the problem with this argument is clear: lines (iv) and (vii) contradict each other. In other words, objecting to line (2) in the above argument by appealing to (LATER) and (LAWSUIT) while accepting (1), leads to an inconsistent argument. Inconsistent arguments aren’t ever sound, since the premises can’t all be true at the same time. One of them must be false. Now (e) was stipulated as true since we’re objecting to line (2), and (f) follows conceptually from (e). (iii) strikes me as false. Simply put, the psychological damage and liability issues may be costs worth accepting to do the morally right thing. This shouldn’t be surprising. Doing the right thing is sometimes demanding.

Starting with line (4), I think we find more objectionable premises. Recall, that premise is:

(4) In acquiring patient consent for a treatment, it is impermissible for a physician to deceive or outright lie to a patient

This effectively says that physicians cannot deceive or lie to patients if they’re to have acquired consent. Another way to state this, is by saying ‘If a physician has lied or deceived a patient when attempting to acquire consent, then the physician has acted impermissibly.’ Suppose a physician has lied or deceived a patient in order to acquire consent. Does that mean the physician has in every case acted impermissibly?

Suppose a patient’s partner has just died, and their patient’s physician recognizes and seeks to recommend a needed surgery to the patient. Suppose the physician is confident the patient will reject the surgery if the physician shares a lot of details about the negative consequences. Were the patient in better spirits, however, the physician is sure the patient would consent to the surgery. The physician downplays the negative consequences and the surgery is pursued successfully. Suppose the patient later learns of the negative consequences, and agrees with the physician’s decision to downplay them in the moment. It seems the physician has acted permissibly here. Moreover, this seems to be justified by something like the following principle:

(PAT) A paternalist action undertaken to help a patient is permissible even if the patient does not consent, if, had the patient been thinking clearly, they would’ve agreed to the action

This justifies a range of paternalist actions. For example, this justifies acting on behalf of a patient who is unconscious, or acting on behalf of a child, or someone intoxicated. Indeed, in some of these cases it seems permissible for a physician to lie or deceive patients for their own good. Suppose a patient is intoxicated and resisting badly needed treatment, but a physician is able to calm them down by, say, relaying that the police will not be called despite the patient’s actions, in full knowledge that the police have been called. This seems permissible. If cases like these are permissible, however, then (4) is false. The argument against (4) can be stated as:

(i)                Suppose a physician has lied or deceived a patient when attempting to acquire consent (ii)               Suppose (PAT) is true of the patient
(iii)               If (i) and (ii), then the physician’s action is permissible
(iv) Hence, the physician’s action is permissible

Which is to say if we assume the part of (4) between the “if” and “then” is true, then we can still show that the part of the statement after the “then” is false, since line (v) above is the opposite of that part of the statement. That’s all it takes to show (4) is false.

Consider lastly (5), which asserts that all treatments prescribed by physicians require patient consent. It seems we’ve already provided a counterexample to this line in the preceding discussion, so I will not belabor the point. Similar remarks apply to (6).

In any event, showing any of these premises false would be sufficient to show this argument is unsound.

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:

• Objective standards of evaluation

• Purpose in nature

• ·One right way to understand nature, i.e. to “carve nature at its joints”

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)