Logic Notes


First things first, I've an undergraduate degree in chemical engineering, I'm a 3rd year NU Philosophy graduate student specializing in logic, and I transferred here from the University at Buffalo, where I'd completed 4 years of graduate school, also specializing in logic. I share this to let you know I'm very familiar with the material covered in this course. In fact, I've taught this course myself about eight times. If you'd like to know more about my familiarity, or would like to see how I apply the formal language we cover in this class to real-world problems, you can check out my work at johnbeverley.com.

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

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

John is bald or John is a man

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

John has hair or John is a man

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


And we would translate the second sentence as:


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


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


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

John either has hair or is funny or is neat

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

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

We might translate this sentence in the following way:


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

John is a bald instructor or a bald student

Which could be captured as:


Not both

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

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

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


Is this previous statement equivalent to:


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

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


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

John is neither bald nor a woman

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

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

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

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


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

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

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

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

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

We would translate all of these in the following manner:

(1) S -> C

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

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

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

The following would be an acceptable translation:

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

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

Only If

Consider the following sentences:

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

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

Should they be translated as the following:

(1) C -> S

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

(2) S -> C

What do you think?

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

Now, consider the following:

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

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

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

(1) S -> C

(2) ~C -> ~S

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

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

Can be translated in the following:

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

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

(4) ~S -> ~C

(5) C -> S

What about the following:

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

 T -> L

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

If and Only If

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

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

We will learn to translate this in the following manner:

S <- -> C

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

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

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

Hopefully, your construction looks like the following:

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

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


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

John goes to the store unless John buys candy

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

~C -> S

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

John goes to the store or John buys candy

How do you think we would translate this sentence?


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

John goes to the store unless John buys candy

Is readily translated as:


Or even as:

~C -> S

That ends our discussion for today.

Santorio's Counterfactual Triviality Result

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

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

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

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

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

Hermeneutical Injustice Entails Marginalization, but Not Conversely


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Which with (HI-HM) entails:

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

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

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

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

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

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

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

Hermeneutical Marginalization Entails Disadvantage, but Not Conversely

Consider next:

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

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

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

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

And second:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

C exhibits (HI) at t

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

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

Works Cited

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[19](Williams, 2019).

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

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

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

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

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

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

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

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

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

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

[28](Fricker, 2016).

[29](Mills, 2007).

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

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

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

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

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

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

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

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

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

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

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

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

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

[43]Because T > P/Q.

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

Al-Farabi's First Existent

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  • Second, AF is committed to the following:

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

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

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

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

  3. Hence, FE has the property of necessary existence

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

  5. Hence, FE exists

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

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

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

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

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

White Ignorance and Musical Manipulation

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Consider next:

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


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

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

Consider too:

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

 And answer:

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

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

What about existing white ignorance? I suggested last session that manipulation might be warranted, and appealed to art and music in particular as a means to instill knowledge into people's conceptual repertoire without them knowing it. Note the parallel here with Mills on acquired concepts. The idea is that people were raised - were manipulated - into having the hierarchy of concepts they have, and so they can be counter-manipulated. Music seems a way to achieve this to some extent. Privileged whites may realize they know more marginalized individuals and their plights, and can empathize with them more, than they previously believed. This would be like having concepts of a chair without yet forming beliefs about chairs. This raises, of course, a moral question, which will be our last for the day:

(Q10) Is it morally justifiable to manipulate the conceptual hierarchy, and thereby influence the web of beliefs and desires of, privileged whites?

More Things Change; More Things Stay the Same

Section 0: Introduction

Change at least involves gain or loss of properties.[1] Gain or loss of properties requires difference in time.[2] Hence, change at least involves difference in time.[3] Intuitively, gain or loss of properties involves some property bearer,[4] i.e. an object.[5] A leaf, for example, might gain a color property – yellow – and lose another – green – in concert with the seasons. Moreover, it seems plausible objects involved in change remain the same through change, at least in some respects. A green leaf that becomes yellow likely retains other properties, e.g. shape, mass, etc. Hence, change appears to involve objects which gain or lose properties over time while often[6] retaining others.

A long-standing debate in contemporary analytic metaphysics is how to make sense of intuitions about the persistence of changing objects over time. Endurantism maintains – roughly – that objects are numerically identical across time and through property gain or loss.[7] The green leaf at t1 is numerically identical to the yellow leaf at t2. David Lewis[8] shaped contemporary discussion by posing the problem of temporary intrinsics for naïve versions of Endurantism. Lewis claimed objects bear intrinsic properties[9] – which do not depend on anything other than their bearer – such as shape and mass, and observed if Endurantism is true, it seems numerically identical objects may bear incompatible intrinsic properties at different times. But since it is plausible to maintain[10] that for any object(s) x and y, and any intrinsic property P, if x=y then x has P just in case y has P, it follows that incompatible properties at distinct times undermine numerical identity over time. This consequence of naïve Endurantism motivated Lewis’s alternative account of persistence – Perdurantism – which maintains an ontology of temporal parts each of which bear intrinsic properties. Characterizing a leaf changing shape over time, for example, involves a temporal part at t1 bearing a certain shape property and a temporal part at t2 bearing a distinct temporal property. Since these temporal parts are distinct objects bearing incompatible intrinsic properties, the problem of temporary intrinsics is no problem at all.

Advocates of Endurantism typically claim it is the commonsense view of persistence. This is both questionable and of unclear value in this metaphysics dispute. Fortunately, this is not the only motivation for accepting Endurantism. For this view of persistence has a native answer to what we might call the tracing problem, i.e. how objects are tracked over time.  According to Endurantism, tracking a given object from t1 to distinct time t2 is a matter of the numerical identity of the object at these distinct times. In contrast, while Perdurantism was designed to avoid the problem of temporary intrinsics, the mere existence of temporal parts bearing (in)compatible intrinsic properties at distinct times provides no answer to how to track a given object over time. For this reason, Perdurantism is often supplemented by claiming temporal parts are proper mereological parts of larger wholes, often characterized as worms stretching through space and time.[11] For Perdurantism thus supplemented, tracking an object over time amounts to tracking temporal parts through space and time. The leaf changing from green to yellow is, strictly speaking, a series of temporal parts – separated like a deck of playing cards viewed from the side – each bearing intrinsic properties. That is, the leaf is an entity extended in both space and time with proper parts appearing in series. Thus far, it seems then that Perdurantism[12] gains the upper hand in characterizing persistence, since it is designed to avoid the problem of temporary intrinsics, and can be straightforwardly supplemented to answer the tracing problem. But Endurantism can be supplemented just as easily to avoid the problem of temporary intrinsics, e.g. eschewing intrinsic properties and relativizing properties to times.[13] The leaf at t1 and t2 are numerically identical, though it bears, say, one shape-at-t1 property at t1 and another shape-at-t2 property at t2. Supplementing Endurantism in this manner results in a plausible contender in the dispute over the nature of persistence.[14]

We could say much more about which of these theories of persistence is preferable in this dispute, but our task here is not arbitration between these rival theories. Rather, we introduce a problem neither Endurantism nor Perdurantism is able to adequately address, even when supplemented as standardly done. In what follows, we examine to what extent Perdurantism and Endurantism can explain how objects generate other objects or sustain themselves over time through property gain and loss. Specifically in Section 1, we motivate the problem of generation, argue it is distinct from both the problem of temporary intrinsics and the tracing problem, and rebut reasons for thinking it is an insubstantial metaphysical problem. We examine prima facie answers to the problem of generation available to Perdurantism and Endurantism, noting the former can ultimately provide no answer to the problem while the latter provides at best inadequate answers. We then examine Endurantism supplemented with causally robust laws of nature in an attempt to address the problem of generation. Noting this version of Endurantism comes close to adequately addressing the problem of generation, we observe it still falls short. In Section 2, we provide a novel solution to the problem of generation based on dispositional properties, which explains how objects generate other objects and sustain themselves through property change over time. We examine how this solution differs from varieties of Endurantism, in particular the version supplemented with robust laws of nature, and argue dispositional properties succeed where robust laws of nature failed.

Section 1: The Problem of Generation

Change appears to involve objects which gain or lose properties over time while – in many cases - retaining other properties. Understood loosely, either Perdurantism or Endurantism might fit this gloss on change.[15] But change is not obviously exhausted by our initial observations. For example, persisting objects appear to generate later associated objects or sustain themselves over time.[16] An oak tree at t1 stands tall in a forest, but is reduced to ash by t2; a home constructed at t3 is given a new coat of paint at t4. A plausible explanation for the generation of ash from oak would seem to involve the existence of the oak being relevant to the existence of the ash; a plausible explanation for the home remaining the same through painting would seem to involve the existence of the home at the former time being relevant to the existence of the home at the latter time. Still, mere relevance is insufficient. That an arsonist remembered to set fire to the oak tree is relevant to the explanation of the existence of ash at t2; that an arsonist forgets to burn down the home at t3 is relevant to the explanation of why the home exists at t4. However, the arsonist’s memory does not seem to explain how the oak tree generates ash or how the home sustains its existence over time. Mere relevance is not enough. Intuitively, the existence of the oak at t1 is causally relevant to the generation of the existence of the ash at t2 and the existence of the home at t3 is causally relevant to sustaining the home at t4. Even so, mere causal relevance is insufficient to characterize generation. That there presumably was a Big Bang is causally relevant to the oak tree generating ash; the existence of construction workers who built the home is causally relevant to the home sustaining itself. But again, neither the Big Bang nor the existence of the construction workers explains respective generations.[17] An explanation of object generation seems to involve matters more local to the object than mere causal relevance captures, i.e. intrinsic properties. This suggests change involves in some cases objects generating other objects or sustaining themselves over time through causally relevant intrinsic properties. Call the task of adequately explaining this additional ‘generation’ aspect of change, the problem of generation.

Identifying a problem is one thing, but showing it is a problem worth pursuing another. To be worth pursuing an answer for, it must be shown the problem of generation is a distinct substantive metaphysical question and a distinct substantive metaphysical question. If the problem is not distinct from, say, the problem of temporary intrinsics or the tracing problem, then we should expect Perdurantism and Endurantism to provide an answer to the problem of generation since each provides respective answers to the other two. Supposing the problem is distinct, if the problem of generation is not a substantive metaphysical question, then it should not be viewed as a cost if a given theory of persistence does not provide an adequate answer. The appearance of object generation might be maintained as nothing more than an appearance. We will explore whether the problem of generation is distinct and substantive within the contexts of Perdurantism and Endurantism, arguing neither theory provides an adequate solution to the problem, and there seem few reasons to think the problem of generation is insubstantial.  

Perdurantism and Generation

Failure to adequately address the problem of generation is easiest to see with respect to Perdurantism. Strictly speaking, a temporal part at t1 is only related to another temporal part at t2 in virtue of being parts of the same whole. But proper parthood does not amount to generation. My index finger and thumb are also proper parts of the same whole, but either generates the other. This is mere difference, and mere difference is not change, any more than a fire poker being hot at one end and cold at another at the same time is. This is not a novel observation. Thomson, for example, famously criticized Perdurantism as “crazy metaphysics” on similar grounds, i.e. since it seems to involve the creation of objects ex nihilo.[18] Defenders of Perdurantism sometimes rebut such criticism by claiming temporal parts of the same mereological whole do generate other temporal parts.[19] For temporal parts bear causal relations to other temporal parts that are part of the same spacetime worm. However, this answer is misleading.[20] Causal links between temporal parts - as understood by defenders of Perdurantism – typically lack any sort of robust connection. Defenders of Perdurantism often understand this theory of persistence against a background commitment to Neo-Humeanism,[21] i.e. the thesis that there are no necessary connections joining events over time, rather, there is just “one thing after another.” As a consequence, there are only regularities through spacetime, though defenders of Neo-Humeanism claim some regularities are better than others, namely, those important to scientific investigation.[22] On this view, temporal parts over time are causally linked, and some of these regularities are more important than others, e.g. a series of temporal parts of a leaf is more important than a series of randomly selected temporal parts. But despite the legwork, it should be clear why this provides no answer to the problem of generation. Generation is more involved than merely identifying useful regularities. A temporal part p1 of a home at t1 generating a temporal part p2 of the same home at t2 is less a matter of whether we find this regularity important, and more a matter of the house. Perdurantism cannot accommodate the needed sort of robust causal connections to adequately answer the problem of generation. But if Perdurantism thus construed provides an answer to both the problem of temporary intrinsics and tracing, then since the theory does not provide an answer to the problem of generation, it seems the latter problem is distinct from the other two.

Defenders of Perdurantism might claim, however, not answering the problem of generation is not a cost, since generation is at best a confused concept. If what is meant by this response is that the pre-theoretic concept of generation is confused, I am willing to concede this may be true. But it seems no more or less confused than many other metaphysical pre-theoretic concepts were or are, e.g. modality, composition. Like these other concepts, intuitions about generation plausibly track something in reality. But this observation, combined with granting the pre-theoretic concept of generation is presently unclear, suggests we need further examination of generation, say, within the context of a systematic metaphysical theory, rather than that we should ignore generation and remain ignorant of it. On the other hand, if advocates of Perdurantism mean instead that generation seems confused within the context of Perdurantism, I concede the point. But Perdurantism is not the only lens through which we might view generation, so this response is hardly compelling.

More forcefully, proponents of Perdurantism may claim this theory of persistence is precisely the lens by which we should view generation, and any other persistence related topics. Such a response seems best understood as conceding that not answering the problem of generation is a cost, but simultaneously contending it is one worth paying. This, moreover, can be motivated by observing Perdurantism fits naturally within a broader systematic metaphysic that provides answers to various linguistic, ethical, and logical[23] problems, as well as answers the problem of temporary intrinsics and tracing. This broader systematic metaphysic is, additionally, parsimonious, well-confirmed, and perspicuous. Since this broader picture answers so many questions, and seems to accommodate many other intuitions, it seems worthwhile to reject other – perhaps less well understood – intuitions, such as that underwriting the problem of generation. This is common enough method in scientific investigations. Tables, apples, etc., are largely comprised of empty space, but our perceptions of these objects suggest otherwise. As we become more sophisticated investigators, we put aside some intuitions that conflict our otherwise well-confirmed, parsimonious, general, perspicuous theory of the world. So too for a broader systematic metaphysical picture that includes Perdurantism as a sub-theory.[24] Hence, advocates of Perdurantism might claim, giving up on the appearance of generation – whatever that appearance amounts to – is an acceptable cost. These are fair points in favor of pushing aside the problem of generation, but note while the Neo-Humean picture is impressive, it is not obviously the end of systematic metaphysical inquiry. Much recent work outside the Neo-Humean status quo has precisely sought to introduce robust causal connections between events, states of affairs, objects, etc., providing grounds on which an adequate answer to the problem of generation might be offered rather than ignored.[25] Insofar as one is moved by the intuition that generation is more robust than mere difference between temporal parts, one should at least be motivated to engage in construction of alternative systematic metaphysical theories amenable to theories of persistence other than Perdurantism. So while defenders of Perdurantism might admit the cost of not answering the problem of generation and claim Perdurantism is worth the price, negotiations are not yet over, and other theories of persistence will likely prove more amenable to generation.

Our tentative conclusions thus far then are that if it is granted that Perdurantism addresses the problem of temporary intrinsics and the tracing problem, it nevertheless does not address the problem of generation, which is plausibly worth addressing. The former conclusion strongly suggests the problem of generation is a distinct metaphysical problem from the other two; the latter conclusion suggests we have as of yet little reason to suspect the problem of generation is not a substantive metaphysical problem worth addressing. We turn next to Endurantism and explore whether this theory of persistence answers the problem of generation, or provides reasons to think this is not a substantive metaphysical problem worth our time.

Endurantism and Generation 

Supposing Endurantism provides an answer the problems of generation and tracing, one might think Endurantism provides an answer to the problem of generation. Not so. To see why, first note that Endurantism has a native explanation for how objects remain the same through the gain or loss of properties: numerical identity. Numerical identity is simple - an equivalence relation over its relata – and primitive – an indefinable commitment of the view. Note second, Endurantism is committed to whatever exists being a brute, unexplained, fact. This should be unsurprising; commitment to such a simple view of existence is something Endurantism shares with Perdurantism. Sure, once something is presumed to exist, both Endurantism and Perdurantism may provide explanations for why later objects exist. But neither theory of persistence is in the business of trying to explain existence proper, or explain – ultimately – why objects exist. Of course, when it comes to persistence, since Endurantism is committed to objects persisting as a matter of numerical identity, these theories sharply come apart. For since the existence of a given object is a brute fact for Endurantism, and objects persist according to a primitive notion of numerical identity, then persistence is ultimately explained by brute facts related by a primitive. This is – roughly – why Endurantism cannot adequately address the problem of generation. But this point is worth belaboring.

The issue the preceding observations raise for addressing the problem of generation in the context of Endurantism is easiest to illustrate by focusing on explaining how a given object sustains itself over time without property gain or loss. If Endurantism cannot adequately answer this aspect of the problem of generation, then it plausibly cannot adequately answer the more general problem of how a given object generates other objects or sustains itself through property loss or gain over time. Now, Endurantism claims numerical identity explains why object o at t1 sustains itself at t2. This is admittedly a more robust causal connection than anything Perdurantism allows. In this respect, Endurantism at least provides an answer to the problem of generation. But this answer is inadequate to explain the corollary problem of generation. For the explanation for why o1 at t1 generates o2 at t2 is because o1=o2, and since numerical identity is primitive and existence brute, this amounts to saying o1 generating o2 is a brute fact primitively related to itself. But asserting that objects sustain themselves is a brute fact bearing a primitive relation to itself seems more a description of the problem than an explanation. And if the Endurantism answer to the corollary problem to the problem of generation is inadequate then it seems transposing this answer to the general problem of generation will be equally unsatisfying. Since Endurantism provides answers to the problems of temporary intrinsics and tracing, but fails to provide a satisfying answer to the problem of tracing, it seems the problem of generation is distinct from the other two problems.  

Defenders of Endurantism might be unhappy with the sparse version of Endurantism employed in the preceding discussion. For Endurantism clearly needs to be supplemented to answer the broader problem of generation, even if we suppose numerical identity is an inadequate explanation of the generation of an object from itself over time. Objects gain and lose intrinsic properties over time, and presumably Endurantism must be supplemented with some machinery to explain how properties are gained and lost. Defenders of Endurantism might claim that whatever explains the gain and loss of intrinsic properties generally, will provide an answer to why objects generate later objects. Nevertheless, it is worth noting that standardly understood, Endurantism is also committed to whether an object having or not having a property at a given time being a matter of brute fact. Strictly speaking, according to Endurantism what explains why object o is a given shape at t1 and another shape at t2 is simply that o is the first shape at t1 and the second at t2. This explanation seems no better than appealing to numerical identity over time. More promising, however,[26] is supplementing Endurantism with commitment to laws of nature as governing the gain and loss of properties over time. For example, there may be a law of nature to the effect that necessarily, for any leaf at t1 with a certain shape in context C1, at t2 in context C2 that numerically identical leaf will have a distinct shape. Causal connections between property instantiation on such a view would be robust. And since these causal links are governed by necessary laws, this seems a better explanation of property gain and loss than simply assuming brute facts about property instantiation, existence, and numerical identity.[27] Moreover, this proposal appears to provide a straightforward answer to the corollary problem of generation: necessarily for any o1 at t1 in context C1, o2 at t2 in context C2 is such that o1=o2, where each context is spelled out appropriately. It seems then, we have discovered a supplement to Endurantism that provides an adequate answer to the problem of generation.

Putting aside worries one might have with laws of nature governing property gain and loss generally speaking,[28] there seems a significant worry worth raising to Endurantism thus supplemented. Simply put, on this proposal whatever was intrinsic about generation vanishes. An object numerically identical to itself over time is not due to the object sustaining itself over time, but rather an extrinsic law of nature generating numerical identity. Similarly, a leaf changing shape is understood, on this proposal, as extrinsic laws of nature governing transitions from one shape to the other. The intrinsic properties of the leaf at best play a role in generation insofar as they satisfy conditions for being governed by a particular law. But an object bearing intrinsic properties that satisfy being governed by an extrinsic law of nature through a process of generation to another set of intrinsic properties, is generation by an indirect route. The object itself plays an ancillary role in generation, and this seems to fall short of our motivating intuition that earlier objects generate later objects or sustain themselves over time.

If the preceding is correct, then it seems the answers provided by Endurantism to the problem of temporary intrinsics and the tracing problem do not adequately answer the problem of generation. Moreover, if the preceding is correct, then supplementing Endurantism with necessary causal laws of nature also falls short of answering the problem of generation, though it gets much closer than other varieties of Endurantism considered. However, at this stage advocates of Endurantism might simply reject anything more must be said to address the problem of generation. They might maintain the answers provided to the problem of generation – either generation being primitive or robust laws of nature - are adequate, since the problem itself deserves no better sort of answer. On the former view, an object o at t1 being numerically identical to t2 despite changing properties is an intrinsic matter to the object o, and numerical identity over time is at least a robust causal connection, even if property instantiation is brute. On the latter view, an object o at t1 being numerically identical at t2 despite changing properties is an extrinsic matter, due to governance by robust laws of nature, and property instantiation is explained by these laws. In either case, the respective advocate might claim, we have as adequate an answer to the problem of generation as we need. In response, I grant advocates of Endurantism of the second stripe make a good case for leaving the problem of generation without a full answer. In light of this second answer, however, I find answering the problem by appealing to primitive identity unsatisfying, so I am much less compelled to consider Endurantism of the first stripe as providing an adequate answer to the problem. Still, part of the difficulty in adjudicating any answer to the problem provided stems from not clearly seeing what an adequate answer to the problem of generation would be. It is thus worth examining what a full answer might be, in route to determining whether we should be satisfied with, say, this second form of Endurantism.   

Section 2: A Third Turn betwixt Them

Dispositional Generation

Neither Perdurantism nor Endurantism of any variety described above permits the existence of irreducible dispositional properties had by objects. Insofar as either countenances the existence of such properties, they are considered reducible, or supervenient, or grounded on other so-called categorical properties had by objects. It is not difficult to see why metaphysical theories have preferred reducing dispositional properties to others in most cases, since dispositional properties are not extensional. Adequately characterizing the shape, mass, electronegativity – that is, categorical properties – of a sample of table salt is something that can be done at a single time and place. In contrast, adequately characterizing the disposition table salt has to dissolving when placed in unsaturated water cannot obviously be done at a single time and place. Had no sample of table salt ever contacted water, it seems table salt would have still had the disposition to dissolve. Characterizing dispositional properties, it is commonly thought, requires extending beyond what happens at a time and place, into what could – but may never – happen. Suffice it to say, systematic metaphysics are much cleaner when dispositional properties can be entirely explained in terms of non-dispositional properties.[29] Otherwise, it seems one must introduce irreducible modal properties into one’s systematic metaphysic.

And yet many recent metaphysicians who advocate various powers-based theories of causation, laws of nature, and persistence, seem to prefer messiness to the neat standard options one finds in contemporary analytic metaphysics.[30] This recent movement suggests the last option we will consider for addressing the problem of generation: objects generate other objects or sustain themselves over time due to irreducible dispositional properties.[31] To illustrate, consider first an object o1 at t1 in context C1 generating the existence of a distinct object o2 at t2 in C2. The dispositional proposal on offer is committed to o1 having dispositional properties that act in concert with other dispositional properties in C1 and together bring about the existence of o2 in C2 at t2. Moreover, leaning further on the notion of dispositional properties acting in concert, we might say that the dispositional properties of o2 in C2 at t2 also act in concert with those properties of the preceding context, object, and time. More cleanly, the first object manifests a disposition to generate the second, and the second manifests a disposition to be generated by the first. On this proposal, moreover, the relevant dispositional properties are intrinsic to the respective objects. Object o1 generating o2 stems from an intrinsic dispositional property had by o1, and o2 permitting – as it were – generation by o1 stems from an intrinsic dispositional property had by o2. Moreover, on this proposal the relevant dispositional properties are causally robust. That is, we can say necessarily, if object o1 exists at t1 in C1, then o2 exists at t2 in C2.[32] We have then, an answer to the problem of generation that permits robust causal connections between generated objects and captures generation as an intrinsic affair. This proposal also answers the corollary problem of generation: necessarily, if object o1 exists at t1 in C1 then o2 exists at t2 in C2 and o1=o2, when the respective contexts are appropriately spelled out. Altogether then, this dispositional proposal provides robust causal connections and intrinsic properties in answering the problem of generation.

Dispositional answer to the problem of generation in hand, we can return to the answer offered by Endurantism supplemented with robust laws of nature. Recall, the latter answer solved the problem by introducing necessary laws of nature that governed objects generating other objects and sustaining themselves over time. While this variety of Endurantism allowed for robust causal connections in generation, we noted it seemed inadequate since the stated robust causal connections were extrinsic to object generation. The dispositional proposal, in contrast, ties robust causal connections to intrinsic properties of the relevant objects involved in generation. Glibly put, the dispositional proposal simply converts laws of nature into intrinsic properties, thereby satisfying the plausible constraint on an adequate answer to the problem of generation that generation be an intrinsic affair between the relevant objects. To that extent, the dispositional view provides a more satisfying answer to the problem than Endurantism supplemented with laws of nature.

That said, one may worry the dispositional proposal shares too much in common with the first Endurantism answer we considered to the problem of generation. There, existence and property instantiation was assumed a brute fact and numerical identity a primitive, which led to the explanation of persistence being brute and primitive. Similarly, one might argue that the dispositional view – thus far described – treats existence as brute, and both persistence and property instantiation as primitive. Hence, insofar as one found the former unsatisfying, one should also find the latter. In response, it is true that on this proposal existence is brute – just as it is on any of the other theories considered – and property instantiation is primitive just as on this rival version of Endurantism. Nevertheless, the properties instantiated on the dispositional proposal are not of the same kind as those one would have on the Endurantism proposal. That a given object instantiates a set of properties may be a primitive unexplainable fact, but if those properties are irreducibly dispositional, there are available explanations for why that object has or loses those properties later, namely, because dispositional properties are directed at other arrangements of properties in the world. Indeed, once the world is peppered with objects instantiating dispositional properties, which is admittedly a brute fact, gain and loss of properties over time is explained by these initial conditions. The same cannot be said for Endurantism of the first stripe, which lacks intrinsic irreducible dispositional properties. Given a world peppered with objects not instantiating irreducible dispositional properties, all properties on such a view will be reducible to some, say, categorical base. But then there is no obvious explanation for how the fact that an object has one set of categorical properties at one time is related to the fact that the same object has another – or the same set of – categorical properties later, other than numerical identity. In short, what distinguishes Endurantism of the first stripe from the dispositional proposal offered here is precisely that the latter provides an adequate answer to the problem of generation. So, even if these theories of persistence are similar, they can be distinguished based on how they address this problem.

Of course, much more must be developed for dispositional accounts of persistence to be considered legitimate contenders.[33] Still, some progress has been made on that front here. We have argued the little remarked on problem of generation finds no adequate answer among varieties of Perdurantism and Endurantism found in the extant literature on persistence. We have observed a novel dispositional solution seems to provide an adequate solution to the problem, while respecting intuitions about what features an answer to this problem should have. Generation, it seems, requires dispositional properties. And that is, perhaps, a surprising change to the standard picture of contemporary analytic metaphysics worth exploring in more detail.

Works Cited

Armstrong, D. M. A World of States of Affairs. Vol. 7. Cambridge University Press, 1997.
Armstrong, D.M. What Is a Law of Nature? Vol. 96. Cambridge University Press, 1983.
Ayer, A. J. Philosophical Essays. Vol. 64. Greenwood Press, 1954.
Benthem, J. (1983). The Logic of Time: A Model-Theoretic Investigation. Synthese Library.
Bird, Alexander. Nature’s Metaphysics: Laws and Properties. Oxford University Press, 2007.
Bird, Alexander. (2016). “Overpowering: How the Powers Ontology has Overreached Itself.” Mind 125, no. 498: 341-383.
Haslanger, S. (2003). Persistence through Time. In the Oxford Handbook of Metaphysics.
Jackson, Frank. From Metaphysics to Ethics: A Defence of Conceptual Analysis. Vol. 1. Oxford University Press, 1998.
Lewis, David. Counterfactuals. Blackwell Publishers, 1973.
Lewis, David. On the Plurality of Worlds. Vol. 97. Blackwell Publishers, 1986.
Lewis, David. (1986b). Causal Explanation. In Philosophical Papers, Volume II.
Lewis, David. Papers in Metaphysics and Epistemology. Cambridge, Uk ;Cambridge University Press, 1999.
Lowe, E. J. “On the Individuation of Powers.” In The Metaphysics of Powers: Their Grounding and Their Manifestations, edited by Anna Marmodoro. Routledge, 2010.
Martin, C.B. The Mind in Nature. Oxford University Press Uk, 2007.
Martin, C.B. “On the Need for Properties: The Road to Pythagoreanism and Back.” Synthese 112, no. 2 (1997): 193–231.
McKitrick, Jennifer. “Dispositional Pluralism,” 2009.
McKitrick, Jennifer. “Manifestations as Effects.” In The Metaphysics of Powers: Their Grounding and Their Manifestations, edited by Anna Marmodoro. Routledge, 2010.
Mumford, Stephen. Dispositions. Vol. 8. Oxford University Press, 1998.
Mumford, Stephen. Laws in Nature. Routledge, 2004.
Shrenk, Markus. “The Powerlessness of Necessity.” Noûs 44, no. 4 (2010): 725–39.
Shoemaker, S. (1969). Time without Change. Journal of Philosophy.
Sider, T. 2001: Four-Dimensionalism: An Ontology of Persistence and Time. Oxford: Oxford University Press.
Sider, T. Writing the book of the world. Oxford: Oxford University Press. (2011).
Thomson, J.J. (1983). Parthood and Identity across Time. Journal of Philosophy.
Tugby, Matthew. “Categoricalism, Dispositionalism, and the Epistemology of Properties.” Synthese 191, no. 6 (2013): 1–16.
Tugby, Matthew. “Graph-Theoretic Models of Dispositional Structures.” International Studies in the Philosophy of Science 27, no. 1 (2013): 23–39.
Van Cleve, J. (1985). Three Versions of the Bundle Theory. Philosophical Studies.
Warmbrod, K. (2017). Time, Change, and Time without Change. Synthese.
Williams, N. (2019). The Powers Metaphysic. Oxford University Press.

[1]There are nearby notions of change, e.g. mereological change. Gain or loss of parts may result in a gain or loss of some properties while retaining others, e.g. a red sphere is divided into two red hemispheres. I focus on property change as the more general notion.  
[2]We suppose time is a linear order of discrete temporal points (Benthem, 1983), though not much depends on this here.
[3]The converse does not seem to hold; time may proceed without change, e.g. two cards stacked against each other in equilibrium (Williams, 2019). (Shoemaker, 1969) argued for this claim, but the soundness of his argument is unclear. That does not mean the conclusion is false, however. See (Warmbrod, 2017).
[4]Trope theories of a certain stripe (van Cleve, 1985) might deny there are objects, but countenance change. We put such options aside for what follows.
[5]I intend to remain neutral over whether, say, objects are states of affairs, bare particulars, composites of tropes, etc.
[6]Change may involve complete loss of properties via destruction, e.g. a vase destroyed by a supernatural force.
[7]This is a standard gloss as found in (Sider, 2001), (Williams, 2019), among others.
[8](Lewis, 1986).
[9]The notion of intrinsic properties is notoriously difficult to characterize. The intuitive gloss suffices for our purposes, but see (Bird, 2007) and (Lewis, 1999), for discussion.
[10]This is, of course, a version of Leibniz’s Law restricted to intrinsic properties. (Ayer, 1954).
[11](Lewis, 1986). I put aside considering Stage Theory varieties of Perdurantism (Sider, 2001), in what follows.
[12]In the remainder, I will use “Perdurantism” to refer to the version of this theory of persistence supplemented with spacetime worms.
[13]E.g. (Haslanger, 2003).
[14]In the remainder, I will use “Endurantism” to refer to the version of this theory of persistence supplemented with relativized temporal properties. Admittedly, this restricts the scope of my conclusion, there is not enough space for a full treatment of varieties of Endurantism here.
[15]Perdurantism has the trickier time, since in most cases of change for this theory of persistence objects either always retain all their properties – if viewed as a spacetime worm – or never retain any – if viewed as temporal parts. 
[16](Armstrong, 1997, pg. 74) observes the “actual bringing into existence” of later temporal parts by earlier temporal parts is a necessary feature of persistence.
[17]Pace what (Lewis, 1986b) says about how we should understand causation. There, Lewis motivates thinking of explanation in purely causal – regularities we find important – terms. For x to explain y, all that is needed is that x exist in the causal history of y, e.g. the Big Bang is an explanation, in some sense, for me writing this paper. This would allow – at the risk of a verbal dispute - advocates of Perdurantism to say causal relations provide all the explanation one needs.
[18](Thomson, 1983).
[19](Sider, 2011).
[20]Some (Williams, 2019), say it is confused. I doubt Sider is confused about his commitments. I take him as providing damage control in the cited passage.
[21]See (Schrenk, 2010), (Jackson, 1998), (Lewis, 1986), and many others for evidence.
[22](Lewis, 1986), (Sider, 2011).
[23](Lewis, 1973; 1986; 1999), (Sider, 2001; 2011).
[24](Lewis, 1986).
[25]See (Martin, 1997; 2007), (Williams, 2019), (Mumford & Anjum, 1998), (Mumford, 2004), (Bird, 2007), (Armstrong, 1987; 1997), (Lowe, 1994), (Tugby, 2013; 2013b) among others.
[26]What follows is inspired by (Armstrong, 1983; 1997)’s characterization of nomic necessitation.
[27]One might worry there are nevertheless brute necessary laws of nature which need further explanation. This is outside the scope of our discussion. That said, even if this is a problematic feature of the variety of Endurantism under discussion here, it seems less problematic than simply brute facts and identity explaining generation.
[28]And there are many. See (Bird, 2007), (Bird, 2016), (Mumford, 2004), (Lewis, 1986) among others.
[29](Bird, 2003), (Jackson, 1998), (Sider, 2011).
[30](McKitrick, 2009; 2016), (Bird, 2003; 2007), (Williams, 2019), (Tugby, 2013, 2013b).
[31]Though I do not have the space to defend this here, I have a preference for fundamental irreducible intrinsic dispositional properties as constituents in states of affairs, i.e. particulars bearing properties. Higher level dispositional properties may be reducible to lower level dispositional properties, but ultimately everything is dispositional, and properties are dispositional all the way down. See (Williams, 2019), (Tubgy, 2013, 2013b), and (Bird, 2007) for similar versions of powers.
[32]One might wonder what it means for, say, o2 to have the dispositional property to be generated at t2 in C2 by o1 at t1 in C1, if at t1 in C1 o2 does not exist. I presume but do not have the space to defend, that the relevant dispositional properties are abstract objects realized in concrete objects when certain conditions obtain. The dispositional properties of o1 at t1 in C1 are realized, then generate C2 at t2 which realizes other dispositional properties, namely, those which act in concert to generate o2 at this time and context.
[33]For example, dispositional theories of persistence must also answer the problem of temporary intrinsics and the tracing problem. Concerning the latter, it seems plausible dispositional properties in concert with other dispositional properties constrain possible processes, e.g. lives, in which an object might participate, providing grounds on which to trace objects. Concerning the former, it seems open to advocates of dispositional theories of persistence to claim, say, an object of a certain shape at a given time may have the power to take on another shape at a later time. In the limiting case, this ‘other’ shape will in fact be the same shape. In more interesting cases, distinct shapes. John at t1 might manifest sitting while it being true of John at t1 that he has the power to stand though it is not manifesting, while John at t2 might manifest standing while it being true of John at t2 that he has the power to sit, though it is not manifesting.

Dijkstra's Demon

A distributed system can be described as connected nodes lacking access to global memory.[1] Nodes of a distributed system maintain local variables with contents specifying the state of that node. Local states of the system are characterized in terms of a given node being able to read its own state and the state of a proximally connected - neighbor - node. The global state of the system is the union of all local states of all nodes of the system.

Disconnect between local and global information makes distributed systems susceptible to certain types of failures. For our purposes, faults are disruptions in expected behavior of a distributed system, which may be classified as e.g. permanent, intermittent, or transient. Following Dijkstra, we will focus on transient faults, faults that occur once then disappear but do not affect the global behavior of the system, e.g. message transmission timeout followed by transmission success. In particular, we will examine the notion self-stabilization for a system S with respect to some property P - defined over the global states of S – which identifies the correct behavior of S. Roughly, a system exhibiting self-stabilization can sustain arbitrary transient faults and return to a desirable system state without external intervention. Self-stabilization, in this respect, is much like a spinning top inscribing small concentric circles on a table. Lightly pressing the top – a transient fault – results in a self-stabilizing top inscribing larger concentric circles, before returning to its behavior of inscribing smaller concentric circles.  Similarly, a distributed system exhibiting self-stabilization can weather transient faults without, say, crashing.

Broadly speaking, there are two types of global state for a given distributed system with respect to property P, called legitimate states – those which satisfy P - and illegitimate states – those which do not satisfy P. According to Dijkstra, legitimate states must be such that:[2]

(CLOSURE) Every transition from a legitimate state results only in a legitimate state[3]
(PAIR) Every pair of legitimate states can be connected by transitions from one to the other[4]

From which it is a corollary that each global state in sequence of transitions between legitimate states is itself legitimate.[5] Moreover, legitimate states must be such that:   

(LEGIT) Every legitimate state has at least one privilege present
(PRIV) Each privilege must be present in at least one legitimate state

Where the privilege is a Boolean function defined in terms of a given node’s state and that of its neighbors. If values of a node and its neighbors are input to this Boolean function, then if the function returns the value “true”, then the privilege is said to be present, and “false” otherwise. If (LEGIT) is true with respect to some distributed system, then in any legitimate state of that system there is at least one node for which the privilege function returns “true.” If (PRIV) is true, then every possible output for the privilege function which returns “true” appears in at least one legitimate state.

Definitions in hand, Dijkstra defined a distributed system S as self-stabilizing with respect to P, on the condition that S satisfies the following two behaviors:

(ONE) The system has at most one privilege present
(CONVERGE) Given an arbitrary global state, the global state of S satisfies P within a finite number of state transitions

If (ONE) is true, a self-stabilizing system must have at most one set of state machine and neighbor inputs that result in “true.” A corollary of (LEGIT) and (PRIV), is that a self-stabilizing distributed system with respect to behavior P has exactly one privilege present in any given legitimate state and all privileges will eventually be represented. If (CONVERGE) is true, then the relevant distributed system satisfies P in finite transitions. Combined with (CLOSURE) and (PAIR), any given pair of legitimate states can be connected by a finite sequence of legitimate state transitions. Altogether, a self-stabilizing distributed system will satisfy P in a finite number of transitions, have one privilege, each privilege will be present in some legitimate state which will never transition to an illegitimate state, and each state in between any pair of legitimate states will involve only legitimate states.  Another assumption worth mentioning here – if just to foreshadow - is that Dijkstra posited a central demon for self-stabilizing distributed systems with the ability to select a privileged node to enact a transition. The selection is arbitrary, and once a privileged node enacts a transition, the central demon arbitrarily chooses another among the available privileged nodes to enact the next transition. No node is permitted to enact a transition unless it has been selected by the central demon. Subtleties associated with the central demon assumption will occupy us later.

Before turning to that discussion, however, it is worth specifying Dijkstra’s self-stabilization definition in detail by considering one of three[6] characterizations Dijkstra provided of a self-stabilizing distributed system. Suppose there are N+1 nodes, numbered 0-N in a ring. For any given machine nr.i, where i is an integer between 0 and N, we adopt the following notation:

L: state of the left neighbor of nr.i, i.e. nr.(i-1)mod(N+1)
S: state of machine nr.i
R: state of right neighbor of nr.i, i.e. nr.(i+1)mod(N+1)

For illustration, suppose we have N=3, so there are N+1=4 machines, numbered 0-3 in a ring. Consider nr.0. We have the following:

L: state of the left neighbor of nr.0, i.e. nr.(-1)mod(4)=nr.3
S: state of machine nr.0
R: state of right neighbor of nr.0, i.e. nr.(1)mod(3)=1

To provide conditions under which such a distributed system self-stabilizes, Dijkstra distinguished exceptional machines from all others.[7] In particular, the conditions are, where K is the number of potential assignments to nodes, N the number of nodes, and N ≤ K:

Exceptional Node: If L=S, then assign (S+1) mod K to S
Other Node: If L≠S, then assign L to S

Without loss, suppose nr.0 is the exceptional machine. If there are N nodes each randomly assigned values in K initially, then any node - but the exceptional node - which has distinct assignments from their left neighbor will be privileged. The central demon will arbitrarily select one of these nodes for transition. Suppose nr.3 is chosen. Then nr.3 must have a state distinct from nr.2. But then nr.3 changes its state to that of nr.2, and so nr.3 loses privilege. If, moreover, nr.4 is given privilege, then it will change its own state to be that of nr.3. The procession should be clear. Ultimately, each node that is not exceptional will be in the same state. When this happens, only nr.0 will be privileged, at which point it will initiate a sequence of transitions moving the privilege around the ring.

Recall how Dijkstra’s central demon operates.[8] The central demon selects a privileged node to enact a transition. The selection is arbitrary, and once a privileged node enacts a transition, the central demon arbitrarily chooses another among the available privileged nodes to enact the next transition. No node is permitted to enact a transition unless it has been selected by the central demon. We can divide four distinct assumptions: 

(UNIQUE) A distributed system has only one central demon
(SOLITARY) A central demon cannot choose more than one privileged node
(RANDOM) A central demon chooses among privileged nodes arbitrarily
(LOSS) A central demon cannot grant/remove privilege from a node without that node enacting a transition  

We might wonder whether rejecting one or more of these assumptions undermines self-stabilization for a given distributed system. Suppose, for example, we reject (UNIQUE) while maintaining the other assumptions. Let there be two central demons. Suppose each demon arbitrarily and independently chooses privileged nodes for transition. If each central demon happens to choose the same node, the transition will proceed as if there was only one central demon. So suppose the central demons choose distinct privileged nodes. Then there will need to be some priority ranking which allows the system to decide which of the selected privileged nodes will make the transition first, since both are permitted to make system transitions. We might add a third central demon that arbitrarily selects a privileged node from the two nodes selected by the first and the second central demon, resulting in the selected node making the first transition. Under these conditions, it seems self-stabilization of a distributed system is not violated, since rejecting (UNIQUE) can be plausibly described – if three central demons are permitted – as a two-step implementation of the central demon operation.[15] Specifically, the setup is isomorphic to having a single central demon that selects two distinct nodes, then arbitrarily selects one pair to go first. More generally, this setup would – with n+1 central demons n of which select distinct privileged nodes and one of which arbitrarily orders the results – amount to a single central demon that selects n privileged nodes then orders them arbitrarily. In other words, a legitimate state will ultimately be reached, and will be closed under legitimate states through further transitions given the other central demon assumptions.

            If we reject (SOLITARY) and maintain the rest, we seem to run into trouble since there is no obvious way for multiple privileged nodes selected to transition to determine which nodes will go first. Since we are assuming (UNIQUE), we cannot resolve this issue by appealing to more central demons. But we might adjust the capabilities of the central demon in line with rejecting (SOLITARY) by allowing the demon that arbitrarily chooses several nodes - say, nr.1, nr.2, and nr.3 – may then select among those nodes a priority ranking indicating which node transitions first, second, etc. As with (UNIQUE), since the central demon’s selection was initially among privileged nodes, and the transition of each node results in a loss of privilege for that node and potential gain of privilege for another, then transitioning in groups of ordered privileged nodes will eventually reach a legitimate state if transitioning through one node at a time. Moreover, once in a legitimate state, under these conditions the distributed system will remain in a legitimate state through transitions. Hence, again it seems rejecting one of Dijkstra’s implicit assumptions with respect to the central demon, namely, (SOLITARY) does not affect self-stabilization.

            If we reject (RANDOM), then the central demon may exhibit a pattern of privilege selection, say, in order of nearest to the exceptional node, say, nr.0, in terms of counterclockwise rotation. For example, if the privileged states include nr.2, nr.7, and nr.8, then the central demon will select nr.2. On this ordering, the central demon’s selection being non-arbitrary will again not have an effect on whether the relevant distributed system will ultimately reach a legitimate state for reasons comparable to those involving the discussion of (UNIQUE) and (SOLITARY). Moreover, once in a legitimate state, the distributed system will not be led into an illegitimate state, since there will be only one privileged node to select, and so only one pattern for the central demon to employ.    

            The preceding discussion was warmup; if we reject (LOSS), then the central demon may arbitrarily alter the state of a node without enacting a transition, as well as arbitrarily choose a privileged state to enact a transition. There are broadly two ways in which this might affect self-stabilization. First, the central demon might remove privilege from a node; second, the central demon might grant privilege to a node. We consider each in turn.

            Suppose the central demon is permitted to remove privilege from a node. Suppose nr.0 is the exceptional privileged state. Then f(nr.0)=f(nr.N). Suppose the central demon removes privilege from nr.0. Then f(nr.0)≠f(nr.N), but also f(nr.0)≠f(nr.1), and so nr.1 will be privileged. In this case, if the relevant distributed system is in a legitimate state, then it remains in a legitimate state despite the central demon’s action. Similar remarks apply to non-exceptional nodes with privilege. On the other hand, suppose there are two privileged nodes, f(nr.1)≠f(nr.2) and f(nr.3)≠f(nr.4), while f(nr.0)≠f(nr.N), f(nr.4)=f(nr.5), f(nr.5)=f(nr.N), and f(nr.2)=f(nr.3). Suppose the central demon removes privilege from nr.1, so that f(nr.1)=f(nr.2)=f(nr.3). Again, the actions of the central demon in this context will neither undermine reaching a legitimate state nor force a transition from a legitimate state to an illegitimate state. These observations suggests rejecting (LOSS) by allowing the central demon to arbitrarily remove privilege from a node does not undermine self-stabilization.

            However, interpreting (LOSS) as allowing the central demon to arbitrarily grant privilege to a node does undermine self-stabilization. To illustrate, suppose there are two privileged nodes, f(nr.1)≠f(nr.2) and f(nr.3)≠f(nr.4), while f(nr.0)≠f(nr.N), f(nr.4)=f(nr.5), f(nr.5)=f(nr.N), and f(nr.2)=f(nr.3). Suppose the central demon’s actions repeat in the following manner: (1) grant privilege to nr.j for some j in N where j≠0, i.e. not exceptional; (2) reverse the transition of nr.j by granting nr.j privilege, e.g. altering the assignment of nr.j. If the central demon operates according to such a pattern – which is reasonable sequence given our rejection of (LOSS) and maintenance of the other assumptions – then a distributed system in an illegitimate state will not necessarily transition to a legitimate state. Moreover, rejecting (LOSS) in this manner makes trouble for maintaining closure over legitimate states as well. To illustrate, suppose a distributed system is in a legitimate state, e.g. f(nr.0)=f(nr.2)=f(nr.1) for N=2 and nr.0 the exceptional node. The central demon might grant nr.0 privilege, resulting in a transition to f(nr.0)≠f(nr.2)=f(nr.1) and nr.1 being privileged, but then alter nr.2 so that f(nr.0)=f(nr.2)≠f(nr.1), resulting in each of nr.0, nr.1, and nr.2 being privileged, i.e. an illegitimate state. This clearly violates (CLOSURE).  

Our focus here Dijkstra’s commitment to a central demon. We identified features of this commitment, distinguishing several of which seem incidental to the maintenance of a self-stabilizing system. However, we did identify one crucial assumption, namely, that the central demon not be able to introduce privilege to the ring, which if rejected would undermine self-stabilization. This seems of particular importance when thinking about the security of networks and fault tolerance, since it seems plausible allowing a central demon to grant single privilege to a system might simulate a type of subtle attack on an otherwise self-stabilizing system, which might go unnoticed due to its maintenance what we identified as incidental central demon assumptions.

[1] Kshemkalyani, A.D. & Singhal, M. (2007). Distributed Computing: Principles, Algorithms, and Systems.
[2] Dijkstra, E.W. (1974). Self-Stabilizing Systems in Spite of Distributed Control. Communications of the ACM. 17(11): 643-644.
[3]More carefully: For any legitimate state s at transition point t, and state s’ at transition point t’, if t<t’, then s’ is a legitimate state.
[4]More carefully: For any legitimate states s, s’’ at respective transition points t, t’’, there is a state s’ at transition point t’ such that t<t’<t’’.
[5]More carefully: For any legitimate states s, s’’ at respective transition points t, t’’, if state s’ at t’ is such that t<t’<t’’, then s’ is a legitimate state.  Proof: Suppose state s’ at t’ is such that t<t’<t’’. There is such an s’ by (PAIR) and s’ is a legitimate state by (CLOSURE).
[6] Dijkstra, E.W. (1986). A Belated Proof of Self-Stabilization. Distributed Computing. 1:5-6. 
[7]This is an assumption worth exploring in more detail, but I focus on other aspects of Dijkstra’s algorithm in what follows. Hence, my not giving this assumption its own name here.
[8]Explanation of the central demon follows (Dijkstra, 1986) closely, supplemented by remarks in (Kshemkalyani & Singhal, 2007). I did not find any similarly detailed analysis of the various aspects of the central demon assumption.
[9]Indeed, since the selection of privileged nodes is arbitrary with Dijkstra’s assumptions, it seems the only difference that arises by rejecting (UNIQUE) is that some two-step (or n-step where n is less than or equal to the number of privileged states when the selection is made) will result in longer transition sequences leading to a legitimate state than others. Nevertheless, central demons selecting groups of privileged nodes to operate in what we might think of as ‘transition chunks’ will ultimately lead to a legitimate state as far as I can see.

Marx's (Essence) Alienation Argument

Marx isn’t concerned with any state of nature myth. His boots are firmly on the ground at the rise of capitalism and he’s an astute observer of economic progress and woes.

As I understand him, Marx is an economic determinist, which is to say that he believes economic developments under certain conditions are deterministic. The economic component doesn’t bring with it a moralistic force. It’d be hard to see how that would even be possible with determinism in the picture. The economic determinism articulated by Marx is one of class struggles leading ultimately to classless society, since each class struggle will result in new classes necessarily bringing into existence other classes that will ultimately overcome them, until there is no class. This is the basic picture.

Suppose *you* are a member of the bourgeoisie though, and I’m some proletariat coming to kick down your door and seize the means of production. I barge in ready to perhaps kill you, and you say “Hey, wait! This was all determined! Don’t hurt me and my family. It wasn’t our fault! We’re determined!” I might respond “Me too!” But this shouldn’t sound like a convincing sort of explanation of the situation. While we may both be involved in an economically determined system, we both get to choose our actions. It’s compatible with Marx’s picture, I believe, that individuals may be blameworthy or praiseworthy for what they choose to do. There is some room then for morality.

But then return to our story. *You* say “Wait, what if I change? Maybe if I pay my workers more, and we create a middle class, then you’ll be happy too, right? Surely not everyone can be wealthy and own the means of production, but if you let me manage the means, then we can all be better off. A rising tide raises all boats!”

(Q1) What can a member of the proletariat say in response to this claim, supposing what the member of the bourgeoisie says is true

I ask this question to get at the heart of justification for agents to engage in class struggle. I think Marx has a compelling argument to this conclusion. I will pitch it in terms of capitalism. Let’s walk through the premises slowly though, since each reveals an important feature of Marx’s – labyrinthine – theory.

Marx’s Alienation Argument (Essence Version)

(1)   Creativity is necessary for human flourishing
(2)   If creativity is necessary for human flourishing and x inhibits humans from manifesting creativity, then x is harmful to humans
(3)   Wage labor inhibits humans from manifesting creativity
(4)   Hence, wage labor is harmful to humans
(5)   Capitalism invariably leads to wage labor
(6)   If x invariably leads to y and y is harmful to humans, then it is justifiable to resist x in proportion to its harmfulness to y
(7)   Hence, it is justifiable to resist capitalism in proportion to its harmfulness to humans

Let’s walk through:

            (Q2) Do you think premise (1) is true?

Marx seems to believe that creativity is essential for human flourishing, i.e. (1). Note, he also thinks that autonomy is essential, and this should make sense since creativity comes along with autonomy. It’s also worth noting Marx emphasizes creativity while Rousseau emphasized autonomy, so in that respect these authors differ.

            (Q3) Do you think premises (2) and (3) are true?

(2) seems true, since inhibiting human flourishing is plausibly a harm. It also seems (3) is true. Think of labor as intimately bound up with creativity; creating is what well-functioning humans do, and labor is how they do it. Humans take items from their imagination, that great wide interior world, and through labor bring those things into existence. Wage labor is a way we attach an abstract ratio to labor, so that we may sell it in the market, as if it were corn. Think about that for a moment. Marx is suggesting wage labor – which is intimately bound up with your essential creativity – makes it easy for you to think of that important aspect of yourself as just another good to be sold on the market.

Let me press the point further: I had a student who once claimed he believed it was permissible to sell himself into legitimate slavery. My first thought on hearing this was “How deep have the capitalist tendrils crept into you that you think you can literally sell yourself on the market like you’re corn.” You’re not corn, and your essential nature shouldn’t be for sale as if it is.

(Q4) Do you think premises (5) and (6) are true?

Here’s where Marx’s economic determinism seems to have force. The very nature of capitalism seems to involve abstracting away from products on the market so that capital can circulate and drive innovation. Put another way, free market capitalism of the sort I’m imagining here requires innovation. Bartering is insufficient to drive innovation, so more abstract means are needed and have been developed, e.g. money. Labor is required to drive innovation, so a natural step in the progress of capitalism is using money to purchase whatever is needed by innovation, in this case labor. This very brief history suggests (5) is true.

With (6), we have what I take to be a compelling premise. Humans can proportionally resist what harms them. But this is more forceful than it might first appear. The sort of harm capitalism engenders in alienating you from your essential nature is significant. Capitalism makes it far too easy to be alienated from who you are and who you should be. Because of the depth of this harm, the proportionality constraint in the consequent of this premise suggests to me we’re justified in doing a great deal to resist capitalism. This, moreover, is precisely what I would say in response to the bourgeoisie who claimed a rising tide raises all boats. This platitude is of course trite because it’s true, as most platitudes are. Nevertheless, it’s plausible to think that while we might be able to survive under capitalism, and we may even be able to live an okay life, it’s not obvious we can thrive under capitalism, and thriving is – as I’m using it here – synonymous with human flourishing. 

Lorde, Lugones, and Change

What follows are notes from a discussion I recently led on Audre Lorde’s The Uses of Anger and Maria Lugones’ World-Traveling and Loving Perception:

Lorde claims anger can be used as a tool. What she seems to mean is that anger can be used as a tool to convey information to others.  Moreover, Lorde maintains that anger can be justified or not. That is, you can be justifiably angry, say, if the target of your anger is appropriately blameworthy, or unjustifiably angry, say, if you’re angry at someone who is not blameworthy or you’re angry for illegitimate reasons. Lorde rightly observes anger as a response to racism is always justified.

Lorde claims anger is distinct from hate. Hate can also be used as a tool to convey information, and hate may be justified in some circumstances, e.g. when one attempts to correct persistent, explicit, racism, and presumably unjustified in others. But note, then conveying information can't be the only feature of anger, since it doesn’t distinguish anger from hate. 

(Q1) What does Lorde think distinguishes anger from hate?

Anger is distinguished from hate based on how it is used and under what conditions it is justified. With respect to how anger and hate are distinguished by what they signal:

  • Anger is used to signal judgment recognition of failure to live up to commonly accepted expectations, e.g. black feminist angry with white feminist's self-serving or ignorant behavior

  • Hate is used to signal recognition of rejection of expectations, e.g. an intransigent and harmful racist who refuses to change

And with respect to how anger and hate are distinguished by conditions under which they're justified:

  • Anger emerges between peers in disagreement, when negotiation and discussion is possible

  • Hate emerges among recalcitrant disputants who are unwilling to negotiate

Anger and hate then have different goals. This should remind you a bit of some differences we discussed recently. Take the view of anger and hate we've uncovered when discussing Lorde and:

(Q2) Use them to characterize the dispute between MLK (in Message to Grassroots) and Malcolm X (in Letter from Birmingham Jail).

It's plausible to think X was under the impression there could be no room for negotiating, since whites were recalcitrant racists, often saying one thing and doing another. This suggests the attitude he seemed to bear - in Lorde's terms - is one of hate. In contrast, MLK found enough common ground to desire negotiation. Recall, he used a moral argument in his letter to support non-violent resistance. This was an appeal to common ground - morality - among disputants. He was nevertheless angry, and justifiably so.

There are standard hallmarks of justifiable attitudes, namely, justifiable attitudes are typically such that, using anger to illustrate:

(1) If you judge action A was a mistake, then you should suspend anger

(2) If you judge the agent in A is not a member of the moral community, then you should suspend anger

These features are often associated with justifiable attitudes because justifiable attitudes presuppose responsibility. For example, if you are justifiably angry with someone, then it seems to follow they're an appropriate target for your anger, i.e. they've some responsibility that's been violated. The idea is supposed to be captured in (1) and (2). Suppose Sam spoils a TV show for me by telling someone nearby, not knowing I could hear. I might be angry, but if I recognize Sam made a mistake, then I shouldn't hold on to that anger. It wouldn't be justified. This accords with (1). On the other hand, if my cat spills my water (assuming cats aren't entities which bear responsibility) then I'm not justified in being angry with my cat. This isn't to say my feelings aren't valid. Rather, it's just to say I can't hold my cat responsible, since she's not a member of the moral community. This accords with (2).

I say this to point to a perhaps puzzling feature of Lorde's characterization of anger. Recall, Lorde writes:

"Anger is the appropriate attitude to racist attitudes, as is fury when the actions arising from those attitudes does not change."

Lorde's speech is largely directed at white academic feminists who plausibly are peers worth negotiating with who have similar interests in refraining from harming each other. Lorde claims anger is justified. But justified anger must align with (1), it seems. But plausibly white academic feminists listening to Lorde made mistakes in their hurtful comments that led to Lorde's experiences of anger. It’s not like they were intentionally being ignorant or racist. But then it seems if anger is justified, then these cases aren't going to count as justified anger.

(Q3) What do you think Lorde would say in response?

I came up with two options, which are surely not exhaustive:

  • One might say Lorde isn't rejecting (1), but instead reject the premise that white academic peers are simply making mistakes. This is a response on epistemic grounds, that white academics should correct their beliefs. They have plenty of evidence indicating they should be more open and less reactive, and less afraid of black women and their concerns. You might say this if you want to preserve Lorde understanding anger as a reactive attitude, while satisfying (1). In this case, reactive attitudes such as anger presuppose responsibility.

  • On the other hand, you might reject (1) and claim even if white academics are simply making mistakes, they’re blameworthy on moral grounds, because people are being harmed and mistreated, and anger is a useful attitude in these contexts to effect change. Put this way, anger wouldn't get its justification by satisfying (1) and (2), but rather it would be justified by its effects, namely, by correcting or preventing moral failings. We might then say that targets of reactive attitudes need not be responsible for their actions to be appropriate targets. A white academic who genuinely makes a mistake that results in the appearance of a racist attitude is nevertheless the appropriate target of anger.

I think given how underspecified the case I gave was, either option might be available. But I'm inclined to think the latter is the better interpretation. First, Lorde doesn't qualify when anger is appropriate to racist attitudes; it's always appropriate. Second, I think it's plausible white academics in the audience agreed anger was appropriate when responding to racism. The problem was they didn't see what they were doing as racist.

This brings us back to what anger is used to convey. Lorde seems - like Truth, Douglass, Walker, and others - to observe inconsistency in implicit and explicit beliefs. Rather than employ irony, interrogatives, etc., Lorde points to a signal white academics can use to recognize the inconsistency they exhibit. The idea seems to be, when you see an angry black woman, don't be afraid.

(Q4) Rather than fear, what do you think Lorde is suggesting white academics do instead?

Note, it can't just be 'think more about what you said'. It has to be something deeper. I say this because, if you recall, Lorde has no use for guilt. Guilt arises when you do something that's judged wrong. Guilt is easy to alleviate. You just apologize or pay penance, etc. It's easy because guilt isn't about you; it's about your actions. I think Lorde is suggesting white academics do more than feel bad. They need to re-evaluate their own values. To get a handle on what she might have in mind, consider:

(Q5) What's the difference between guilt and shame?

Guilt concerns actions; shame concerns you. When you're guilty, you can pay for it, brush it off, but it's not about you. When you recognize shame, you recognize you're broken. That's not about what you do; it may be correlated though. It's much more personal. Also, it's much harder to alleviate. You can pay a fine to get over guilt. To get over shame, you either have to change as a person, or ignore it altogether.

For Lorde, that likely justifies using anger to reveal to white academics that they've exhibited racist attitudes. White women didn't realize they were being racist because shame hides. Even when presented with the anger of black women, it's easier to interpret that as something wrong with black women, so that it's unjustified, rather than as justified anger indicting them because they're racist. This is why, I think, white academic women are "more afraid of the anger of black women than of their own racist attitudes." They're focusing on the wrong thing because shame is too painful. This, I think, is why Lorde ends the speech by inviting those in the audience to join the discussion beyond guilt. Recognition of the uses of anger is a way to get there.

There's much more to say about the uses of anger, and I've only guided us along one strand here. But where we've ended up might leave you wondering if spotting anger is enough. It would be little help to have white women constantly on the lookout for anger so they can reactively correct their own values. To be fair, I don't think Lorde is suggesting that's all that should be done. But she doesn't say much more. Fortunately, Lugones provides further assistance through world-traveling.

(Q6) Remind yourself of Lugones, in particular the difference between arrogant and loving perception

Here we have recognition of the failing each of us have in applying stereotypes to other individuals. In many ways we're inclined to treat others as objects rather than subjects. That is, we tend to treat individuals are carrying the same properties with them no matter what world they inhabit. But importantly, we should recognize that each of us inhabits many worlds, and ha many properties that vary by context. There is no single unifying element. We're the intersection of worlds, if anything. Lugones discusses this generally, for each of us, but it's easily applied to the white academics we just discussed. What's needed is not simply recognition of inconsistencies, but awareness of the many ways in which individuals inhabit different worlds. What's needed is openness and vulnerability to being wrong, and willingness to change one's mind. World-traveling seems crucial to developing integrity, since world traveling seems precisely how one might develop integrity.

Lugones observes that being comfortable in one world is dangerous. This is because one might instill values that are never contradicted. This might emerge in white academics not being able to see their own ignorance, which is a topic we examine in more detail next time.

Rousseau's Reductio of the State of Nature Myth

Rousseau is often read as engaged in the same project as Hobbes and Locke, namely, employing the state of nature myth as a way to distinguish what humans have by nature - and so what doesn't need political justification or explanation in political philosophy - and what is gained by governance - and so what does require political explanation or justification. Indeed, Rousseau in the Discourse seems to be claiming Hobbes and Locke just didn't take the state of nature myth seriously enough, and if they had, they'd have started with primitive man, a creature full of possibility - in the form of potential dispositions - but lacking instincts one might find among animals. Among these potential dispositions is the ability to reason, but importantly, this isn't something primitive man comes equipped with; it must be cultivated at the outset like any disposition. On this way of reading Rousseau, he incurs a significant explanatory burden, having to - like Hobbes and Locke before him - provide a plausible story for how one gets from the so-called primitive individuals to modern individuals. Hobbes and Locke claim inhabitants in the state of nature come equipped with the ability to reason, which makes the transition stories offered more plausible. Rousseau’s explanation, however, seems much less plausible…

Simply put, it is not at all clear how a non-reasoning entity, only perceiving tokens, lacking language, with its limited drives, ever develops such characteristics as we find them in modern individual. Of course, it might simply be argued this transition must have occurred, since modern individuals clearly exist. But while it's obvious modern individual exist (hello!), it's not so clear they made this transition from primitive individuals. These observations, along with what I take to be Rousseau's rather dismissive putative explanation of the transition, coupled with his emphasis on the problems one finds in moderns society while suggesting we can't return to our primitive state, suggest to me we should read Rousseau in a slightly different way. Namely, as providing a reductio argument against the very idea of employing a state of nature myth as Hobbes and Locke had. On this reading, Rousseau is not engaged in the same project as these philosophers. Rather, he's undermining a core starting position of their respective theorizing. He's then turning to concrete problems that come from governance to indicate since we can't separate ourselves from governance, we should focus on ourselves under governance.

More specifically, the argument I have in mind is the following:

Rousseau’s Reductio of the State of Nature Myth

(1)   SUPPOSE: The state of nature myth reveals basic human nature
(2)   If (1), then primitive individuals exhibit basic human nature
(3)   If primitive individuals exhibit basic human nature, then transition from primitive individual to modern individuals is possible
(4)   Hence, transition from primitive individuals to modern individuals is possible
(5)   Transition from primitive individuals to modern individuals is not possible
(6)   Hence, the state of nature myth does not reveal basic human nature

The first premise is assumed by Hobbes and Locke. (2) is Rousseau’s contribution, since he claims taking the state of nature myth seriously entails primitive individuals - as he understands them - will be the appropriate sort of entity to reveal basic human nature. If this is so, then the transition to modern individuals must be possible, i.e. (3), and so by logic the consequent follows, i.e. (4). But I claim Rousseau believes (5) as well, i.e. he doesn’t think it is possible for this transition to occur. If so, then since we’ve derived a contradiction from our assuming (1), we must take that back, and so we have (6) which is the negation of (1).

That said, premise (5) is – I think – ambiguous, and this may make it seem less plausible than it is. Consider the following three ways to read “possible” in this premise:

  • Metaphysical – As a matter of fact, independent of what humans think about it, it is impossible for primitive individuals to transition to modern individuals

  • Epistemic – The putative transition from primitive individuals to modern individuals is not something we could know about

  • Nomological – It is incompatible with the laws of nature that it’s possible for primitive individuals to transition to modern individuals

If we read (5) in the metaphysical sense, then it’s clearly false. The world doesn’t care what we know or don’t.

If we read (5) in the epistemic sense, then it seems (5) might be true, but then I think Rousseau would reject (3). Simply put, there’s no reason to think there is a connection between the existence of primitive individuals and what we could or couldn’t know about them.

However, if we read (5) in the nomological sense, then it seems (5) might be true, and (3) might be as well. With respect to the former, Rousseau would be claiming the laws of nature rule out this transition, and he might motivate this by reflecting on the difficulties inherent in bridging a non-reasoning creature to the sort of reasoning creatures we are, among other things. Additionally, (3) might still be accepted since there’s plausibly a link between primitive individuals revealing basic human nature and nomological possibility.

I’ll let you sort out whether you find the preceding convincing or not.

Sketches of Love

What follows treats love as consisting entirely of desires and motivational profile:
x loves y just in case x desires goods for y up to and greater than what x takes y to deserve
We might have as a dual:
x hates y just in case x desires bad for y up to a greater than what x takes y to deserve

Clarification 1: When John loves Sally, John wants good things to happen to Sally in general. John might want goods for Sally even if John isn't involved in Sally obtaining said goods.

Clarification 2: When John merely likes Sally, John wants good things for Sally that Sally deserves. Note, John not wanting Sally to receive goods greater than what John thinks Sally deserves is not equivalent to John wanting Sally to not receive goods greater than what John thinks Sally deserves. The latter - but not the former - would lead to John being upset if Sally did receive such goods.

Clarification 3: One might hold - as Velleman does - that John desires goods for Sally out of respect for her capacity for practical reasoning. I would not accept this though. It seems to me love for another person is love of that other person's qualities, because that's all there is to the other person. I can't imagine a table absent extension, color, shape, etc.; I can't imagine Sally absent all her qualities, so how could I love such a thing?

  • Response 1: If one loves another only for their qualities, then since these qualities can be instantiated elsewhere, the beloved is not unique, and that seems counterintuitive.

  • Rejoinder: While true qualities can be instantiated elsewhere, quality combinations are rarer. There are many blue-eyed individuals, but fewer blue-eyed brown-haired individuals. Attending to the configuration of a beloved sharply restricts the likelihood of another individual exhibiting the same quality set. Moreover, everyone has a height, but each person has a specific height. For each quality, each person has both a determinable and determinate aspects. Focusing on the determinate aspect sharply restricts the likelihood of another exhibiting the same determinate quality set. It is not simply that Sally has blue eyes, brown hair, etc., but that Sally has this shade, hue, and saturation, along with her many other features, which make her rather rare.

  • Response 2: If a beloved perished but all the beloved's qualities were found in a duplicate, would we love the duplicate? Likely not, so there must be something beyond the mere qualities.

  • Rejoinder: I’m not sure what to make of this exotic thought experiment, but I’m inclined to say – if all the properties are the same, including memories, etc. – then ‘yes’. Cp. Hurka who asks if our beloved is replaced with a clone with all the same properties would we still feel a sense of loss. He infers from answering this affirmatively that there is something special about the beloved beyond properties. I think this inference is fallacious. Of course I’d still feel a sense of loss, someone has died. Death is a loss. This doesn’t yet show there’s something beyond the properties of my beloved.

Clarification 4: Some qualities we dislike are found in those we love. John might dislike when others interrupt him in general, but dislike it much less when one interrupts him in a charismatic or charming manner. Similarly, things we dislike in general we might even enjoy if done by our lover because we generally like when things are done, say, cleverly or charismatically, and we find our lover clever or charismatic.

Fake Coins Puzzle


There are 12 coins before you, one of which is fake. The fake coin is either heavier than or lighter than the other 11 coins. The legitimate coins all weigh the same. You have a balance scale you can use to weigh the coins. You can use the scale at most three times. How do you find the fake coin?


Number the coins 1-12. Separate the coins into a pile of 1,2,3,4, a pile of 5,6,7,8, and a pile of 9,10,11,12. Let "f" denote the fake coin. Let the predicate "H" denote heavy and the predicate "L" denote light.

Weigh 1: 1,2,3,4 x 5,6,7,8. There are three possible outcomes:
Outcome I: 1,2,3,4 = 5,6,7,8. f is among 9,10,11,12.
Weigh 1.2: 1,9 x 10,11, where 1 is clearly not f. There are three possible outcomes:
Outcome I: 1,9 = 10,11. f is 12. DONE.
Outcome II: 1,9 > 10,11. Either H(9) or L(10) or L(11).
Weigh 1.2.3: 10 x 11. There are three possible outcomes:
Outcome I: 10 = 11. Then f is 9. DONE.
Outcome II: 10 > 11. Then f is 11. DONE.
Outcome III: 10 < 11. Then f is 10. DONE.
Outcome III: 1,9 < 10,11. Either L(9) or H(10) or H(11).
Weigh 1.2.3: 10 x 11. There are three possible outcomes:
Outcome I: 10 = 11. Then f is 9. DONE.
Outcome II: 10 > 11. Then f is 10. DONE.
Outcome III: 10 < 11. Then f is 11. DONE.
Outcome II: 1,2,3,4 > 5,6,7,8. f is either H(1), H(2), H(3), H(4), L(5), L(6), L(7), or L(8).
Weigh 1.2: 4,5,6,7 x 8,9,10,11. There are three possible outcomes:
Outcome I: 4,5,6,7 = 8,9,10,11. Then f is either H(1) or H(2) or H(3).
Weigh 1.2.3: 1 x 2. There are three possible outcomes:
Outcome I: 1 = 2. Then f is 3. DONE.
Outcome II: 1 > 2. Then f is 1. DONE.
Outcome III: 1 < 2. Then f is 2. DONE.
Outcome II: 4,5,6,7 > 8,9,10,11. Then f is either H(4) or L(8).
Weigh 1.2.3: 1 x 4. There are two possible outcomes:
Outcome I: 1 = 4. Then f is 8. DONE.
Outcome II: 1 < 4. Then f is 4. DONE.
Outcome III: 4,5,6,7 < 8,9,10,11. Then f is either L(5) or L(6) or L(7).
Weigh 1.2.3: 5 x 6. There are three possible outcomes:
Outcome I: 5 = 6. Then f is 7. DONE.
Outcome II: 5 < 6. Then f is 5. DONE.
Outcome III: 5 > 6. Then f is 6. DONE.
Outcome III: 1,2,3,4 < 5,6,7,8. f is either L(1), L(2), L(3), L(4), H(5), H(6), H(7), or H(8).
Weigh 1.2: 10,11,12,1 x 2,3,4,5. There are three possible outcomes:
Outcome I: 10,11,12,1 = 2,3,4,5. Then f is either H(6) or H(7) or H(8).
Weigh 1.2.3: 6 x 7. There are three possible outcomes:
Outcome I: 6 = 7. Then f is 8. DONE.
Outcome II: 6 > 7. Then f is 6. DONE.
Outcome III; 6 < 7. Then f is 7. DONE.
Outcome II: 10,11,12,1 > 2,3,4,5. Then f is either L(2) or L(3) or L(4).
Weigh 1.2.3: 2 x 3. There are three possible outcomes:
Outcome I: 2 = 3. Then f is 4. DONE.
Outcome II: 2 > 3. Then f is 3. DONE.
Outcome III: 2 < 3. Then f is 2. DONE.
Outcome III: 10,11,12,1 < 2,3,4,5. Then f is either L(1) or H(5).
Weigh 1.2.3: 1 x 4. There are two possible outcomes:
Outcome I: 1 = 4. Then f is 5. DONE.
Outcome II: 1 < 4. Then f is 1. DONE.

Garbage Logic


One sunny afternoon John asks Sally how she's doing, and Sally responds that she isn't happy. Sally then quotes the song by the band Garbage - "I'm only happy when it rains." John then claims Sally has committed a fallacy. Is John correct?


To get a feel for the question, consider whether you think the following is a good inference:

(i) S is only happy if it rains
(ii) It does not rain
(iii) Hence, S is not happy

Let "It rains" be denoted by Q and "S is happy" by P. If you think (i) has the form (Q->P) then this will be invalid. You might think this because "if" on its own seems to be introducing "It rains" as the antecedent of a material conditional. Then (i) is equivalent to: "It rains, only if S is happy." That is:

(1) It rains only if S is happy (Q->P)
(2) It does not rain (~Q)
(3) Hence, S is not happy (~P)

On the other hand, if you think (i) has the form (P->Q), then the argument is valid. You might think this because "only if" is typically taken to introduce the consequent of a material conditional, and "S is only happy if..." is plausibly read as "S is happy only if...". Then (i) is equivalent to "S is happy only if it rains." That is:

(4) S is happy only if it rains (P->Q)
(5) It does not rain (~Q)
(6) Hence, S is not happy (~P)

There are two further options as the setup permits another reading:

(iv) S is only happy if it rains
(v) S is not happy
(vi) Hence, it does not rain

So that taking "if" to introduce the antecedent, we have the valid:

(7) It rains only if S is happy (Q->P)
(8) S is not happy (~P)
(9) Hence, it does not rain (~Q)

And if you take "only happy if" to introduce the consequent, we have the invalid:

(10) S is happy only if it rains (P->Q)
(11) S is not happy (~P)
(12) Hence, it does not rain (~Q)

So, whether a fallacy has been committed depends on whether Sally intended to infer "it does not rain" or "Sally is not happy, as well as whether "Sally is only happy if it rains" should be read as "Sally is happy only if it rains" or "It rains only if Sally is happy."

Concerning the first, I take Sally to be supporting the claim "I'm not happy" by appealing to the fact that it is not raining, which is common knowledge. If this is correct, then the second premise of the argument should be "It does not rain." So we can rule out setup (vi)-(vi).

Concerning the second, I take Sally to be claiming that if she's happy, then it rains. That is, Sally is making a valid argument and John is incorrect. This reading is also consistent with Sally not being happy, but it raining nevertheless. In other words, all we know is that if Sally is happy then it's raining, and if it's not raining then Sally isn't happy. This is also a bit sadder. Sally isn't even happy all and only those times it rains. Rather, Sally is only happy some of the times it rains.

Exhaustive Paradox


John asks Sally if she is tired.
Sally responds: "I'm not tired, I'm exhausted."
John responds: "Well, I'm glad to hear you aren't exhausted!"

Sally is perplexed. But so is John. Explain both perplexities.


Clearly, what Sally means is that she is not just tired. That is, she is both exhausted and tired. So John suggesting she is not exhausted is perplexing to Sally.

Still, claiming to not be tired and to be exhausted is an odd way to claim to be both tired and exhausted. At least, John thinks so. He reasons that for any agent S, if S is exhausted then S is tired, since being exhausted is an extreme form of being tired. Hence, to claim:

  1. S is exhausted


       2. S is tired

So claiming, in addition:

       3. S is not tired

Is inconsistent. But John is trying to be charitable, and so’d rather not attribute an inconsistency to Sally. Rather, John takes Sally at her word when she claims "I'm not tired." Moreover, John believes, as is plausible:

        4. S is not tired


        5. S is not exhausted

And since John is a nice guy, he's glad to hear Sally isn't exhausted given that she isn't tired. Of course, that still leaves Sally as speaking inconsistently, since she explicitly says she is exhausted, and this conflicts with (5). In other words, if John assumes Sally speaks consistently then either Sally is not tired and not exhausted or tired and exhausted, either of which conflicts with Sally’s expressed claim. John is perplexed because he seems forced to conclude his friend Sally is inconsistent.


Consider the task of teaching someone to whistle. A natural strategy when teaching someone to whistle is to describe to your pupil how they should hold their mouth, tongue, etc., so that they may imitate the sound you make when you successfully whistle. This is not, however, a very successful pedagogical strategy. This strategy amounts to throwing true claims at the pupil and hoping they stick. A less natural strategy, a better strategy I think, is to have the pupil attempt to whistle themselves and, of course, fail. As they fail to whistle, however, you manipulate your mouth, tongue, etc., so that you imitate the sound they produce in their failure. Once you are able to imitate their sound, do so while slowly manipulating your mouth, tongue, etc., to the whistle position you have mastered. Once you understand the steps, describe each step to your pupil so they see how to get from their noise to your whistle. In other words, teach them how to whistle from what they already know, not from what you already know. 

For the Sake of Argument...

I had an instructor who thought hard about formal systems that might underwrite analysis of speech acts like supposition and asserting. He argued as a matter of logic, asserting entailed supposing, though supposing did not entail asserting. For example, the following would be counted as valid:

  1. John AST(The store is open)

  2. Hence, John SUP(The store is open)

While the following would not count as valid:

  1. John SUP(The store is open)

  2. Hence, John AST(The store is open)

I agree with the latter not counting as valid. Asserting seems clearly associated with a norm of truth in every case, while supposing does not. John might claim to know p while supposing not p, without intuitive conflict. In contrast, John claiming to know p while asserting not p, seems a misuse of asserting, i.e. a lie. He's surely asserted, but he's violated a norm.

Does this make trouble for the first argument too? Not obviously. John asserting p comes with a norm of assertion, and if it's entailed John supposes p as well, we might think John's supposing in this case comes with a norm of assertion as well. That doesn't mean John can't suppose without the norm, and indeed, in many cases he will do just that.

That said, I do think there's trouble holding the first entailment. Supposing as an attitude seems to me to involve - in every case - direction towards some further goal. John doesn't simply suppose the store is open. Rather, John supposes the store is open for a reason. This is clearest, I think, in situations where one might suppose something for the sake of contradiction, i.e. reductio proofs. John might suppose p with the intention of drawing out some inconsistency in a premise set combined with background logical constraints. This strikes me as how supposing works in natural language as well. When John supposes the store is open, it's natural to ask - if you aren't already party to reason for the supposition - why John is supposing such a thing, e.g. do you need milk? do you have a shift today?

This feature of supposing in mind, return to the first argument. If John asserts the store is open, then if this argument is valid, it follows John supposes the store is open. But if John supposes the store is open, then there is some goal X John has in mind which motivates this supposition. Hence, in every case of assertion, there is some goal X agents have in mind which motivates the assertion. I find this implausible.

I'll detail why in another post. In the meantime, what do you think?

A Simple Question


Mathematician S is thinking of a number which is either 1, 2, or 3. Mathematician P can ask S only one question to determine which number S is thinking of. S can only answer "Yes", "No", or "I don't know" to the question posed by P.


What question might P ask to determine which number S is thinking of?


There are many questions P might ask to determine S's number. I'll share what I'd ask S: If n is an odd integer larger than any you've divided any number into, is n divisible without remainder by the number you're thinking of? Let m be S's number. There are three options:

  1. S knows n is divisible without remainder by m iff m is 1
  2. S knows n is not divisible without remainder by m iff m is 2
  3. S does not know whether n is divisible without remainder by m or not iff m is 3

To see other question P might ask, check out the forum where I came across the puzzle here.