The Fifth Way, remixed even more

In the previous two posts (here and here) I offered interpretations or remixes of Aquinas’s Fourth and Fifth ways read as ways of showing how a theistic Aristotelianism solves a pressing problem that the basic Aristotelian metaphysics cannot solve.

Here I want to do again for the Fifth Way, but now I will depart further from the text, and so while the previous two posts might have been interpretations, this one is much more of just a remix of the Fifth Way, with some ingredients from my version of the Fourth Way thrown in.

On Aristotelian metaphysics, each substance aims at its own good. The good of a substance is defined by the substance’s form, and the form points the substance at that good. But this good is just an internal good of the substance. Think of this internal good as akin to MacIntyre’s internal goods of a practice. The directedness at the internal goods is largely a matter of a priori metaphysical reasoning about substance. But now let’s go back to the things themselves—for, after all, the Five Ways are supposed to be empirical. If we do that, we come across two facts I want to stress.

First, the internal goods of substances tend to be intelligible to us as goods independently of the forms of these substances. Squirrels grow and reproduce. We understand growing and reproduction as valuable features. Imagine that squirrels instead characteristically scratched themselves to near-death. Even if their nature specified such self-scratching as their end, without a further more comprehensive story such self-scratching wouldn’t be intelligible to us as a good. Now, it is true that we tend to judge things by ourselves: it is also our human good to grow and to reproduce, and so it is easy for us to recognize that as good in squirrels. But I do not think we should say that when we judge squirrels’ growth and reproduction as a good thing independently of the form of the squirrel we are simply mistaken—and yet if we were just imposing merely human standards, we would be mistaken.

We might make the point as follows. It is good for a squirrel to fulfill its form by growing and reproducing. But it is also good, in a different sense of “good”, that the squirrel’s form includes growth and reproduction. This different sense of “good” is missing from basic Aristotelianism, a point central to my reading of the Fourth Way.

So we have something that calls for an explanation: Why is the squirrel’s form aimed at something that is actually good in this further sense?

And here is a related and but less abstract question. The teleology of a squirrel harmonizes to a significant extent with the goods of other species. We have an ecology. A “circle of life”.

The squirrel’s activity, thus, is not only directed at its internal good, and that internal good is intelligible as a good apart from its internal form, but the pursuit of that internal good harmonizes with the goods of other things in nature. This coordination between the ends of different species is something that basic Aristotelianism has a serious difficulty explaining.

There are thus two senses in which there are external goods found in nature: first, the internal goods are themselves typically intelligible as goods independently of the forms that define them; second, the end-directed activities of the organisms are good for the ecology at large. Both of these call for an explanation, and Aquinas’ suggested explanation seems excellent: “Therefore some intelligent being exists by whom all natural things are directed to their end.”

Note that the ecological dimensions might be explained evolutionarily, as long as we have an explanation of the coincidence between the normative and the statistical, a coincidence that forms the heart of my previous reading/remix of the Fifth Way.

The Fifth Way, also remixed

Thomas writes:

We see that things which lack intelligence, such as natural bodies, act for an end, and this is evident from their acting always, or nearly always, in the same way, so as to obtain the best result. Hence it is plain that not fortuitously, but designedly, do they achieve their end. Now whatever lacks intelligence cannot move towards an end, unless it be directed by some being endowed with knowledge and intelligence; as the arrow is shot to its mark by the archer. Therefore some intelligent being exists by whom all natural things are directed to their end; and this being we call God.

Central to Aristotle’s thought is the normative thesis that all substances have proper functions or ends defined by their immanent forms. Moreover, Aristotle makes the statistical claim that for the most part things things function correctly—they function to fulfill their ends.

The statistical claim is epistemologically important: that an activity or structure is usually exhibited by members of a kind is a central piece of evidence for that activity’s or structure’s correctness. But logically the statistical facts and the normative facts are independent: it is logically possible for all sheep to be three-legged, or for only a few pecan trees to produce pollen.

To see that we are committed to the connection between the normative and the statistical facts, consider the ridiculousness of the hypothesis that one of the ends of salmon is to prove theorems about high-dimensional topology. The utter unsuitability of the salmon brain to that end is conclusive evidence against the hypothesis. But this is only if we think there is a connection between the normative and the statistical facts—without such a connection, we could simply suppose that all salmon fall short of their topological researcher nature.

Note, too, just how massive the coincidence between the normative and statistical facts is: we see it across millions of species.

As Aquinas concedes, in intelligent substances we have some hope of an explanation of the coincidence: the intelligent substance consciously aims at its self-fulfillment. (Though leaning on this may be too much of a concession, because we still need to explain why this aiming isn’t futile, like a crank’s attempts to trisect angles.) But why do unintelligent substances’ activities in fact harmonize with their self-fulfillment, and do so massively, across all the millions of species we have? Why is it that we do not salmon-like fish with mathematical activity as their purpose, snake-like reptiles with flying as their end, and apes whose primary purpose is turning their bodies into gold by exposure to solar radiation?

A theistic explanation of the massive coincidence is compelling, and it provides another theistic solution to the shortcomings of a pure Aristotelian system.

The Fourth Way, remixed

I’m playing with a reading—or perhaps remix—of Aquinas’ Fourth and Fifth Ways as giving a theistic solution to a problem that non-theistic Aristotelianism has no solution to. In this post, I will discuss the Fourth Way, and in the next, the Fifth.

The Fourth Way starts with the principle that degreed predicates, predicates where it makes sense to talk of “more” and “less”, are predicated in comparison to a maximal case. Infamously, however, given modern science, Aquinas’ down-to-earth illustration of that principle, namely that heat is predicated in comparison to the maximal case—allegedly, fire—is not not an example of the principle, but is actually a counterexample to it. There just is no such thing as maximum heat.

But nevermind heat. Aquinas wants to apply the Fourth Way to goodness. Now, the Aristotelian system that he has adopted already has an account of the good: a thing is good to the extent that it fulfills its proper function, a proper function that is defined by the thing’s form. Note that this account, too, does not match Aquinas’ gradation principle: unlike in Plato, forms are not self-predicating, so rather than the Form of the Sheep being the most ovine thing possible, the Aristotelian form of the sheep is immanent in each sheep, directing each sheep to an ovine perfection that no object actually meets.

But the Aristotelian account of the good is incomplete. While it allows us to compare the goodness of things within a kind—the four-legged sheep better fulfills its form than a three-legged one—there are also meaningful value comparisons between kinds. When Jesus says that we are “worth more than many sparrows” (Mt. 10:31), what he is saying is entirely commonsense. The human has much more good than the sparrow. The sparrow has more good than the worm. And the worm has more good than a mushroom. There really is a something like a great chain of being in reality. These comparisons, however, are not simply grounded in the immanent forms of things. The form of the worm need make no reference to mushrooms, nor that of a mushroom to worms.

Note that these interspecies value comparisons not only cannot be read off from the immanent forms, but sometimes they are in a kind of tension with the immanent forms. An earthworm’s form limits the neural development of the worm. Were the worm to grow a brain as big as a dog’s, it wouldn’t be able to burrow as well. And a mushroom that walked around would fail to be properly rooted as a mushroom ought.

Interspecies value comparison is a genuine problem that Aristotelianism faces, though some Aristotelians are willing to bite the bullet and deny the meaningfulness of such comparisons. Platonism did not face this problem—it could just talk of varying degrees of participation in the Form fo the Good—but Platonism lacked a satisfactory solution to the problem of intraspecies comparisons (Platonism’s solution would be to posit a self-exemplified Form for each species, which would involve the absurd idea that there is a perfect Sheep, which somehow manages to be both a sheep and immaterial, and we have all sorts of silly questions about whether it is male or female, what color it is, whether it has an even or an odd number of hairs, etc.)

A theistic Aristotelianism, however, has a solution to the problem of interspecies value comparison, in addition to non-theistic Aristotelianism’s solution to the intraspecies’ problem. There is a great chain of being defined by the ways in which the various species participate in the being that has all perfections. The human exemplifies intellection, the sparrow approximates omnipresence through rapid movement and exemplifies a significant degree of intelligence, the worm approximates omnipresence less well and has a lower degree of intelligence, while the mushroom at least exemplifies life. What grounds the goodness of these qualities independently of the forms of the things they are found in, and what makes for their axiological directionality (more intelligence is better than less), is then comparison to the maximal case, namely God.

Note that while this gives something like a great chain of being, it need not exactly be a great chain of being. We should not seek after a strictly total ordering—a partial ordering matches intuition better.

I don’t have a knock-down argument that theistic Aristotelianism is the only good Aristotelian solution to the problem of interspecies comparison. But it is a very good solution, and so once we have accepted basic Aristotelianism, it gives us significant reason to adopt the theistic version.

An earlier, more compact, version of this argument is here.

The General Composition Question

Peter van Inwagen distinguishes the General Composition Question (GCQ), which is to give necessary and sufficient conditions for the claim that the xs compose y without mereological vocabulary, from the Special Composition Question (SCQ), which is to give non-mereological necessary and sufficient conditions for the claim that there is a y such that the xs compose y again without mereological vocabulary. He thinks that he can answer the SCQ as:

1. The xs compose something iff there is exactly one x or the activity of the xs constitutes a life.

But he doesn’t try to give an answer to the GCQ, and suspects an answer can’t be given.

It is now seeming to me that van Inwagen should give a parallel answer to GCQ as well:

2. The x compose y iff the xs compose* y.

3. The xs compose* y iff every one of the xs is a part* of y and everything that overlaps* y overlaps* at least one of the xs.

4. x overlaps* y iff x and y have a part* in common.

5. x is a part* of y iff x = y or x’s activity constitutes engagement in the life of y.

Here, (3) and (4) mirror the standard mereological definition of composition and overlap, but with asterisks added. The asterisked concepts, however, bottom out in non-mereological concepts.

One might worry that constitution is a mereological concept. But if it is, then van Inwagen’s answer to the SCQ is also unsatisfactory because it uses constitution.

I feel that (2)–(5) might have some simple counterexample, but I can’t see one (or at least not one that isn't also a counterexample to van Inwagen's answer to the SCQ).

By the way, there is a cheekier answer to the GCQ:

6. The xs compose y iff the xs and y satisfy the predicate “composes” of the actual world’s late 20th century philosophical English language.

Note that here the response does not make any use of mereological vocabulary, since “‘composes’” (unlike “composes”) is not a piece of mereological vocabulary, but a piece of metalinguistic vocabulary.

Kantian antinatalism

Intuitively:

1. It is permissible to deliberately have children.

But there is a powerful Kantian antinatalist argument against (1). To decide rationally to have a child, one needs to have a purpose for the child’s existence. But to have a purpose for another person’s existence, no matter how good that purpose might be, is to treat that other person as a means rather than as an end. And that’s wrong.

Assuming the Kantian thesis that it is wrong to have an end for another person’s existence, the only way to block the argument against (1) is to find a way to rationally motivate having a child without having to have a purpose for the child’s existence. How can this be done?

So one needs a reason to have a child which is not grounded in having a purpose for the child. Such reasons can exist. For instance, if I promise you to make a scarf, my reason to make the scarf is grounded in my promise to make the scarf rather than in any purpose for the scarf itself.

This points to a way out of the Kantian antinatalist argument. A couple might have a duty, perfect or imperfect, to attempt to have a child. If so, they need not have a purpose for the child, but only a purpose to attempt having a child. Such a duty could come from a divine command or from some kind of natural law perspectives (both of which are compatible with the broadly Kantian opposition to treating others as mere means).

Few people, apart from Catholics, Orthodox Jews and optimistic utilitarians, think there is any duty to have children. But thinking that there is such a duty may be the best way to get out of Kantian antinatalism.

Divine command, natural law and arbitrariness

People often levy an arbitrariness objection against divine command theory:

1. If God simply chooses what we ought, why did he choose to command kindness rather than cruelty?

It occurs to me that an advocate of theistic natural law probably cannot levy the arbitrariness object. For there is a structurally very similar question about theistic natural law:

2. If God simply chooses which natures to create, why did he choose to create beings with our basic physical structure and a nature that requires kindness rather than beings with our basic physical structure but a nature that requires cruelty?

It might be retorted that logical space does not contain a nature that specifies cruelty and yet the same basic physical structure as ours. This is plausible to me, but the main reason to doubt that there could be such a nature is some theistic story such as that all natures are ways of imitating God, and it is incompatible with divine goodness that he be imitable in such a cruel way. And this, in turn, is quite parallel to the standard divine command response to (1), that it is incompatible with divine goodness that he command cruelty to beings like us.

I think theistic natural law does have advantages over divine command theory. But a better resolution to the arbitrariness objection does not seem to be one of these advantages.

The composition of a substance

Start with this plausible observation:

1. Any part of me either is an accident of me or has an accident.

For consider this: my corporeal parts all have accidents of size, shape, color, etc. And my non-corporeal parts are my soul or form, as well as my accidents. My soul has accidents: such as the accident of thinking about this or that. And my accidents are my accidents.

Now, add this plausible thesis:

2. Any accident of a part of me is identical with an accident of me.

Thus, my arm’s being tanned is identical with my being tanned-in-the-arm. Further:

3. An accident of a thing is a part of that thing.

Given 1-3, we conclude the following:

4. Any part of me has at least one accident of me as a part.

For suppose that x is a part of me. Then by (1), x is an accident of me or has an accident. If x is an accident of me, then x has an accident of me, namely x itself, as an improper part. If x has an accident y, then y is a part of x by (3) and identical with an accident of me by (2), so once again x has an accident of me as a part.

Now the standard definition of composition is:

5. The xs compose y if and only if every part z of y has a part in common with at least one of the xs.

It follows from (4) and (5) that:

6. I am composed of my accidents.

For every part of me has one of my accidents as a part by (4), and that accident is of course an improper part of one of my accidents.

But (6) seems really wrong!

Thomas Aquinas has a nice way out of (6). One of my parts is my esse, my act of being, and my esse has no proper parts, and no parts in common with any of my accidents. If Aquinas is right, then it seems (4) needs to be modified to:

7. Any part of me is either my esse or has at least one accident of me as a part.

Replacing (4) with (7) in the argument, we get:

8. I am composed of my esse and my accidents.

But that seems wrong, too. For the omission of form is really glaring.

One could get out of (8) if one supposed that my form has its own esse as a part of it. But that doesn’t seem right.

My own view is that (8) may actually be correct if we stipulate “compose” to be defined by (5). But what that points to is the idea that “compose” is not rightly defined by (5).

Distancing oneself from one's brain

It can be quite useful for someone suffering from a variety of brain conditions, such as obsessive compulsive disorder, to deliberately distance themselves from their brain’s unfortunate doings, by saying to themselves things like: “That’s not me, just my brain.”

If physicalism is true, then brains are either identical with us or at least are the core of who we are. But “That’s not me, just me” is a contradiction while “That’s not me, just the core of my being” isn’t much of a distancing. A similar issue arises in second and third person contexts: if physicalism is true, one must admit brain problems to be grounded in that which is at the core of the other’s being.

The dualist, on the other hand, can pull off the distancing much more easily: “That’s not my soul, just my brain” makes perfect sense. An impairment in the brain is just an impairment of a body part, albeit one of the most important ones.

Of course, that something is a helpful way of thinking does not prove that it’s true. But it is an insight from the beginnings of Western philosophy that truth is generally better for us than falsehood, and so that something is a helpful way of thinking is some evidence that it is true. We may, thus, have some evidence for dualism here.

Being subject to a Dutch Book

I’ve periodically wondered why doing poorly when faced with a Dutch Book is supposed to be a sign of irrationality, but it’s not a sign of irrationality that rational people do poorly when faced with someone who hits all and only rational people on the head with a baseball bat.

This occurred to me today:

1. One cannot get a rational person to act against their own interest except by force, luck or superior information.

2. Putting a Dutch Book over someone with inconsistent credences does not require force, luck or superior information.

This seems to get at some of the intuition as to why being subject to a Dutch Book is supposed to be a sign of irrationality.

But I don’t know how much confidence we should have in (1). The exception clause already admits three exceptions. This sounds ad hoc. Would we be very surprised if more exceptions had to be added?

Still, there is some plausibility to (1), at least for self-interested rationality.

Consciousness of one's choices

Here is a plausible thesis:

1. Consciousness of one’s choice is necessary for moral responsibility.

I go back and forth on (1). Here is a closely related thesis that is false:

2. Knowledge of one’s choice is necessary for moral responsibility.

For imagine Alice who on the basis of a mistaken interpretation of neurosience thinks there are no choices. Then it could well be that Alice does not know that she is making any choices. But surely this mistake does not take away her moral responsibility for her choice.

Alice presumably still has consciousness of her choice, much as the sceptic still has perception of the external world. So Alice isn’t a counterexample to (1). But I wonder if (1) is very plausible once one has realized that (2) is false. For once we have realized that (2) is false, we realize that in Alice’s case the consciousness of her choice is not knowledge-conferring. And such consciousness just does not seem significant enough to matter for moral responsibility.

Against digital phenomenology

Suppose a digital computer can have phenomenal states in virtue of its computational states. Now, in a digital computer, many possible physical states can realize one computational state. Typically, removing a single atom from a computer will not change the computational state, so both the physical state with the atom and the one without the atom realize the same computational state, and in particular they both have the same precise phenomenal state.

Now suppose a digital computer has a maximally precise phenomenal state M. We can suppose there is an atom we can remove that will not change the precise phenomenal state it is in. And then another. And so on. But then eventually we reach a point where any atom we remove will change the precise phenomenal state. For if we could continue arbitrarily long, eventually our computer would have no atoms, and then surely it wouldn’t have a phenomenal state.

So, we get a sequence of physical states, each differing from the previous by a single atom. For a number of initial states in the sequence, we have the phenomenal state M. But then eventually a single atom difference destroys M, replacing it by some other phenomenal state or by no phenomenal state at all.

The point at which M is destroyed cannot be vague. For while it might be vague whether one is seeing blue (rather than, say, purple) or whether one is having a pain (rather than, say, an itch), whether one has the precise phenomenal state M is not subject to vagueness. So there must be a sharp transition. Prior to the transition, we have M, and after it we don’t have M.

The exact physical point at which the transition happens, however, seems like it will have to be implausibly arbitrary.

This line of argument suggests to me that perhaps functionalists should require phenomenal states to depend on analog computational states, so that an arbitrarily small of the underlying physical state can still change the computational state and hence the phenomenal state.

Functionalism and pain-likeness

Say that a functional property F is pain-like provided that a human is in pain if and only if the human has F.

Assuming functionalism, there is a functional property F₀ which is pain. Property F₀ will be pain-like, but it won’t be the only pain-like property. For there will be infinitely many ways of tweaking F₀ to generate functional properties F₁, F₂, ... that in humans are instantiated precisely when F₀ is, but that differ in instantiation among aliens. For instance, F₁ could be F₀ conjoined with the property of not currently thinking a thought that has seventeen levels of embedding (I take it that humans can’t think a thought with more than about three levels of embedding), while F₂ could be F₀ conjoined with the property of not consciously exercising magnetic sense, and so on.

There will thus be infinitely many pain-like properties that differ in when different aliens instantiate them. One of these pain-like properties, F₀, is pain. And now we have a difficult question for functionalism: What grounds the fact that this particular pain-like property is pain? Why is it that having F₀ is necessary and sufficient for hurting but having F₁ isn’t? What’s so special about F₀? Why is it that F₀ picks out a phenomenally unified type, but the other properties need not?

Fading knowledge of qualia

I am one of those people who do not have vivid memories of pains.

Suppose I stub my toe. While the toe is hurting, I know what the toe’s hurting feels like. After it stops hurting, for a while I still know what that felt like. But I know it less and less well as my memory fades, until eventually I know very little how it felt like. The whole process might take only a few minutes.

Thus, that mysterious “knowing what it’s like” involving qualia is something that comes with a parameter that varies as to how well you know it.

This should worry physicalists. Thin physicalists should worry because it doesn’t seem that the fading corresponds to any knowledge of the underlying physical reality. Thick physicalists who think that Mary just acquires a new recognitional concept when she sees red should worry, because it does not seem that there is any gradual loss of a concept. I continue to have the same “that experience” concept (the demonstrative “that” points to the same past experience, and does so in a first-personal way) and the recognitional abilities it enables (I can tell if another pain is like that one or not), even as my knowledge of what “that experience” is like fades.

It’s also not completely clear what a dualist should say about the fading of the knowledge. Normally, when knowledge fades, what happens is either that we lose details (as when I forget much of what I once learned in school about the Metis uprising), or we find the dispositional knowledge harder to make occurrent. But the fading is neither of these. Maybe what is happening is that our present knowledge becomes a less good representation of what it is the knowledge of.

A posteriori necessities

The usual examples of a posteriori necessities are identities between kinds and objects under two descriptions, at least one of which involves a contingent mode of presentation, such as water (presented as “the stuff in this pond”, say) and H₂O.

Such a posteriori necessities are certainly interesting. But we should not assume that these exhaust the scope of all a posteriori necessities.

For instance, Thomas Aquinas was committed to the existence of God being an a posteriori necessity: he held that necessarily God existed, but that all a priori arguments for the existence of God failed, while some a posteriori ones, like the Five Ways, succeeded.

For another theistic example, let p be an unprovable mathematical truth. Then p is, presumably, not a priori knowable. But God could reveal the truth of p, in which case we would know it a posteriori, via observation of God’s revelation. And, plausibly, mathematical truths are necessary.

For a third example, we could imagine a world where there is an odd law of nature: if anyone asserts a false mathematical statement, they immediately acquire hideous warts. In that world, all mathematical truths, including the unprovable ones, would be knowable a posteriori.

A defense of probabilistic inconsistency

Evidence E is misleading with regard to a hypothesis H provided that Bayesian update on E changes one’s credence in H in the direction opposed to truth. It is known that pretty much any evidence is misleading with regard to some hypothesis or other. That’s no tragedy. But sometimes evidence is misleading with regard to an important hypothesis. That’s no tragedy of the shift in the credence of that important hypothesis is small. But it could be tragic if the shift is significant—think of a quack cure for cancer beating out the best medication in a study due to experimental error or simply chance.

In other words, misleadingness by itself is not a big deal. But significant misleadingness with respect to an important hypothesis can be tragic.

Suppose I am lucky enough to start with consistent credences in a limited algebra F of propositions including q, and suppose I have a low credence in a consistent proposition q. Now two friends, whom I know for sure to speak only truth, speak to me:

• Alice: “Proposition q is actually true.”

• Bob: “She’s right, as always, but the fact that q is true is significantly misleading with respect to a number of quite important hypotheses in F.”

What should I do? If I were a perfect Bayesian agent, my likelihoods would be sufficiently well defined that I would just update on Alice saying her piece and Bob saying her piece, and be done with it. My likelihoods would embody prior probability assignments to hypotheses about the kinds of reasons that Alice and Bob could have for giving me their information, the kinds of important hypotheses in F that q could be misleading about, etc.

But this is too complicated for a more ordinary Bayesian agent like me. Suppose I could, just barely, do a Bayesian update on q, and gain a new consistent credence assignment on F. Even if Bob were not to have said anything, updating on q would not be ideal, because the ideal agent would update not just on q, but on the facts that Alice chose to inform me of q at that very moment, in those very words, in that very tone of voice, etc. But that’s too complicated for me. For one, I don’t have enough clear credences in hypotheses about different informational choices Alice could have made. So if all I heard was Alice’s announcement, updating on q would be a reasonable choice given my limitations.

But with Bob speaking, the consequences of my simply updating on q could be tragic, because Bob has told me that q is significantly misleading in regard to important stuff. What should I do? One possibility is to ignore both statements, and leave my credences unchanging, pretending I didn’t hear Alice. But that’s silly: I did hear her.

But if I accept q on the basis of Alice’s statement (and Bob’s confirmation), what should I do about Bob’s warning? Here is one option: I could raise my credence in q to 1, but leave everything else unchanged. This is a better move than just ignoring what I heard. For it gets me closer to the truth with regard to q (remember that Alice only says the truth), and I don’t get any further from the truth regarding anything else. The result will be an inconsistent probability assignment. But I can actually do a little better. Assuming q is true, it cannot be misleading about propositions entailed by q. For if q is true, then all propositions entailed by q are true, and raising my credences in them to 1 only improves my credences. Thus, I can safely raise my credence in everything entailed by q to 1. Similarly, I can safely lower my credence in anything that entails ∼q to 0.

Here, then, is a compromise: I set my credence in everything in F entailed by q to 1, and in everything in F that entails ∼q to 0, and leave all other credences for things in F unchanged. This has gotten me closer to the truth by any reasonable measure. Moreover, the resulting credences for F satisfy the Zero, Non-negativity, Normalization, Monotonicity, and Binary Non-Disappearance axioms, and as a result I can use a Level-Set Integral prevision to avoid various Dutch Book and domination problems. [Let’s check Monotonicity. Suppose r entails s. We need to show that C(r)≤C(s). Given that my original credences were consistent and hence had Monotonicity, the only way I could lack Monotonicity now would be if q entailed r and s entailed ∼q. Since r entails s, this would mean that q would entail ∼q, which would imply that q is not consistent. But I assumed it was consistent.]

I think this line of reasoning shows that there are indeed times when it can be reasonable to have an inconsistent credence assignment.

By the way, if I continue to trust the propositions I had previously assigned extreme credences to despite Bob’s ominous words, an even better update strategy would be to set my credence to 1 for everything entailed by q conjoined with something that already had credence 1, and to 0 for everything that when conjoined with something that had credence 1 entails ∼q.