More decision theory stuff

Suppose there are two opaque boxes, A and B, of which I can choose one. A nearly perfect predictor of my actions put $100 in the box that they thought I would choose. Suppose I find myself with evidence that it’s 75% likely that I will choose box A (maybe in 75% of cases like this, people like me choose A). I then reason: “So, probably, the money is in box A”, and I take box A.

This reasoning is supported by causal decision theory. There are two causal hypotheses: that there is money in box A and that there is money in box B. Evidence that it’s 75% likely that I will choose box A provides me with evidence that it’s close to 75% likely that the predictor put the money in box A. The causal expected value of my choosing box A is thus around $75 and the causal expected value of my choosing box B is around $25.

On evidential decision theory, it’s a near toss-up what to do: the expected news value of my choosing A is close to $100 and so is that of my choosing B.

Thus, on causal decision theory, if I have to pay a $10 fee for choosing box A, while choosing box B is free, I should still go for box A. But on evidential decision theory, since it’s nearly certain that I’ll get a prize no matter what I do, it’s pointless to pay any fee. And that seems to be the right answer to me here. But evidential decision theory gives the clearly wrong answer in some other cases, such as that infamous counterfactual case where an undetected cancer would make you likely to smoke, with no causation in the other direction, and so on evidential decision theory you refrain from smoking to make sure you didn’t get the cancer.

In recent posts, I’ve been groping towards an alternative to both theories. The alternative depends on the idea of imagining looking at the options from the standpoint of causal decision theory after updating on the hypothesis that one has made a specific choice. In current my predictor cases, if you were to learn that you chose A, you would think: Very likely the money is in box A, so choosing box A was a good choice, while if you chose B, you would think: Very likely the money is in box B, so choosing box B was a good choice. As a result, it’s tempting to say that both choices are fine—they both ratify themselves, or something like that. But that misses out the plausible claim that if there is a $10 fee for choosing A, you should choose B. I don’t know how best to get that claim. Evidential decision theory gets it, but evidential decision theory has other problems.

Here’s something gerrymandered that might work for some binary choices. For options X and Y, which may or may not be the same, let e_X(Y) be the causal expected value of Y with respect to the credences for the causal hypotheses updated with respect to your having chosen X. Now, say that the differential restrospective causal expectation d(X) of option X equals e_X(X) − e_X(Y). This measures how much you would think you gained, from the standpoint of causal decision theory, in choosing X rather than Y by the lights of having updated on choosing X. Then you should the option that provides a bigger d(X).

In the case where there is a $10 fee for choosing box A, d(B) is approximately $100 while d(A) is approximately $90, so you should go for box B, as per my intuition. So you end up agreeing with evidential decision theory here.

You avoid the conclusion you should smoke to make sure you don’t have cancer in the hypothetical case where cancer causes smoking but not conversely, because the differential retrospective causal expectation of smoking is positive while the differential retrospective causal expectation of not smoking is negative, assuming smoking is fun (is it?). So here you agree with causal decision theory.

What about Newcomb’s paradox? If the clear box has a thousand dollars and the opaque box has a million or nothing (depending on whether you are predicted to take just the opaque box or to take both), then the differential retrospective causal expectation of two-boxing is a thousand dollars (when you learned you two-box, you learn that the opaque box was likely empty) and the differential retrospective causal expectation of one-boxing is minus a thousand dollars.

So the differential retrospective causal expectation theory agrees with causal decision theory in the clear case (cancer-causes-smoking), the difficult case (Newcomb), but agrees with evidential decision theory in the $10 fee variant of my two-box scenario, and the last seems plausible.

But (a) it’s gerrymandered and (b) I don’t know how to generalize it to cases with more than two options. I feel lost.

Maybe I should stop worrying about this stuff, because maybe there just is no good general way of making rational decisions in cases where there is probabilistic information available to you about how you will make your choice.

Position: Assistant Professor of Bioethics, Tenure Track, Department of Philosophy, Baylor University

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My AI policy

I’ve been wondering what to allow and what to disallow in terms of AI. I decided to treat AI as basically persons and I put this in my Metaphysics syllabus:

Even though (I believe) AI is not a person and its products are not “thoughts”, treat AI much like you would a person in writing your papers. I encourage you to have conversations with AIs about the topics of the class. If you get ideas from these conversations, put in a footnote saying you got the idea from an AI, and specifically cite which AI. If you use the AI’s words, put them in quotation marks. (If your whole paper is in quotation marks, it’s not cheating, but you haven’t done the writing yourself and so it’s like a paper not turned in, a zero.) Just as you can ask a friend to help you understand the reading, you can ask an AI to help you understand the reading, and in both cases you should have a footnote acknowledging the help you got. Just as you can ask a friend, or the Writing Center or Microsoft Word to find mistakes in your grammar and spelling, you can ask an AI to do that, and as long as the contribution of the AI is to fix errors in grammar and spelling, you don’t need to cite. But don’t ask an AI to rewrite your paper for you—now you’re cheating as the wording and/or organization is no longer yours, and one of the things I want you to learn in this class is how to write. Besides all this, last time I checked, current AI isn’t good at producing the kind of sharply focused numbered valid arguments I want you to make in the papers—AI produces things that look like valid arguments, but may not be. And they have a distinctive sound to them, so there is a decent chance of getting caught. When in doubt, put in a footnote at the end what help you got, whether from humans or AI, and if the help might be so much that the paper isn’t really yours, pre-clear it with me.

An immediate regret principle

Here’s a plausible immediate regret principle:

1. It is irrational to make a decision such that learning that you’ve made this decision immediately makes it rational to regret that you didn’t make a different decision.

The regret principle gives an argument for two-boxing in Newcomb’s Paradox, since if you go for one box, as soon as you have made your decision to do that, you will regret you didn’t make the two-box decision—there is that clear box with money staring at you, but if you go for two boxes, you will have no regrets.

Interestingly, though, one can come up with predictor stories where one has regrets no matter what one chooses. Suppose there are two opaque boxes, A and B, and you can take either box but not both. A predictor put a thousand dollars in the box that they predicted you won’t take. Their prediction need not be very good—all we need for the story is that there is a better than even probability of their having predicted you choosing A conditionally on your choosing A and a better than even probability of their having predicted you choosing B conditionally on your choosing B. But now as soon as you’ve made your decision, and before you opened the chosen box, you will think the other box is more likely to have the money, and so your knowledge of your decision will make it rational to regret that decision. Note that while the original Newcomb problem is science-fictional, there is nothing particularly science-fictional about my story. It would not be surprising, for instance, if someone were able to guess with better than even chance of correctness about what their friends would choose.

Is this a counterexample to the immediate regret principle (1), or is this an argument that there are real rational dilemmas, cases where all options are irrational?

I am not sure, but I am inclined to think that it’s a counterexample to the regret principle.

Can we modify the immediate regret principle to save it? Maybe. How about this?

2. No decision is such that learning that you’ve rationally made this decision immediately makes it rationally required to regret that you didn’t make a different decision.

On this regret principle, regret is compatible with non-irrational decision making but not with (known) rational decision making.

In my box story, it is neither rational nor irrational to choose A, and it is neither rational nor irrational to choose B. Then there is no contradiction to (2), since (2) only applies to decisions that are rationally made. And applying (2) to Newcomb’s Paradox no longer yields an argument for two-boxing, but only an argument that it is not rational to one-box. (For if it were rational to one-box, one could rationally decide to one-box, and one would then regret that.)

The “rationally” in (2) can be understood in a weaker way or a stronger way (the stronger way reads it as “out of rational requirement”). On either reading, (2) has some plausibility.

An odd decision theory

Suppose I am choosing between options A and B. Evidential decision theory tells me to calculate the expected utility E(U|A) given the news that I did A and the expected utility E(U|B) given the news that I did B, and go for the bigger of the two. This is well-known to lead to the following absurd result. Suppose there is a gene G that both causes one day to die a horrible death and makes one very likely to choose A, while absence of the gene makes one very likely to choose B. Then if A and B are different flavors of ice cream, I should always choose B, because E(U|A) ≪ E(U|B), since the horrible death from G trumps any advantage of flavor that A might have over B. This is silly, of course, because one’s choice does not affect whether one has G.

Causal decision theorists proceed as follows. We have a set of “causal hypotheses” about what the relevant parts of the world at the time of the decision are like. For each causal hypothesis H we calculate E(U|H∧A) and E(U|H∧B), and then we take the weighted average over our probabilities, and then decide accordingly. In other words, we have a causal expected utility of D

• E_c(U|D) = ∑_HE(U|H∧D)P(H)

and are to choose A over B provided that E_c(U|A) = E_c(U|B). In the gene case, the “bad news” of the horrible death on G is a constant addition to E_c(U|A) and to E_c(U|B), and so it can be ignored—as is right, since it’s not in our control.

But here is a variant case that worries me. Suppose that you are choosing between flavors A and B of ice cream, and you will only ever ever get to taste one of them, and only once. You can’t figure out which one will taste better for you (maybe one is oyster ice cream and the other is sea urchin ice cream). However, data shows that not only does G make one likely to choose A and its absence makes one likely to choose B, but everyone who has G derives pleasure from A and displeasure from B and everyone who lacks G has the opposite result, and all the pleasures and displeasures are of the same magnitude.

Now, background information says that you have a 3/4 chance of having G. On causal decision theory, this means that you should choose A, because likely you have G, and those who have G all enjoy A. Evidential decision theory, however, tells you that you should choose B, since if you choose B then likely you don’t have the terrible gene G.

In this case, I feel causal decision theory isn’t quite right. Suppose I choose A. Then after I have made my choice, but before I have consumed the ice cream, I will be glad that I chose A: my choice of A will make me think I have G, and hence that A is tastier. But similarly, if I choose B, then after I have made my choice, and again before consumption, I will be glad that I chose B, since my choice B will make me think I don’t have G and hence that B was a good choice. Whatever I choose, I will be glad I chose it. This suggests to me that my there is nothing wrong with either choice!

Here is the beginning of a third decision theory, then—one that is neither causal nor evidential. An option A is permissible provided that causal decision theory with the causal hypothesis credences conditioned on one’s choosing A permits one to do A. An option A is required provided that no alternative is permissible. (There are cases where no option is permissible. That’s weird, I admit.)

In the initial case, where the pleasure of each flavor does not depend on G, this third decision theory gives the same answer as causal decision theory—it says to go for the tastier flavor. In the second case, however, where the pleasure/displeasure depends on G, it permits one to go for either flavor. In a probabilistic-predictor Newcomb’s Paradox, it says to two-box.

Gaze dualism and omnisubjectivity

I have toyed with a pair of theories.

The first is what I call gaze-dualism. On gaze-dualism, our sensory conscious experiences are constituted by a non-physical object—the soul—“gazing” at certain brain states. When the sensory data changes—say, when a sound goes from middle A to middle C—the subjective experience changes. But this change need not involve an intrinsic change in the soul. The change in experience is grounded in a change in the gazed-at brain state, a brain state that reflects the sensory data, rather than by a change in the gazing soul. (This is perhaps very close to Aquinas’ view of sensory consciousness, except that for Aquinas the gazed-at states are states of sense organs rather than of the brain.)

The second is an application of this to God’s knowledge of contingent reality. God knows contingent reality by gazing at it the way that our soul gazes at the brain states that reflect sensory data. God does not intrinsically change when contingent reality changes—the change is all on the side of the gazed-at contingent reality.

I just realized that this story makes a bit of progress on what Linda Zagzebski calls “omnisubjectivity”—God’s knowledge of all subjective states. My experience of hearing a middle C comes from my gazing at a brain state B_C of my auditory center produced by nerve impulses caused by my tympanic membrane vibrating at 256 Hz. My gaze is limited to certain aspects of my auditory center—my gaze tracks whatever features of my auditory center are relevant to the sound, features denoted by B_C, but does not track features of my auditory center that are not relevant to the sound (e.g., the temperature of my neurons). God’s gaze is not so limited—God gazes at every aspect of my auditory center. But in doing so, he also gazes at B_C. This does not mean that God has the same experience as I do. My experience is partly constituted by my soul’s gaze at B_C. God’s experience is partly constituted by God’s gaze at B_C. Since my soul is very different from God, it is not surprising that the experiences are different. However, God has full knowledge of the constituents of my experience: myself, my gaze, and B_C, and God’s knowledge of these is basically experiential—it is constituted by God’s gazing at me, my gaze, and B_C. And God also gazes at their totality. This is, I think, all we need to be able to say that God knows my sensory consciousness states.

My non-sensory experiences may also be constituted by my soul’s gazing at a state of my brain, but they may also be constituted by the soul’s gazing at a state of the soul. And God gazes at the constituents and whole again.

Diversity of inner lives

There is a vast and rather radical diversity in the inner conscious lives of human beings. Start with the differences in dreams: some people know immediately whether they are dreaming and others do not; some are in control of their dreams and others are not; some dream in color and others do not. Now move on to the differences in thought. Some think in pictures, some in words with sounds, some in a combination of words with sounds and written words, and some without any visual or aural imagery. Some people are completely unable to imagine things in pictures, others can do so only in a shadowy and unstable way, and yet others can do so in detail. Even in the case of close friends, we often have no idea about how they differ in these respects, and to many people the diversity in inner conscious lives comes as a surprise, as they assume that almost everyone is like them.

But in their outer behavior, including linguistic behavior, people seem much more homogeneous. They say “I think that tomorrow is a good day for our bike trip” regardless of whether they thought it out in pictures, in sounds, or in some other way. They give arguments as a sequence of logically connected sentences. Their desires, while differing from person to person, are largely comprehensible and not very surprising. People are more homogeneous outside than inside.

This contrast between inner heterogeneity and outward homogeneity is something I realized yesterday while participating in a workshop on Linda Zagzebski’s manuscript on dreams. I am not quite sure what to make of this contrast philosophically, but it seems really interesting. We flatten our inner lives to present them to people in our behavior, but we also don’t feel like much is lost in this flattening. It doesn’t really matter much whether our thoughts come along with sights or sounds. It would not be surprising if there were differences in skill levels that correlated with the characteristics of inner life—it would not be surprising if people who thought more in pictures were better at low-dimensional topology—but these differences are not radical.

Many of us as children have wondered whether other people’s conscious experiences are the same as ours—does red look the same (bracketing colorblindness) and does a middle C sinewave sound the same (bracketing hearing deficiencies)? I have for a while thought it not unlikely that the answer is negative, because I am attracted to the idea that central to how things look to us are the relationships between different experiences, and different people have sets of experiences. (Compare the visual field reversal experiments, where people who wear visual field reversal glasses initially see things upside-down but then it turns right-side-up, which suggests to me that the directionality of the visual field is constituted by relationships between different experiences rather than being something intrinsic.) I think the vast diversity in conscious but non-sensory inner lives gives us some reason to think that sensory consciousness also differs quite a bit between people—and gets flattened and homogenized into words, much as thoughts are.

Extrinsic well-being and the open future

Klaus: Sometimes how well or badly off you are at time t₁ depends on what happens at a later time t₂. A particularly compelling case of this is when at t₁ you performedan onerous action with the goal of producing some effect E at t₂. How well off you were in performing the action depends on whether the action succeeded—which depends on whether E eventuates at t₂. But now suppose the future is open. Then in a world with as much indeterminacy as ours, in many cases at t₁ it will be contingent whether the event at t₂ on which your well-being at t₁ depends eventuates. And on open future views, at t₁ there will then be no fact of the matter about your well-being. Hence, the future is not open.

Opie: In such cases, your well-being should be located at t₂ rather than at t₁. If you jump the crevasse, it is only when you land that you have the well-being of success.

Klaus: This does not work as well in cases where you are dead at t₂. And yet our well-being does sometimes depend on what happens after we are dead. The action at t₁ might be a heroic sacrifice of one’s life to save one’s friends—but whether one is a successful hero or a tragic hero depends on whether the friends will be saved, which may depend on what happens after one is already dead.

Opie: Thanks! You just gave me an argument for an afterlife. In cases like this, you are obviously better off if you manage to save your friends, but you aren’t better off in this life, so there must be life after death.

Klaus: But we also have the intuition that even if there were no afterlife, it would be better to be the successful hero than the tragic hero, and that posthumous fame is better than posthumous infamy.

Opie: There is an afterlife. You’ve convinced me. And moral intuitions about how things would be if our existence had a radically different shape from the one it in fact has are suspect. And, given that there is an afterlife, a scenario without an afterlife is a scenario where our existence has a radically different shape. Thus the intuition you cite is unreliable.

Klaus: That’s a good response. Let me try a different case. Suppose you perform an onerous action with a goal within this life, but then you change your mind about the goal and work to prevent that goal. This works best if both goals are morally acceptable, and switching goals is acceptable. For instance you initially worked to help the Niners train to win their baseball game against the Logicians, but then your allegiance shifted to the Logicians in a way that isn't morally questionable. And then suppose the Niners won. Your actions in favor of the Niners are successful, and you have well-being. But it is incorrect to locate that well-being at the time of the actual victory, since at that time you are working for the Logicians, not the Niners. So the well-being must be located at the time of your activity, and at that time it depends on future contingents.

Opie: Perhaps I should say that at the time Niners beat the Logicians, you are both well-off and badly-off, since one of your past goals is successful and the other is unsuccessful. But I agree that this doesn’t quite seem right. After all, if you are loyal to your current employer, you’re bummed out about the Logicians’ loss and you’re bummed out that you weren’t working for them from the beginning. So intuitively you're just badly off at this time, not both badly and well off. So, I admit, this is a little bit of evidence against open future views.

Consciousness and the open future

Plausibly:

1. There is a “minimal humanly observable duration” (mhod) such that a human cannot have a conscious state—say, a pain—shorter than an mhod, but can have a conscious state that’s an mhod long.

The “cannot” here is nomic possibility rather than metaphysical possibility.

Let δ denote an mhod. Now, suppose that you feel a pain precisely from t₀ to t₂. Then t₂ ≥ t₀ + δ. Now, let t₁ = t₀ + δ/2. Then you feel a pain at t₁. But at t₁, you only felt a pain for half an mhod. Thus:

2. At t₁, that you feel pain depends on substantive facts about your mental state at times after t₁.

For if your head were suddenly zapped by a giant laser a quarter of an mhod after t₁, then you would not have felt a pain at t₁, because you would have been in a position to feel pain only from t₀ to t₀ + (3/4)δ.

But in a universe full of quantum indeterminacy:

3. These substantive facts are contingent.

After all, your brain could just fail a quarter of an mhod after t₁ due to a random quantum event.

But:

4. Given an open future, at t₁ there are no substantive contingent facts about the future.

Thus:

5. Given an open future, at t₁ there is no fact that you are conscious.

Which is absurd!

Discrete time and Aristotle's argument for an infinite past

Aristotle had a famous argument that time had no beginning or end. In the case of beginnings, this argument caused immense philosophical suffering in the middle ages, since combined with the idea that time requires change it implies that the universe was eternal, contrary to the Jewish, Muslim and Christian that God created the universe a finite amount of time ago.

The argument is a reductio ad absurdum and can be put for instance like this:

1. Suppose t₀ is the beginning of time.

2. Before t₀ there is no time.

3. It is a contradiction to talk of what happened before the the beginning of time.

4. But if (1) is true, then (2) talks of what is before the beginning of time.

5. Contradiction!

It’s pretty easy to see what’s wrong with the argument. Claim (2) should be charitably read as:

• Not (before t₀ there is time).

Seen that way, (2) doesn’t talk about what happened before t₀, but is just a denial that there was any such thing as time-before-t₀.

It just struck me that a similar argument could be used to establish something that Aristotle himself rejects. Aristotle famously believed that time was discrete. But now argue:

6. Suppose t₀ and t₁ are two successive instants of time.

7. After t₀ and before t₁ there is no time.

8. It is a contradiction of what happened when there is no time.

9. But if (7) is true, then (7) talks of what is when there is no time.

10. Contradiction!

Again, the problem is the same. We should take (7) to deny that there is any such thing as time-after-t₀-and-before-t₁.

So Aristotle needed to choose between his preference for the discreteness of time and his argument for an infinite past.

What if there is no tomorrow?

There are two parts of Aristotle’s theory that are hard to fit together.

First, we have Aristotle’s view of future contingents, on which

1. It is neither true nor false that tomorrow there will be a sea battle

but, of course:

2. It is true that tomorrow there will be a sea battle or no sea battle.

Of course, nothing rides on “tomorrow” in (1) and (2): any future metric interval of times will do. Thus:

3. It is true that in 86,400,000 milliseconds there will be a sea battle or not.

(Here I adopt the convention that “in x units” denotes the interval of time corresponding to the displayed number of significant digits in x. Thus, “in 86,400,000 ms” means “at a time between 86,399,999.5 (inclusive) and 86,400,000.5 (exclusive) ms from now.”)

Second, we have Aristotle’s view of time, on which time is infinitely divisible but not infinitely divided. Times correspond to what one might call happenings, the beginnings and ends of processes of change. Now which happenings there will be, and when they will fall with respect to metric time (say, 3.74 seconds after some other happening), is presumably something that is, or can be, contingent.

In particular, in a world full of contingency and with slow-moving processes of change, it is contingent whether there will be a time in 86,400,000 ms. But (3) entails that there will be such a time, since if there is no such time, then it is not true that anything will be the case in 86,400,000 ms, since there will be no such time.

Thus, Aristotle cannot uphold (3) in a world full of contingency and slow processes. Hence, (3) cannot be a matter of temporal logic, and thus neither can (2) be, since logic doesn’t care about the difference between days and milliseconds.

If we want to make the point in our world, we would need units smaller than milliseconds. Maybe Planck times will work.

Objection: Suppose that no moment of time will occur in exactly x₁ seconds, because x₁ falls between all the endpoints of processes of change. But perhaps we can still say what is happening in x₁ seconds. Thus, if there are x₀ < x₁ < x₂ such that x₀ seconds from now and x₂ seconds from now (imagine all this paragraph being said in one moment!) are both real moments of time, we can say things about what will happen in x₁ seconds. If I will be sitting in both x₀ and x₂ seconds, maybe I can say that I will be sitting in x₁ seconds. Similarly, if Themistocles is leading a sea battle in 86,399,999 ms and is leading a sea battle in 86,400,001 ms, then we can say that he is leading a sea battle in 86,400,000 ms, even though there is no moment of time then. And if he won’t lead a sea battle in either 86,399,999 ms or in 86,400,000 ms, neither will he lead one in 86,400,000 ms.

Response: Yes, but (3) is supposed to be true as a matter of logic. And it’s logically possible that Themistocles leads a sea battle in 86,399,999 ms but not in 86,400,001 ms, in which case if there will be no moment in 86,400,000 ms, we cannot meaningfully say if he will be leading a sea battle then or not. So we cannot save (3) as a matter of logic.

A possible solution: Perhaps Aristotle should just replace (2) with:

4. It is true that will be: no tomorrow or tomorrow a sea battle or tomorrow no sea battle.

I am a bit worried about the "will" attached to a “no tomorrow”. Maybe more on that later.

An attempt to define possible futures for open futurism

On all-false open future (AFOF), future contingent claims are all false. The standard way to define “Will p” is to say that p is true in all possible futures. But defining a possible future is difficult. Patrick Todd does it in terms of possible worlds apparantly of the classical sort—ones that have well-defined facts about how things are at all times. But such worlds are not in general possible given open future views—it is not possible to simultaneously have a fact about how contingent events go on all future days (assuming the future is infinite).

Here is an approach that maybe has some hope of working better for open future views. Take as primitive not classical possible worlds, but possible moments, ways that things could be purely at a time. Possible moments do not include facts about the past and future.

Now put a temporal ordering on the possible moments, where we say that m₁ is earlier than m₂ provided that it is possible to have had m₁ obtaining before m₂.

For a possible moment m, define:

• open m-world: a maximal set of possible moments including m such that (a) all moments in the set other than m are earlier or later than m and (b) the subset of moments earlier than m is totally ordered

• possible history: a maximal totally ordered set of possible moments

• possible future: a possible history that contains m.

Exactly one possible moment is currently actual. Then:

• possible future: a possible future of the currently actual moment.

Now consider the problem of entailment on AFOF. The problem is this. Intutiively, that I will freely mow my lawn entails that I will mow my lawn, but does not entail that I will eat my lawn. However, since on AFOF “I will freely mow my lawn” is necessarily false—it is false at every possible moment, since “will” claims concerning future contingent claims are always false—both entailments have necessarily false antecedents and hence are trivially true.

Given a set S of moments and a moment m ∈ S, any sentence of Prior’s (or Brand’s) temporal logic can be evaluated for truth at (S,m). We can now define two modalities:

• p is OW-necessary: p is true at (W,m) for every open m-world W

• p is PH-necessary: p is true at (H,m) for every possible history H that contains m.

And now we have two entailments: p OW/PH-entails q if and only if the material conditional p → q is OW/PH-necessary.

Then that I will freely mow my lawn is OW-impossible, but PH-possible, and that I will freely mow my lawn OW-entails that I will eat my lawn, but does not PH-entail it. The open futurist can now say that our intuitive concept of entailment, in temporal contexts, corresponds to PH-entailment rather than OW-entailment.

I think this is helpful to the open futurist, but still has a serious problem. Consider the sentence “I will mow or I will not-mow.” On AFOF, this is false. But it is true at every possible history. Hence, it is PH-necessary. Thus, PH-necessity does not satisfy the T-axiom. Thus PH-entailment is such that a truth can PH-entail a falsehood. For instance, since “I will mow or I will not-mow” is PH-necessary, it is PH-entailed by every tautology.

On trivalent logics, if "I will mow or I will not-mow" is neither true nor false, we have a similar problem: a truth PH-entails a non-truth.

There are is a more technical problem on some metaphysical views. Suppose that it is contingent whether time continues past a certain moment. For instance, suppose there is no God and empty time is impossible, and there is a particle which can indeterministically cease to exist, and the world contains just that particle, so at any time it is possible that time is the last—the particle can pop out of existence. Oddly, because of the maximality condition on possible histories, there is no possible future where the particle pops out of existence.

I wonder if there is a better way to define entailment and possible futures that works with open future views.

Aristotelianism and transformative technology

The Aristotelian picture of us is that like other organisms, we flourish in fulfilling our nature. Our nature specifies the proper way of interacting with the world. We do not expect an organism’s nature to specify proper ways of interacting with scenarios far from its niche: how bats should fly in weightless conditions; how cats should feed in an environment with unlimited food supply; how tardigrades should live on the moon.

But with technology, we have shifted far from the environment we evolved for. While adaptability is a part of our nature, some technological innovations seem to go beyond the adaptability we expect, in that they appear to impact central aspects of the life of the social beings we are: innovations like the city, writing, and fast and widely accessible global communication. We should not expect for our nature specify how we should behave with respect to these new social technologies. We should have a skepticism that our nature contains sensible answers to questions about how we should behave in these cases.

Thus we appear to have an Aristotelian argument for avoiding the more transformative types of technology, since we are more likely to have meaningful answers to questions about how to lead our lives if our lives are less affected by social transformations. To be on the safe side, we should live in the country, and have most of our social interaction with a relatively small number of neighbors in person.

The theistic Aristotelian, however, has an answer to this. While evolution cannot foresee the Internet, God can, and he can give us a normative nature that specifies how we should adapt to vast changes in the shape of our lives. We do not need to avoid transformative technology in general, though of course we must be careful lest the transformation be for ill.

Optimalism and logical possibility

Optimalism holds that, of metaphysical necessity, the best world is actualized.

There are two ways to understand “the best world”: (1) the best of all metaphysically possible worlds and (2) the best of all (narrowly) logically possible worlds.

If we understand it in sense (1), then the best world is the best out of a class of one, and hence it’s also the worst world in the same class. So on reading (1), optimalism=pessimalism.

So sense (2) seems to be a better choice. But here is an argument against (2). It seems to be an a posteriori truth that I am living life L_AP (the life in our world associated with the name “Alexander Pruss”) and that Napoleon is living life L_NB (the life in our world associated with the name “Napoleon Bonaparte”). There seems to be a narrowly logically possible world just like this one where I live L_NB and Napoleon lives L_AP. That world with me and Napoleon swapped is neither better nor worse than this one. Hence our world is not the best one. It is tied or incommensurable with a whole bunch of worlds where the identities of individuals are permuted.

Maybe my identity is logically tied to certain aspects of my life, though? Leibniz certainly thought so—he thought it was tied to all the aspects of my life. But this is a controversial view.

All-false open futurism

On All-False Open Futurism (AFOF), any future tensed statement about a future contingent must be false. It is false that there will be a sea battle tomorrow, for instance.

Suppose now I realize that due to a bug, tomorrow I will be able to transfer ten million dollars from a client’s account to mine, and then retire to a country that won’t extradite me. A little angel says to me:

1. Your freely taking your client’s money without permission tomorrow entails your being a thief tomorrow.

I don’t want to be a thief, tomorrow or ever, so I am about to decide not to do it. But now a little devil convinces me of AFOF and says that while (1) is true, so is:

2. Your freely taking your client’s money without permission tomorrow entails your being a saint tomorrow.

Perhaps I am not very good at modal logic and the devil needs to explain. Given AFOF, it is necessarily false that I will freely take my client’s money without permission tomorrow, and a necessary falsehood entails everything. So, the devil adds, I might as well buy my plane tickets now.

The angel, however, grants AFOF for the sake of argument, but says that notwithstanding (2), the following holds:

3. Tomorrow it will be the case your taking your client’s money without permission entails your being a thief.

For the entailment holds always.

At this point, we have an interesting question. Given AFOF, should I guide my actions by the entailment between future-tensed claims in (2) or by the future-tensed entailment claim in (3)? The angel urges that the devil’s reasoning undercuts all rationality, while the angel’s reasoning does not, and hence is superior.

But the devil has one more trick up his sleeve. He notes that it is a contingent question whether there will be a tomorrow at all. For God might freely decide to end time before tomorrow. Thus, that there will be a tomorrow is false on AFOF. But (3) implies that there will be a tomorrow, and so (3) is false as well. I try to argue on the basis of Scripture that God has made promises that entail a future eternity, but the devil is a lot better at citing the Bible than I, and convinces me that God might transfer us to a timeless state or maybe eternal life is a supertask lasting from 8 to 9 pm tonight. And in any case, surely it should not depend on revelation whether the angel has a good argument not to take the client’s money. This is a problem for AFOF.

Maybe this is the way out. The angel could say this:

4. Necessarily, if there will be a tomorrow, then it will be true tomorrow that taking your client’s money without permission entails your being a thief.

But while this conditional is true on AFOF, if the devil has made his case that God hasn’t promised there will be a tomorrow, he can respond with:

5. Necessarily, if God hasn’t promised there will be a tomorrow and there will be a tomorrow, then it will be true tomorrow that taking your client’s money without permission entails your being a saint.

For the antecedent of the conditional here is necessarily false on AFOF, it being contingent that there will be a tomorrow absent a divine promise. And it seems that (5) is even more relevant to guiding action than (4), then.

Maybe the defender of AFOF can insist that the future must be infinite. But this does not seem plausible.

Yet another counterexample to act utilitarianism

It is wrong to torture a stranger for 99 minutes in order to avoid 100 minutes of equal torture to oneself.

Entailment and Open Future views

This is probably an old thing that has been discussed to death, but I only now noticed it. Suppose an open future view on which future contingents cannot have truth value. What happens to entailments? We want to say:

1. That Jones will freely mow the lawn tomorrow entails that he will mow the lawn tomorrow

and to deny:

2. That Jones will freely mow the lawn tomorrow entails that he will not mow the lawn tomorrow.

Now, a plausible view of entailment is that:

3. p entails q if and only if it is impossible for p to be true while q is false.

But if future contingents cannot have truth value, then that Jones will freely mow the lawn tomorrow cannot be true, and hence by (3) it entails everything. In particular, both (1) and (2) will be true.

Presumably, the open futurist who believes future contingents cannot have truth value will give a different account of entailment, such as:

4. p entails q if and only if there is no history in which p is true and q is false.

But what is a history? Here is a possible story. For a time t, let a t-possibility be a maximal set of propositions that could all be true together at t. Given the open future view we are exploring, a t-possibility will not include any propositions reporting contingent events after t. If t₁ < t₂, and A₁ is a t₁-possibility while A₂ is a t₂-possibility, we can say that A₁ is included in A₂ provided that for any proposition p in A₁, the proposition that p was true at t₁ is a member of A₂. We can then say that a history h is a function that assigns a t-possibility h(t) to every time t such that h(t₁) is included in h(t₂) whenever t₁ < t₂.

(Technical note: Open theism implies a theory of tensed propositions, I assume. Thus if A is a t₁-possibility, then it is not a t₂-possibility if t₂ ≠ t₁, since any t-possibility will include the proposition that t is present.)

But what does it mean to say that a proposition p is true in a history h. Here is a plausible approach. Suppose t₀ is the present time. Given a proposition p that says that s, let p_t0 be the backdated proposition that at t₀ it was such that s (with whatever shifts of tense are needed in s to make this grammatical). Then p is true in h provided that there is a time t₁ > t₀ such that p_t0 is a member of h(t₁). In other words, a proposition p is true in h provided that eventually h settles its truth value.

This works nicely for letting us affirm (1) and deny (2). In every history in which it becomes true that Jones will freely mow the lawn it becomes true that Jones will mow the lawn, while this is not so if we replace the consequent with “Jones will not mow the lawn.” But what about statements that quantify over times? Consider:

5. Jones will mow the lawn, and for every time t at which Jones will mow the lawn, there will be a time t′ that is more than a year after t such that Jones will freely mow the lawn at t′.

This entails:

6. Jones will mow the lawn, and for every time t at which Jones will mow the lawn, there will be a time t′ that is more than a year after t such that Jones will mow the lawn at t′.

but does not entail:

7. Jones will not mow the lawn.

But there is no history h at which (5) is true by the above account of truth-at-a-history given our open future view. For let t₀ be the present and let p be the proposition expressed by (5). Then at any future time t and any history h, the proposition p_t0 is not a member of h(t). For if it were a member of h(t), it would be affirming the existence of an infinite number of future free mowings, and such a proposition cannot be true on our open future view. Since there is no history h at which (5) is true, by (4) we have it that (5) entails both (6) and (7), which is the wrong result.

What if instead of saying that future contingents lack truth value, we say that they are all false? This requires a slight modification to the account of p being true at a history. Instead of saying that p is true at h provided that there is some future time t such that p_t0 is in h(t), we need to say that there is some future time t such that p_t0 is in h(t′) for all t′ ≥ t. This gives the right truth values for (1) and (2), but it also makes (7) true.

I think the above open futurist accounts of entailment work nicely for statements with a single unbounded quantifier over times, but once we get alternating quantifiers like in (5), where the second conjunct is of the form ∀t∃t′ϕ, things break down.

Perhaps the open futurist just needs to be willing to bite the bullet and say that (5) entails (7)?

Open Theism and divine promises

Open Theist Christians tend to think that there are some things God knows about the future, and these include the content of God’s promises to us. God’s promises are always fulfilled.

But it seems that the content of many of God’s promises depends on free choices. For imagine that all the recipients of God’s promise freely choose to release God from the promise; then God would be free not to follow the promise, it appears, and so he could freely choose not to act in according to the promise. Thus there seems to be a sequence of creaturely and divine free choices on which the content of the promise does not come about.

This argument may not work for all of God’s promises. Some of God’s promises are covenants, and it may be that covenants are a type of agreement in which neither party can release the other. There may be other unreleasable promises: perhaps when x promises to punish y, that’s a promise y cannot release x from. But do we have reason to think that God makes no “simple promises”, promises other than covenants and promises of punishment?

I do not think this is a definitive argument against open theism. The open theist can bite the bullet and say that God doesn’t always know he will fulfill his promises. But it is interesting to see that on open theism, God’s knowledge of the future is even more limited than we might have initially thought.

Open theism and the Incarnation

Here is a very plausible pair of claims:

1. The Son could have become incarnate as a different human being.

2. God foreknew many centuries ahead of time which human being the Son would become incarnate as.

Regarding 1, of course, the Son could not have been a different person—the person the Son is and was and ever shall be is the second person of the Trinity. But Son could have been a different human being.

Here is a sketch of an argument for 1:

1. If the identity of a human being depends on the body, then if the Son became incarnate as a 3rd century BC woman in India, this would be a different human being from Jesus (albeit the same person).

2. If the identity of a human being depends on the soul, then God could have created a different soul for the Son’s incarnation.

3. The identity of a human being depends on either the body or the soul.

I don’t have as good an argument for 2 as I do for 1, but I think 2 is quite plausible given what Scripture says about God’s having planned out the mission of Jesus from of old.

Now add:

3. If the Son could have become incarnate as a different human being, which human being he became incarnate as depends on a number of free human choices in the century preceding the incarnation.

Now, 1, 2 and 3 leads to an immediate problem for an open theist Christian (my thinking on this is inspired by a paper of David Alexander, though his argument is different) who thinks God doesn’t foreknow human free choices.

Why is 3 true? Well, if the identity of a human being even partly depends on the body (as is plausible), given that (plausibly) Mary was truly a biological mother of Jesus, then if Mary’s parents had not had any children, the body that Jesus actually had would not have existed, and an incarnation would have happened with a different body and hence a different human being.

Objection: God could have created Mary—or the body for the incarnation—directly ex nihilo in such a case, or God could have overridden human free will if some human were about to make a decision that would lead to Mary not existing.

Response: If essentiality of origins is true, then it is logically impossible for the same body to be created ex nihilo as actually had a partial non-divine cause. But I don’t want the argument to depend on essentiality of origins. Instead, I want to argue as follows. Both of the solutions in the objection require God to foreknow that he would in fact engage in such intervention if human free choices didn’t cooperate with his plan. God’s own interventions would be free choices, and so on open theism God wouldn’t know that he would thus intervene. One might respond that God could resolve to ensure that a certain body would become available, and a morally perfect being always keeps his resolutions. But while perhaps a morally perfect being always keeps his promises, I think it is false that a morally perfect being always keeps his resolutions. Unless one is resolving to do something that one is already obligated to do, it is not wrong to change one’s mind in a revolution. I suppose God could have promised someone that he would ensure the existence of a certain specific body, but we have no evidence of such a specific promise in Scripture, and it seems an odd maneouver for God to have to make in order to know ahead of time who the human that would save the world is.

What if the identity of a human depends solely on the soul? But then the identity of the human being that the Son would become incarnate as would depend on God’s free decision which soul to create for that human being, and the same remarks as I made about resolutions in the previous paragraph would apply.

The Reverse Special Composition Question

Van Inwagen famously raised the Special Composition Question (SCQ): What is an informative criterion for when a proper plurality of objects composes a whole.

There is, however, the Reverse Special Composition Question (RSCQ): What is an informative criterion for when an object is composed of a proper plurality?

The SCQ seems a more fruitful question when we think of parts as prior to the whole. The RSCQ seems a more fruitful question when we think of wholes as prior to the parts.

If by parts we mean something like “integral parts”, we have a pretty quick starter option for answering the RSCQ:

1. An object is composed of a proper plurality of parts just in case it takes up more than a point of space.

I am not inclined to accept (1) because I like the possibility of extended simples, but it is a pretty neat and simple answer. Suppose that (1) is correct. Then we have a kind of simplicity argument for the thesis that the whole is prior to its parts. If the parts are prior to the whole, SCQ is a reasonable question, but doesn’t have an elegant and plausible answer (let us suppose). If the whole is prior to the parts, SCQ is not a reasonable question but RSCQ instead is, and RSCQ has an elegant and plausible answer (let us suppose). So we have some reason to accept that the whole is prior to the parts.

Natural kinds across categories

Most philosophical discussions of natural kinds concern entities in the category of substance: particles, chemical substances, organisms, etc. But I think we shouldn’t forget that there is good reason to posit natural kinds of entities in other categories.

For instance, you and I are each engaging in a token activity that falls under the natural kind (say) mammalian breathing. The natural kind specifies some essential properties of the kind, namely that it is a kind of filling and/or emptying of the lungs, as well as some teleological features, such as that the filling and emptying should be rhythmic. Instances of the kind may be better or worse: given that I am congested after a long drawn-out cold, likely your breathing is better than mine.

There are, plausibly, such things as natural activities, which fall under activity natural kinds. These may kinds may include gravitational attraction, mating, fish respiration, etc.

Dispositions, too, may fall under natural kinds, indeed a nested sequence of them. We might say that some dispositions are habits, and some habits are virtues. Thus, perhaps, you and I each have a certain disposition to rationally withstand danger, a disposition that is a token of courage, a kind of virtue. Your and my courages are different: for instance, perhaps, I am more willing to withstand social danger while you are more willing to withstand physical danger. Whether indeed virtues are natural kinds seems to me to be a central question for the metaphysics of virtue ethics.

There may be natural kinds of relations, too. Thus, I think marriage is a natural kind. On the other hand, I think presidency is not.

Reasons and direct support

A standard view of reasons is that reasons are propositions or facts that support an action. Thus, that I promised to visit is a reason to visit, that pain is bad is a reason to take an aspirin, and that I am hungry is a reason to eat.

But notice that any such facts can also be a reason for the opposite action. That I promised to visit is a reason not to visit, if you begged me not to keep any of my promises to you. That pain is bad is a reason not to take an aspirin and that I am hungry is a reason not to eat when I am striving to learn to endure harship.

One might think that this kind of contingency in what the reasons—considered as propositions or facts—support disappears when the reasons are fully normatively loaded. That I owe you a visit is always a reason to visit, and that I ought to relieve my hunger is always a reason to eat.

This is actually mistaken, too. That I owe you a visit is indeed always a reason to visit. But it can also be a reason—and even a moral one—not to visit. For instance, if a trickster informs me that that if I engage in an owed visit to you, they will cause you some minor harm—say, give you a hangnail—then the fact that I owe you a visit gives me a reason not to visit you, though that reason will be outweighed (indeed, it has to be outweighed, or else it wouldn’t be true that I owe you the visit).

In fact, plausibly, that an action is the right one is typically also a moral reason not to perform the action. For whenever we do the right thing, that has a potential of feeding our pride, and we have reason not to feed our pride. Of course, that reason is always outweighed. But it’s still there. And we might even say that the fact that an action is wrong is a reason, albeit not a moral one, to perform that action in order to exhibit one’s will to power (this is a morally bad reason to act on, but one that is probably minimally rational—we understand someone who does this).

All this suggests to me that we need a distinction: some reasons directly support doing something. That I owe you a visit directly supports my visiting you, but only indirectly supports my not visiting you to avoid pride in fulfilling my duties.

But now it is an interesting question what determined what reasons directly support what action. One option is that the relation is due to entailment: a reason directly supports ϕing provided that that reason entails that ϕing is good or right. But this misses the hyperintentionality in reasons. It is necessarily true that it’s right for me to respect my neighbor; a necessary truth is entailed by every proposition; but that my neighbor is annoying is not directly a reason to respect my neighbor. One might try for some “relevant entailment”, but I am dubious. Perhaps the fact that an action is wrong relevantly entails that there is reason to do it to exhibit one’s will to power, but that ϕing is wrong is directly a reason not to ϕ, and only indirectly a reason to ϕ.

I suspect the right answer is that this direct support relation comes from our human nature: if it is our nature to be directly motivated to ϕ because of R, then R directly supports ϕing. Hmm. This may work for epistemic support, too.

Habitual action

Alice has lived a long and reasonable life. She developed a lot of good habits. Every morning, she goes on a walk. On her walk, she looks at the lovely views, she smells the flowers in season, she gathers mushrooms, she listens to the birds chirping, she climbs a tree, and so on. Some of these things she does for their own sake and some she does instrumentally. For instance, she climbs a tree because she saw research that daily exercise promotes health, but she smells the flowers for the sake of the smelling itself.

She figured all this out when she was in her 30s, but now she is 60. One day, she realizes that for a while now she had forgotten the reasoning that led to her habits. In particular, she no longer knows which of her daily activities have innate value and which ones are merely instrumental.

So what can we say about her habitual activities?

One option is that they retain the teleology with which they were established. Although Alice no longer remembers that she climbs a tree solely for the sake of health, that is indeed what she climbs the tree for. On this picture, when we perform actions from habit, they retain the teleology they had when the habit was established. In particular, it follows that agential teleology need not be grounded in occurrent mental states of the agent. This is a difficult bullet to bite.

The other option is that they have lost their teleological characterization. This implies, interestingly, that there is no fact about whether the actions are being done for their own sake or instrumentally. In particular, it follows that the standard diviion of actions into those done for their own sake and those done instrumentally is not exhaustive. That is also a difficult bullet to bite.

I am not sure what to say. I suspect one lesson is that action is more complicated than we philosophers think, and our simple characterizations of it miss the complexity.

Acting without knowledge of rightness

Some philosophers think that for your right action to be morally worthy you have to know that the action is right.

On the contrary, there are cases where an action is even more morally worthy when you don’t know it’s right.

1. Alice is tasked with a dangerous mission to rescue hikers stranded on a mountain. She knows it’s right, and she fulfills the mission.

2. Bob is tasked with a dangerous mission to rescue hikers stranded on a mountain. He knows it’s right, but then just before he heads out, a clever philosopher gives him a powerful argument that there is no right or wrong. He is not fully convinced, but he has no time to figure out whether the argument works before the mission starts. Instead, he reasons quickly: “Well, there is a 50% chance that the argument is sound and there is no such thing as right and wrong, in which case at least I’m not doing anything wrong by rescuing. But there is a 50% chance that there is such a thing as right and wrong, and if anything is right, it’s rescuing these hikers.” And he fulfills the mission.

Bob’s action is, I think, even more worthy and praiseworthy than Alice’s. For while Alice risks her life for a certainty of doing the right thing, Bob is willing to risk his life in the face of uncertainty. Some people would take the uncertainty as an excuse, but Bob does not.

Acting because of and for reasons

It seems that:

1. If you pursue friendship because friendship is non-instrumentally valuable, then you pursue friendship non-instrumentally.

But not so. Imagine a rich eccentric offers you $10,000 to pursue something that is non-instrumentally valuable. You think about it, correctly decide friendship is non-instrumentally valuable, and pursue it to gain the $10,000. You are pursuing friendship because it is non-instrumentally valuable, but you are pursuing it merely instrumentally.

More generally, is there any conditional of the form:

2. If you pursue friendship because p, then you pursue friendship non-instrumentally

that is true in all cases, where p states some known reason for the pursuit of friendship? I don’t think so. For the rich eccentric can tell you that you will get $10,000 if it is both the case that p and you pursue friendship. In that case, if you know that it is the case that p, then your reason for pursuing friendship is p, since it is given p, and only given p, that you will get $10,000 for your pursuit of friendship.

Maybe the lesson from the above is that there is a difference between doing something because of a reason and doing it for the reason. That friendship is non-instrumentally valuable is a reason. In the first rich eccentric case, you are pursuing because of that reason, but you are not pursuing it for that reason. Thus maybe we can say:

3. If you pursue friendship for the reason that friendship is non-instrumentally valuable, then you pursue friendship non-instrumentally.

In the case where you are aiming only at the $10,000, you are pursuing friendship for the reason that pursuing friendship will get you $10,000, or more explicitly for the conjunctive reason that (a) if friendship is non-instrumentally valuable it will get you $10,000 to pursue it and (b) it is non-instrumentally valuable. But you are nonetheless pursuing friendship because it is non-instrumentally valuable.

There is thus a rather mysterious “acting for R” relation in regard to actions which does not reduce to “acting because R”.

A failed Deep Thought

I was going to post the following as Deep Thoughts XLIII, in a series of posts meant to be largely tautologous or at least trivial statements:

1. Everyone older than you was once your age.

And then I realized that this is not actually a tautology. It might not even be true.

Suppose time is discrete in an Aristotelian way, so that the intervals between successive times are not always the same. Basically, the idea is that times are aligned with the endpoints of change, and these can happen at all sorts of seemingly random times, rather than at multiples of some interval. But in that case, (1) is likely false. For it is unlikely that the random-length intervals of time in someone else’s life are so coordinated with yours that the exact length of time that you have lived equals the sum of the lengths of intervals from the beginning to some point in the life of a specific other person.

Of course, on any version of the Aristotelian theory that fits with our observations, the intervals between times are very short, and so everyone older than you was once approximately your age.

One might try to replace (1) by:

2. Everyone older than you was once younger than you are now.

But while (2) is nearly certainly true, it is still not a tautology. For if Alice has lived forever, then she’s older than you, but she was never younger than you are now! And while there probably are no individuals who are infinitely old (God is timelessly eternal), this fact is far from trivial.

Punishment, causation and time

I want to argue for this thesis:

1. For a punishment P for a fault F to be right, P must stand in a causal-like relation to P.

What is a causal-like relation? Well, causation is a causal-like relation. But there is probably one other causal-like relation, namely when because of the occurrence of a contingent event E, God knows that E occurred, and this knowledge in turn explains why God did something. This is not exactly causation, because God is not causally affected by anything, but it is very much like causation. If you don’t agree, then just remove the ``like’’ from (1).

Thesis (1) helps explain what is wrong with punishing people on purely statistical grounds, such as sending a traffic ticket to Smith on the grounds that Smith has driven 30,000 miles in the last five years and anyone who drove that amount must have committed a traffic offense.

Are there other arguments against (1)? I think so. Consider forward-looking punishment where by knowing someone’s present character you know that they will commit some crime in ten days, so you punish them now (I assume that they will commit the crime even if you do not punish them). Or, even more oddly, consider circular forward-looking punishment. Suppose Alice has such a character that it is known that if we jail her, she will escape from jail. But assume that our in society an escape from jail is itself a crime punishable by jail, and that Alice is not currently guilty of anything. We then jail her, on the grounds that she will escape from jail, for which the punishment is us now jailing her.

One may try to rule out the forward-looking cases on the grounds that instead of (1) we should hold:

2. For a punishment P for a fault F to be right, P must come after F.

But that’s not right. Simultaneous causation seems possible, and it does not seem unjust to set up a system where a shoplifter feels punitive pain at the very moment of the shoplifting, as long as the pain is caused by the shoplifting.

Or consider this kind of a case. You know that Bob will commit a crime in ten days, so you set up an automated system that will punish him at a preset future date. It does not seem to be of much significance whether the system is set to go off in nine or eleven days.

Or consider cases where Special Relativity is involved, and the punishment occurs at a location distant from the criminal. For instance, Carl, born on Earth, could be sentenced to public infamy on earth for a crime he commits around Alpha Centauri. Supposing that we have prior knowledge that he will commit the crime on such and such a date. If (2) is the right principle, when should we make him infamous on earth? Presumably after the crime. But in what reference frame? That seems a silly question. It is silly, because (2) isn’t the right principle—(1) is better.

Objection: One cannot predict what someone will freely do.

Response: One perhaps cannot predict with 100% certainty what someone will freely do, but punishment does not require 100% certainty.

Punishment, reward and theistic natural law

I’ve always found punishment and (to a lesser extent) reward puzzling. Why is it that when someone does something wrong is there moral reason to impose a harsh treatment on them, and why is it that when someone does something right—and especially supererogatory—is there moral reason to do something nice for them?

Of course, it’s easy to explain why it’s good for our species that there be a practice of reward and punishment: such a practice in obvious ways helps to maintain a cooperative society. But what makes it morally appropriate to impose a sacrifice on the individual for the good of the species in this way, whether the good of the person receiving the punishment or the good of the person giving the reward when the reward has a cost?

Punishment and reward thus fit into a schema where we would like to be able to make use of this argument form:

1. It would be good (respectively, bad) for humans if moral fact F did (did not) obtain.

2. Thus, probably, moral fact F does obtain.

(The argument form is better on the parenthetical negative version.) It would be bad for humans if we did not have distinctive moral reasons to reward and punish, since our cooperative society would be more liable to fall apart due to cheating, freeriding and neglect of others. So we have such moral reasons.

As I have said on a number of occasions, we want a metaethics on which this is a good argument. Rule-utilitarianism is such a metaethics. So is Adams’ divine command theory with a loving God. And so is theistic natural law, where God chooses which natures to exemplify because of the good features in these natures. I want to say something about this last option in our case, and why it is superior to the others.

Human nature encodes what is right and wrong for. Thus, it can encode that it is right for us to punish and reward. An answer as to why it’s right for us to reward and punish, then, is that God wanted to make cooperative creatures, and chose a nature of cooperative creatures that have moral reasons to punish and reward, since that improves the cooperation.

But there is a way that the theistic natural law solution stands out from the others: it can incorporate Boethius’ insight that it is intrinsically bad for one to get away unpunished with wrongdoing. For our nature not only encodes what is right and wrong for us to do, but also what is good or bad for us. And so it can encode that it is bad for us to get away unpunished. It is good for us that it be bad for us to get away unpunished, since its being bad for us to get away unpunished means that we have additional reason to avoid wrongdoing—if we do wrong, we either get punished or we get away unpunished, and both options are bad for us.

The rule-utilitarian and divine-command options only explain what is right and wrong, not what is good and bad, and so they don’t give us Boethius’ insight.

What is an existential quantifier?

What is an existential quantifier?

The inferentialist answer is that an existential quantifier is any symbol that has the syntactic features of a one-place quantifier and obeys the same logical rules of an existential quantifier (we can precisely specify both the syntax and logic, of course). Since Carnap, we’ve had good reason to reject this answer (see, e.g., here).

Here is a modified suggestion. Consider all possible symbols that have the syntactic features of a one-place quantifier and obeys the rules of an existential quantifier. Now say that a symbol is an existential quantifier provided that it is a symbol among these symbols that maximizes naturalness, in the David Lewis sense of “naturalness”.

Moreover, this provides the quantifier variantist or pluralist (who thinks there are multiple existential quantifiers, none of them being the existential quantifier) with an answer to a thorny problem: Why not simply disjoin all the existential quantifiers to make a truly unrestricted existential quantifier, and say that that is the existential quantifier? THe quantifier variantist can say: Go ahead and disjoin them, but a disjunction of quantifiers is less natural than its disjuncts and hence isn’t an existential quantifier.

This account also allows for quantifier variance, the possibility that there is more than one existential quantifier, as long as none of these existential quantifiers is more natural than any other. But it also fits with quantifier invariance as long as there is a unique maximizer of naturalness.

Until today, I thought that the problem of characterizing existential quantifiers was insoluble for a quantifier variantist. I was mistaken.

It is tempting to take the above to say something deep about the nature of an existential quantifier, and maybe even the nature of being. But I think it doesn’t quite. We have a characterization of existential quantifiers among all possible symbols, but this characterization doesn’t really tell us what they mean, just how they behave.

Combining epistemic utilities

Suppose that the right way to combine epistemic utilities or scores across individuals is averaging, and I am an epistemic act expected-utility utilitarian—I act for the sake of expected overall epistemic utility. Now suppose I am considering two different hypotheses:

• Many: There are many epistemic agents (e.g., because I live in a multiverse).

• Few: There are few epistemic agents (e.g., because I live in a relatively small universe).

If Many is true, given averaging my credence makes very little difference to overall epistemic utility. On Few, my credence makes much more of a difference to overall epistemic utility. So I should have a high credence for Few. For while a high credence for Few will have an unfortunate impact on overall epistemic utility if Many is true, because the impact of my credence on overall epistemic utility will be small on Many, I can largely ignore the Many hypothesis.

In other words, given epistemic act utilitarianism and averaging as a way of combining epistemic utilities, we get a strong epistemic preference for hypotheses with fewer agents. (One can make this precise with strictly proper scoring rules.) This is weird, and does not match any of the standard methods (self-sampling, self-indication, etc.) for accounting for self-locating evidence.

(I should note that I once thought I had a serious objection to the above argument, but I can't remember what it was.)

Here’s another argument against averaging epistemic utilities. It is a live hypothesis that there are infinitely many people. But on averaging, my epistemic utility makes no difference to overall epistemic utility. So I might as well believe anything on that hypothesis.

One might toy with another option. Instead of averaging epistemic utilities, we could average credences across agents, and then calculate the overall epistemic utility by applying a proper scoring rule to the average credence. This has a different problematic result. Given that there are at least billions of agents, for any of the standard scoring rules, as long as the average credence of agents other than you is neither very near zero nor very near one, your own credence’s contribution to overall score will be approximately linear. But it’s not hard to see that then to maximize expected overall epistemic utility, you will typically make your credence extreme, which isn’t right.

If not averaging, then what? Summing is the main alternative.

Closed time loop

Imagine two scenarios:

1. An infinitely long life of repetition of a session meaningful pleasure followed by a memory wipe.

2. A closed time loop involving one session of the meaningful pleasure followed by a memory wipe.

Scenario (1) involves infinitely many sessions of the meaningful pleasure. This seems better than having only one session as in (2). But subjectively, I have a hard time feeling any preference for (1). In both cases, you have your pleasure, and it’s true that you will have it again.

I suppose this is some evidence that we’re not meant to live in a closed time loop. :-)

Shuffling an infinite deck

Suppose infinitely many blindfolded people, including yourself, are uniformly randomly arranged on positions one meter apart numbered 1, 2, 3, 4, ….

Intuition: The probability that you’re on an even-numbered position is 1/2 and that you’re on a position divisible by four is 1/4.

But then, while asleep, the people are rearranged according to the following rule. The people on each even-numbered position 2n are moved to position 4n. The people on the odd numbered positions are then shifted leftward as needed to fill up the positions not divisible by 4. Thus, we have the following movements:

• 1 → 1

• 2 → 4

• 3 → 2

• 4 → 8

• 5 → 3

• 6 → 12

• 7 → 5

• 8 → 16

• 9 → 6

• and so on.

If the initial intuition was correct, then the probability that now you’re on a position that’s divisible by four is 1/2, since you’re now on a position divisible by four if and only if initially you were on a position divisible by two. Thus it seems that now people are no longer uniformly randomly arranged, since for a uniform arrangement you’d expect your probability of being in a position divisible by four to be 1/4.

This shows an interesting difference between shuffling a finite and an infinite deck of cards. If you shuffle a finite deck of cards that’s already uniformly distributed, it remains uniformly distributed no matter what algorithm you use to shuffle it, as long as you do so in a content-agnostic way (i.e., you don’t look at the faces of the cards). But if you shuffle an infinite deck of distinct cards that’s uniformly distributed in a content-agnostic way, you can destroy the uniform distribution, for instance by doubling the probability that a specific card is in a position divisible by four.

I am inclined to take this as evidence that the whole concept of a “uniformly shuffled” infinite deck of cards is confused.

Four-flour pancakes

I was watching an old Aunt Jemima pancake mix commercial which touted it as being made from four flours: wheat, corn, rye and rice, and I decided to see what pancakes made them are like. I started with this wheat flour pancake recipe, but tweaked some things, and made them this morning. Pretty good. Perhaps more hearty than standard pancakes, and the texture was a bit more crunchy, which I liked.

• 1/2 cup of wheat flour

• 1/2 cup of whole-grain rye flour

• 1/2 cup of corn flour

• 1/2 cup of (non-glutinous) rice flour

• 4 3/4 teaspoons baking powder

• 4 teaspoons white sugar

• 1/3 teaspoon salt

• 1 2/3 cup milk

• 4 tablespoons melted butter

• 1 large egg

• 4 teaspoons apple sauce (or skip and use 1 1/3 egg, if you have some use for the remaining 2/3 of the egg)

• cooking spray (I used canola spray)

• optional: chocolate chips

Mix dry ingredients. Add wet ingredients. Mix well. Heat pan to medium heat. Spray with oil. Put a big serving spoon of mix on the pan. If you want to add chocolate chips, drop them in on top. Wait until the edges are getting dry. (It was surprisingly fast, about 1-2 minutes, and they would burn easily when I wasn’t fast enough.) Flip and brown the other side (again, it’s fast).

Yields 9-10 not very large pancakes. The frying took half an hour with two pans in simultaneous use. I measured out all the ingredients the night before and pre-mixed the dry ingredients so I could be fast in the morning before a pickleball game.

The value of moral norms

Here is a very odd question that occurred to me: Is it good for there to be moral norms?

Imagine a world just like this one, except that there are no moral norms for its intelligent denizens—but nonetheless they behave as we do. They feel repelled by the idea of murder and torture, and find the life of a Mother Teresa attractive, but there are no moral truths behind these things.

Such a world would have one great advantage over ours: there would be no moral evil. That world’s Hitler and Stalin would cause just as much pain and suffering, but they wouldn’t be wicked in so doing. Given the Socratic insight that it is worse to do than to suffer evil, a vast amount of evil would disappear in such a world. At least a third of the evil in the world would be gone. Our world has three categories of evil:

I. Undergoing of natural evils

2. Undergoing of moral evils, and

3. Performance of moral evils.

The third category would be gone, and it is probably the biggest of the three. Wouldn’t that be worth it?

Here is one answer. For cooperative intelligent social animals, a belief in morality is very useful. But to live one’s life by a belief that is false seems a significant harm. Cooperative intelligent social animals in the alternative world would be constantly deceived by their belief in morality. That is a great evil. But is it as great an evil as all Category III evils taken together? I suspect it is but a small fraction of the sum of all Category III evils.

Here is a second answer. In removing moral norms, one would admittedly remove a vast category of evils, but also a vast category of goods: the performance of moral good. If we have the intuition that having moral norms is a good thing—that it would be a disappointment to learn that moral norms were an illusion—then we have to think that the performances of moral good are a very great thing indeed, one comparable to the sum of all Category III evils.

I am attracted to a combination of the two answers. But I can also see someone saying: “It doesn’t matter whether it’s worth having moral norms or not, but it is simply impossible to have cooperative intelligent social animals that believe in morality without their being under moral norms.” A Platonist may say that on the grounds that moral norms are necessary. A theist may say it on the grounds that it is contrary to the character of a perfect God to manufacture the vast deceit that would be involved in us thinking there are moral norms if there were no moral norms. These aren’t bad answers. But I still feel it’s good that there really are moral norms.

Philosophy and child-raising

Philosophy Departments often try to attract undergraduates by telling them about instrumental benefits of philosophy classes: learning generalizable reading, writing and reasoning skills, doing better on the LSAT, etc.

But here is a very real and much more direct reason why lots of people should take philosophy classes. Most people end up having children. And children ask lots of questions. These questions include philosophical ones. Moreover, as they grow, especially around the teenage years, philosophical questions come to have special existential import: why should I be virtuous, what is the point of life, is there life after death, is there a God, can I be sure of anything?

For children’s scientific questions, there is always Wikipedia. But that won’t be very helpful with the philosophical ones. In a less diverse society, where parents can count on agreeing philosophically with the schools, parents could outsource children’s philosophical questions to a teacher they agree with. Perhaps religious parents can count on such agreement if they send their children to a religious school, but in a public school this is unlikely. (And in any case, outsourcing to schools is still a way of buying into something like universal philosophical education.) So it seems that vast numbers of parents need philosophical education to raise their children well.

Hyperreal infinitesimal probabilities and definability

In order to assign non-zero probabilities to such things as a lottery ticket in an infinite fair lottery or hitting a specific point on a target with a uniformly distributed dart throw, some people have proposed using non-zero infinitesimal probabilities in a hyperreal field. Hajek and Easwaran criticized this on the grounds that we cannot mathematically specify a specific hyperreal field for the infinitesimal probability. If that were right, then if there are hyperreal infinitesimal probabilities for such a situation, nonetheless we would not be able to say what they are. But it’s not quite right: there is a hyperreal field that is "definable", or fully specifiable in the language of ZFC set theory.

However, for Hajek-Easwaran argument against hyperreal infinitesimal probabilities to work, we don’t need that the hyperreal field be non-definable. All we need is that the pair (^*R,α) be non-definable, where ^*R is a hyperreal field and α is the non-zero infinitesimal assigned to something specific (say, a single ticket or the center of the target).

But here is a fun fact, much of the proof of which comes from some remarks that Michael Nielsen sent me:

Theorem: Assume ZFC is consistent. Then ZFC is consistent with there not being any definable pair (^*R,α) where ^*R is a hyperreal field and α is a non-zero infinitesimal in that field.

[Proof: Solovay showed there is a model of ZFC where every definable set is measurable. But every free ultrafilter on the powerset of the naturals is nonmeasurable. However, an infinite integer in a hyperreal field defines a free ultrafilter on the naturals—given an infinite integer M, say that a subset A of the naturals is a member of the ultrafilter iff |M| ∈ ^*A. And a non-zero infinitesimal defines an infinite integer—say, as the floor of its reciprocal.]

Given the Theorem, without going beyond ZFC, we cannot count on being able to define a specific hyperreal non-zero infinitesimal probability for situations like a ticket infinite lottery or hitting the center of a target. Thus, if a friend of hyperreal infinitesimal probabilities wants to be able to define one, they must go beyond ZFC (ZFC plus constructibility will do).

Doxastic moral relativism

Reductive doxastic moral relativism is the view that an action type’s being morally wrong is nothing but an individual or society’s belief that the action type is morally wrong.

But this is viciously circular, since we reduce wrongness to a belief about wrongness. Indeed, it now seems that murder is wrong provided that it is believed that it is believed that it is believed ad infinitum.

A non-reductive biconditional moral relativism fares better. This is a theory on which (a) there is such a property as moral wrongness and (b) necessarily, an action type has that property if and only if it is believed that it does. Compare this: There is such a property as mass, and necessarily an object has mass if and only if God believes that it has mass.

There is a biconditional-explanatory version. On this theory (a) there is such a property as moral wrongness and (b) necessarily, an action type has that property if and only if, and if so then because, it is believed that it does.

While both the biconditional and biconditional-explanatory versions appear logically coherent, I think they are not particularly plausible. If there really is such a property as moral wrongness, and it does not reduce to our beliefs, then it just does not seem particularly plausible to think that it obtains solely because of our beliefs or that it obtains necessarily if and only if we believe it does. The only clear and non-gerrymandered examples we have of properties that obtain solely because of our beliefs or necessarily if and only if we believe they do are properties that reduce to our beliefs.

All this suggests to me that if one wishes to be a relativism, one should base the relativism on a different attitude than belief.