There is no courage in acting contrary to justice

There is an old debate on whether one can exhibit courage when acting in an unjust cause. I used to think that one can. But now that seems obviously wrong, given that courage is a mean between defect and excess of daring:

1. Needlessly braving danger is not courageous.

2. Unjust actions are needless.

3. So, unjustly braving danger is not courageous.

Perhaps one might object to 2, on the grounds that unjust actions might be needed for some good. But one does need to do them, since no one needs to achieve the good at the expense of unjustice.

One can also vary the above argument into an a fortiori one: If braving danger pointlessly is not courageous, then a fortiori braving danger for the sake of an unjust goal is not courageous.

All that said suggests, however, that the traditional term “foolhardiness” for excess of daring isn’t quite right. For we wouldn’t call every unjust person who acts daringly for the unjust end “foolhardy”. I guess the person who acts daringly for an unjust end is worse than foolhardy: the foolhardy person’s end is good but not sufficient to justify braving the danger, while when the end is unjust, it is not only not sufficient to justify braving the danger, but it is sufficient to justify not braving the danger.

A causal powers account of the favoring relation for reasons in a choice

Suppose we accept the following causal power account of what it means for reasons to enter deliberation:

1. A complex of reasons R counts as entering into a choice C in favor of an act of will A precisely when R confers on the agent a causal power to A as the outcome of C.

And suppose we also add:

2. In a choice C, there are two or more incompatible acts of will each of which is favored by its own complex of reasons entering C.

Finally, let’s add:

3. If you have a causal power to ϕ as the outcome of C, then it is causally possible for you to ϕ when you are in C.

It follows from 1-3 that:

4. In any choice, there are two or more causally possible incompatible acts of will.

And that’s a version of the Principle of Alternate Possibilities.

What about Frankfurt cases? Well, the above metaphysics of reasons gives a very nice response to non-theistic Frankfurt cases: No finite being can make you choose act of will A in C. For if someone did so, by (3), they would have to take away your causal power to will anything incompatible with A, and by (1), they would have to take out of the choice the complexes of reasons favoring acts of will incompatible with A, and in doing so they would thus be ensuring that by (2) there is no choice (but, rather, a shoo-in, where the reasons entering the deliberation end up favoring only one action).

What about theistic Frankfurt cases? Could God, without taking away the causal power for acts of will alternative to A, simply refuse to cooperate with such acts of will? Maybe. But I think in that case, he still wouldn't be making you choose A. At most, God could ensure you don't choose any alternative. But since you had a power for non-A, you wouldn't have to go for A. At the same time, you couldn't go for any alternative to A. Thus, I think, it would be possible for you to get into a position where you can't will contrary to A, but you can refrain from willing A. The only way God could take that away from you would be by taking a way the alternate powers, and in doing so he would be making you not make a choice.

A naive argument that ought implies can

It’s just occurred to me that there is a really quick argument for the ought-implies-can principle:

1. If you do the morally best you can in a situation S, you’ve done everything you ought in S.

2. You can always do the morally best you can.

3. So, you can always do what you ought.

I understand “the best” in the weak sense that if there is a tie for the best, then doing any tied action counts as doing the best.

There is one gap. While (2) is true for us in practice, it won’t be true in certain infinitary situations, such as Satan’s Apple. But we do not in fact find ourselves in such situations, so for us, ought does imply can.

Animal consciousness

I wonder if a non-theist can be reasonably confident that non-human animals feel pain.

Start with functionalism. The precise functional system involved with feeling pain in us has no isomorph in non-human animals. For instance, in us, damage data from the senses is routed through a decision subsystem that rationally weighs moral considerations along with considerations of self-interest prior to deciding whether one should flee the stimulus, while in non-human animals there are (as far as we know) no moral considerations.

We can now have two hypotheses about what functional system is needed for pain: (a) there needs to be a weighing of damage data along with specifically moral consideration inputs, or (b) there just needs to be a weighing of damage data along with other inputs of whatsoever sort.

We cannot do any experiments to distinguish the two hypotheses. For the two hypotheses predict the same overt behavior. And even self-experimentation will be of no use. I suppose one could—at serious ethical risk—try to disable the brain’s processing of moral data, and prick oneself with a pin and check if it hurts. But while the two hypotheses do make different predictions as to what would happen in such a case, they do not make different predictions as to what one would remember after the experiment was done or how one would behave during the experiment.

Similar problems arise for every other theory of mind I know of. For in all of them, it seems we are not in a position to know precisely which range of neural structures gives rise to pain. For instance, on emergentism we know that pain emerges from our neural structures, but it seems we have no way of knowing how far we can depart from our neural structures and still get pain. On Searle-style biologism, where functionalistically irrelevant biological detail is essential for mental properties, it seems we have no way of figuring out which biological biological details permit mental function. And so on.

I know of only one story about how we can be reasonably confident that non-human animals feel pain: God, who knows everything, creates us with the intuition that certain behaviors mean pain, and in fact these behaviors do occur in non-human animals.

Lying is dishonest

I thought I posted this argument, but can’t find it, so I’m writing it up again.

1. If honesty is a virtue, dishonesty is a vice.

2. If dishonesty is a vice, then acting dishonestly is always vicious.

3. Acting viciously is always wrong.

4. Lying is always acting dishonestly.

5. So, lying is always acting viciously. (1, 2, 4)

6. So, lying is always wrong. (3, 5)

An argument for something close to property dualism

1. There are fundamental irreducible mental properties.

2. There are fundamental irreducible physical properties.

3. Necessarily, anything that has a physical property is a physical thing.

4. Recombination: Fundamental irreducible properties are all mutually compatible.

5. So, it is possible for something to have both a mental and a physical property. (1, 2 and 4)

6. So, it is possible for a physical thing to have a mental property. (3 and 5)

This seems to imply at least the logical possibility of property dualism. But not quite: for property dualism, you need that a purely physical thing has a mental property. And I think there are no purely physical things, because each substance has an immaterial form.

On a criticism of union theories of love

On some union models of love, like Robert Nozick’s, our well-being extends to include our beloved: good and bad things happening to our beloved count as happening to us.

A standard criticism of the union models (I first saw it in Jennifer Whiting’s criticism of Aristotle) is that we end up pursuing the other’s good not for their sake but for our own, since their good is a part of our well-being.

This criticism seems to me to only apply if one adds to such a union model the thesis that our actions are always solely in pursuit of our own good. But such a thesis leads to the problem that we don’t pursue other people’s good for their own sake independently of the union of love. The criticism, thus, is not a criticism of the union model of love, but of an egoistic theory of motivation.

The fact that the other’s good is a part of my good does not entail that I pursue the other’s good because it is my good. After all, we sometimes do things that we know benefit us but do them for reasons other than the benefit to ourselves. If after adding up the scores, I see that I am the winner of a game, my announcing the scores benefits me. However, I do not announce them because this benefits me, but because it’s the truth.

It is true that if I were omnirational, and if my own good were not excluded by a higher-order reason, then whenever an action benefited me, that benefit would be a part of my reasons for the action. But that is not objectionable: on the contrary, it is a part of the charm of love that the lover acts not just for the sake of the beloved but also for their own sake. That fact helps make the lover’s generosity not be a demeaning condescension.

Perhaps the criticism comes from a deeper mistake about love, the mistake of thinking that when we act lovingly, then typically the love is itself a part of the reasons for the action. For if the love is constituted by the other’s good being included in mine, and if the love is a reason for the action, then it does seem that when I act because of the love, I act because of the other’s good being included in mine. However, typically when we act lovingly, we do not act because we love. If my friend needs help, helping them is loving, but to reason “I love, so I should help” is to think a thought too many. Instead, one should just reason: “They need help.” My antecedent love makes it more likely that I will act on that reason, and my acting on that reason is partially constitutive of the continuation of the love, but the love is not itself the reason. After all, imagine that five minutes before finding out that my friend needed something, I stopped loving them. That would be no excuse not to help!

In fact, it seems to me that the best kind of union model would say something like this: What makes it be the case that my beloved’s good is a part of my good, what makes my beloved be “another me”, is the fact that I am pursuing my beloved’s good for their own sake. In other words, one could hold that love is constituted by union, but the union is constituted by pursuit of the beloved’s good.

Eliminativist relational dualism

Here is a combination of views that, as far as I know, is missing from the literature:

• eliminativism about persons

• multigrade relational dualism.

Let me explain the view. There are no people on earth. There are just particles arranged humanwise. No particle by itself has mental properties and there is no whole having mental properties. But there is irreducibly collective activity mental activity. The humanwise-arranged particles responsible for this post stand in non-physical mental relations, such as collectively being aware of the smoothness of the spacebar and collectively intending to communicate a novel philosophy of mind view. These relations are multigrade in the sense that there is no specific number of particles that are needed to stand in such a relation.

There are about 10²⁸ (give or take an order of magnitude, depending on whether we count just the brain or the whole body) particles jointly responsible for this post, but some particles are always flying off and terminating their participation in the relations and others are joining, which is why the mental relation is multigrade.

The availability of the view shows that arguments, like those of van Inwagen and Merricks, for the existence of complex wholes based on our mental function need more work. As does Descartes’ “I think therefore I am”: perhaps all we can say at the outset is is “There is thinking so there is one or more things that individually or jointly engage in thought.”

The view has the very attractive feature that it is compatible with nihilism about parthood: there need be no part-to-whole relation. This allows for a very nice and simple ideology.

The view is a dualist view, and hence puzzles about phenomenal properties, the unity of consciousness and intentionality can be solved much like in property dualism. (E.g., consciousness is unified by joint possession of a consciousness property.)

But the typical property dualist has two things to explain: why a single entity arises from a bunch of particles arranged a certain way and why that entity gains mental properties. The eliminative relational dualist only needs to explain the latter.

At the same time, some of the difficulties with the more normal kinds of eliminativism about persons (think of Unger and the Churchlands) are neatly solved. The idea of thought without any subject of thought is absurd. But we can draw on reflections in social epistemology to get a model for thought with an irreducibly plural subject of thought.

As I think is often the case with metaphysical views, the main difficulties arise in ethics. There is no particular difficulty about being responsible. The particles that engaged in a joint action are jointly responsible. The problem, however, is with holding responsible. Particles are always leaving and entering the mental relations. Many of those particles that were responsible for the robbery last year are now scattered across the city, and while (at least for last year’s robbery) a bunch of them are still clumped together, it’s impossible to punish them without punishing a plurality of particles that includes a number of particles that had nothing to do with the robbery. And this is nothing compared to the difficulty of punishing cannibalism, since we will end up punishing many victimized particles.

On one argument for dualism

I’ve never been impressed with the argument that our conscious mental states just seem very different from physical states like neuronal firings. When teaching today, I thought of a reason why not to be impressed with the argument. The following thing could easily happen. You first learned language A, and you learned that a flower called X in A smells a certain way ϕ, but when learned this you didn’t actually see the flower—you just smelled it. Years later, you learned language B, and you learned from a photo what a flower called Y in B has appearance ψ. Now you say: to smell ϕ is very different from looking ψ, so X ≠ Y. That’s clearly a poor line of thought. Smells are very different from visual appearances, but the same object can have a smell and a visual appearance. It seems to me that the mistake here isn’t very different from the argument that conscious mental states just don’t seem to be like neuronal firings…

Of course, I am not a physicalist. But generally I think arguments for dualism from intentionality are much stronger than ones from phenomenal consciousness.

Gratitude to the cosmos

Some non-theists, without thinking that the cosmos is a person, want to say that we can be appropriately grateful to the cosmos. This is supposed to do justice to our deep human need to be grateful for the good things to happen to us.

I have two lines of thought that this doesn’t work. Both start with the thought that the cosmos’s connection the good and bad events in our lives is relevantly symmetric. The cosmos is not an agent, so no kind of Principle of Double Effect can be employed to say that the good stuff is to be attributed to the cosmos and the bad stuff is not. Moreover, since the cosmos is not an agent, its activity is beyond moral justification.

Now, my first line of thought. Suppose Fred has, with no moral justification, fed me poison and an hour later he gave me an antidote. I should not be grateful for the antidote. Similarly, if I get cancer and then the cancer goes into remission, I shouldn’t be grateful to the cosmos for the remission. Yet cancer going into remission is a paradigm case of the sort of thing that we feel the need to be grateful for. But since the cosmos gave us the cancer, and did so with no moral justification, there is no call to be grateful for the cosmos taking the cancer away. (The reason for my “with no moral justification” clause is this: If the poison constituted a case of morally justified capital punishment, and the antidote constituted a morally justified pardon, then gratitude for the antidote is appropriate.)

The second is this. Given that the cosmos’s relation to the bad stuff in our lives is relevantly like its relation to the good stuff:

1. If it is appropriate to be grateful to the universe for good stuff, it’s appropriate to be resentful against the universe for bad stuff.

But:

2. It is not appropriate to be resentful against the universe.

First, intuitively, such resentment seems a paradigm case of a spiritually unfruitful attitude. I think we have all felt resentments against non-agential things—say, pieces of machinery—but clearly such resentments are something to be ashamed of.

Second, I should feel no resentment against people who, without in any way doing anything wrong, have caused bad things to happen to me. If someone running in the dark from a vicious animal accidentally knocks me down because she didn’t see me, no resentment is appropriate, because there was nothing inappropriate. Everything the cosmos does to me is in some sense an accident, because the cosmos is not an agent.

Perhaps the last argument could be countered by saying that even if the cosmos is not an agent, it might have a teleology, and perhaps we could be resentful when it departs from it (and grateful when it follows it). But I don’t think the cosmos is a substance, and only substances have an intrinsic teleology (as opposed to a teleology induced by external agency—which in this case would require something like theism).

Domination and probabilistic consistency

Suppose that ≼ is a total preorder on simple utility functions on some space Ω with an algebra of subsets. Define f ≺ g iff f ≼ g but not g ≼ f. Think of ≼ as a decision procedure: you are required (permitted) to choose g over f iff f ≺ g (g ≼ f).

Suppose ≼ doesn’t allow choosing a dominated wager:

1. If f < g everywhere, then f ≺ g.

Let 1_A be the function that is 1 on A and 0 outside A. Define Ef = sup{c : c ⋅ 1_Ω ≼ f}. Here are some facts about E:

2. If c < Ef < c′, then c ⋅ 1_Ω ≺ f ≺ c′⋅1_Ω.

3. E(c ⋅ 1_Ω)=c

4. If f ≤ g everywhere, then Ef ≤ Eg.

5. If Ef < Eg, then f ≺ g.

(But we can’t count on its being the case that f ≺ g if and only if Ef < Eg.)

Now consider what I’ve called the independent and cumulative decision procedures for sequences of choices. On an independent decision procedure, at each stage you must choose a wager that is ≼-maximal (and you may choose any of the maximal ones). On a cumulative decision procedure, at each stage you must choose a wager that when added to what you’ve already chosen yields a ≼-maximal wager (and you may choose any of the maximal ones).

I think (I haven’t written it all down) I can prove that the following conditions are equivalent:

6. E is an expected value with respect to a finitely-additive probability P on Ω.

7. The independent decision procedure applied to a sequence of binary choices never permits you to choose a sequence of wagers whose sum is strictly dominated by the sum of a different sequence of wagers you could have chosen.

8. The cumulative decision procedure applied to a sequence of binary choices never permits you to choose a sequence of wagers whose sum is strictly dominated by the sum of a different sequence of wagers you could have chosen.

The probability P is defined by P(A)=E(1_A).

All that said, I think that when your credences are inconsistent, you may need to decide neither independently nor cumulatively, but holistically, taking into account what wagers you made and what wagers you expect you will make.

Norms and the causal theory of reference

1. We can refer to norms.

2. We can only refer to the kinds of things that cause effects in us. (Causal theory of reference.)

3. So, norms are a kind of thing that causes an effect in us.

4. Norms are non-physical.

5. So, something non-physical causes an effect in us.

6. So, either we are not entirely physical, or the non-physical affects the physical, or both.

Normative powers

Consider:

1. Purely physical things have only physical powers.

2. Normative powers (i.e., powers of producing normative effects, such as promises and commands) are not physical powers.

3. We have normative powers.

4. So, we are not purely physical.

I guess what I am not sure about in this argument is whether “power” is used univocally between “physical powers” and “normative powers”.

A bad argument from hiddenness

Consider the following variant of the argument from hiddenness:

1. If God exists, no mature human is ignorant of God’s existence through no fault of their own.

2. Some mature humans are ignorant of God’s existence through no fault of their own.

3. So, God doesn’t exist.

It’s occurred to me that premises like (3) are either nonsense, or trivially false, or far beyond our capacity to know to be true.

For to evaluate whether some x is ignorant of God’s existence through no fault of their own requires asking something like this:

4. Would x still have been ignorant of God’s existence had x lived a morally perfect life?

But it does not seem likely that there is a sensible positive answer to (4). Here is a quick argument for this. Those who deny Molinism are going to say that either the proposition asked about in (4) has no truth value or that it is trivially false. And even some Molinists will say this about (4), because Molinists are committed to there being conditionals of free will only when the antecedent is maximally specified, while “x lived a morally perfect life” is too unspecified. The question is much like:

5. Had Napoleon been born in South America, would he still have been a great military leader?

There are many ways for Napoleon to have been in South America, and they are apt to result in different answers to the question about whether he was a great military leader.

But even if (4) has a truth value, perhaps because (4) is to be interpreted in some probabilistic way or because we have an expansive version of Molinism that makes (4) make sense, it is far beyond our epistemic powers to know the answer to (4) to be true. Here is why. Our lives are full of wrongdoing. Our lives would likely be unrecognizable had they been morally perfect. To ask what we would have thought and known in the counterfactual scenario where we live a morally perfect life is to ask about a scenario further from actuality than Napoleon’s being born in South America.

Now, that said, there are times when we can evaluate counterfactuals that involve a massive change to the antecedent on the basis of certain generalities. For instance, while we have no answer to (5), we do have a negative answer to:

6. Had Napoleon suffered a massive head injury rendering him incapable of interpersonal communication, would he still have been a great military leader?

Similarly, if an atheist had suffered a head injury removing the capacity for higher level thought, the shape of their life would have been very different, but at least we can say that they wouldn’t have been an atheist, because they wouldn’t have had the concepts necessary to form the belief that there is no God. So, indeed, sometimes counterfactuals that take us far afield can be evaluated sensibly on general grounds.

But I do not think we have good general grounds for a positive answer to (4), unless we have independent grounds to doubt the truth and rationality of theism:

7. There are no good grounds for reasonably believing in God, and a person who lives a morally innocent life won’t believe things groundlessly, so they won’t believe in God.

8. There are people who grow up in societies where there is no concept of God, and they would not be aware of God no matter what the shape of their lives would have been.

Obviously, (7) requires independent grounds to doubt the rationality of theism. And if God exists, then for all we know, he has a general practice of making those who are morally perfect be aware of him, so (8) is dubious if God exists.

Of course, an atheist might think (7) is true, but this is unlikely to be a helpful move in an argument against the existence of God. After all, similarly, a theist might think the following is true:

9. God will ensure that every morally perfect mature human is aware of him.

Indeed, a typical Christian thinks that there have only ever been one or two people—Jesus and maybe Mary—who have been morally perfect, and both candidates were aware of God.

Divine hiddenness as a problem for atheists

One might think that divine hiddenness is a problem for the theist but not at all for the atheist. That is not so clear to me. Consider the plausible evolutionary psychology stories about theistic belief, such as that social animals as smart as us will be sufficiently able to outwit the social enforcement of cooperative behavior and the best evolutionary solution is to have us believe in a being who misses nothing and whose judgment cannot be escaped. But given such good evolutionary stories about theistic belief, why are there so many who do not believe?

I am not saying the problem has no good answer, just that there is still a problem there, even if theism is false.

Towards a postcorpuscular ontology

My intuition is that quantum physics presents a picture of reality on which fundamental particles rarely if ever exist simpliciter. Most of the time, the world is in a superposition of the particle existing and not-existing, though perhaps with a much heavier weight being given to the one state rather than the other. Perhaps just at the moment of quantum collapse a particle simply exists. But immediately afterwards, there will be some interaction at the tail end of the wavefunction that makes the particle’s “existence” be in a superposition. And superposed existence is not real existence, since superposed existence comes in degrees, while real existence does not (at least not in the relevant sense of “degrees”).

If my intuition is right, then over the past hour, I take it that on a quantum picture at most instants of time no particles of my body were really existing. Maybe occasionally some particles flashed into being due to some collapse, but at most times there weren’t any particles there.

This means that at most times over the past hour one of the following was true:

1. I didn’t exist

2. I existed immaterially

3. I existed materially without having any particles.

Option (1) leads to ethical and theological difficulties. On that view, I am constantly popping in and
out of existence. But if so, then I am constantly dying and being resurrected. And that robs death and resurrection of their deep moral significance.

Option (2) leads to the interesting question whether I always exist immaterially, or only when none of my particles exist. If always, we get a very strong dualism. If sometimes, then we get a very funny semi-dualism: most of the time I’m immaterial.

Option (3) seems to me to be the most plausible. But on option (3), we should not think of material existence as a function of being constituted by particles. The kind of picture of material existence we get from van Inwagen, where living things come into existence by having their constituent particles get caught up in a life is untenable. Perhaps, instead, material existence is a function of having a certain kind of relationship to the wavefunction of the universe (perhaps a relationship of partly constituting or being partly constituted by that wavefunction).

If my argument is right, then Aristotelian metaphysicians should stop worrying very much about the pesky problem of what happens to the identities of fundamental particles when they get incorporated into our bodies. If there are ever any particles at all, then on quantum grounds independent of Aristotelian metaphysics, they are evanescent beings that do not persist long enough—for their existence soon becomes superposed—to cause much of a problem on that score. I suppose it could still be a problem if they come back into existence later. But it is dubious whether the numerically same particles can come back into existence. Indeed, the whole business of the particles “in the body” is so dubious on quantum grounds, that there is little theoretical cost to such seemingly absurd solutions as saying that there are no electrons in the body—for it seems we should anyway think that most of the time there aren’t any electrons in the body.

In the above, I allowed that perhaps when we have the right eigenstate, for a very short time a particle exists. But even that, I think, is dubious. The change from the system being in an eigenstate of particle number and not being in an eigenstate of particle number seems to be a merely quantitative change in the wavefunction, and hence we have little reason to think it corresponds to substantial generation or corruption.

There is one way out of all of the above: to accept a Bohmian interpretation of quantum mechanics. If I am right, then much contemporary metaphysics is being done on the implicit assumption that something like Bohmianism is right. But why assume that?

Constructive empiricism and pairs

Van Fraassen thinks that when we accept a scientific theory, we should be bracket the theory’s claims about unobservable entities, but believe everything else.

An oddity has occurred to me. Suppose a theory talks about certain microorganisms that are just under the minimum size for human visual observation. But when you have two things that are just under the minimum observable size side-by-side, the pair is observable. So, oddly, we will believe in pairs without believing in individuals.

For further oddity, now imagine that Alpha and Beta are such a side-by-side pair. Then we believe in Alphabeta, the pair of Alpha and Beta. Suppose Alpha swims a little away from Beta. Now, Alphabeta disappears from view. But Alphabeta is still observable. To observe Alphabeta, all we need to do is to coax Alpha and Beta to swim to each other. So on van Fraassen grounds, we should still continue to believe in Alphabeta even when temporarily we cannot see it due to the separation of Alpha from Beta. (Compare: a very thin sheet is still observable when it is edge-on, even though it can only be seen when tilted to the line of sight.)

But it is absurd to believe in a pair of organisms, at different ends of a test-tube, without believing in either organism.

One way out for van Fraassen is to adopt a sparse ontology on which there are no pairs. But while I like such an ontology, I don’t think van Fraassen will want to do that, as he wants to believe in observable objects that science talks about, such as planets.

A new argument for presentism

Here’s an interesting argument favoring presentism that I’ve never seen before:

1. Obviously, a being that fails to exist at some time t is not a necessary being.

2. If presentism is true, we have an elegant explanation of (1): If x fails to exist at t₁, then at t₁ it is true that x does not exist simpliciter, and whatever is true at any time is possibly true, so it is possible that x does not exist simpliciter, and hence x is not a necessary being.

3. If presentism is false, we have no equally good explanation of (1).

4. So, (1) is evidence for presentism.

I don’t know how strong this argument is, but it does present an interesting explanatory puzzle for the eternalist:

5. Why is it that non-existence at a time entails not being necessary?

Here’s my best response to the argument. Consider the spatial parallel to (1):

6. Obviously, a being that fails to exist at some location z is not a necessary being.

It may be true that a being that fails to exist at some location is not a necessary being, since in fact the necessary being is God and God is omnipresent. But even if it’s true, it’s not obvious. If Platonism were true, then numbers would be counterexamples to (6), in that they would be necessary beings that aren’t omnipresent.

But numbers seem to be not only aspatial but also atemporal. And if that’s right, then (1) isn’t obvious either. (In fact, if numbers are atemporal, then they are a counterexample to presentism, since they don’t exist presently but still exist simpliciter.)

What if the presentist insists that numbers would exist at every time but would not be spatial? Well, that may be: but it’s far from obvious.

What if we drop the “Obviously” in (1)? Then I think the eternalist theist can give an explanation of (1): The only necessary being is God, and by omnipresence there is no time at which God isn’t present.

Maybe one can use the above considerations to offer some sort of an argument for presentism-or-theism.

A problem for Level Set Integrals

Suppose that you have inconsistent but monotone credences: if p entails q then P(Q)≥P(p). Level Set Integrals (LSI) provide a way of evaluating expected utilities that escapes Dutch Books and avoids domination failure: if E(f)≥E(g) then g cannot dominate f.

Sadly, by running this simple script, I’ve just discovered that LSI need not escape multi-shot domination failure. Suppose you have these monotonic credences for a coin toss:

• Heads: 1/4

• Tails: 1/4

• Heads or Tails: 1

• Neither: 0.

Suppose you’ll first be offered a choice between these two wagers:

• A: $1 if Heads and $1 if Tails
• A′: $3 if Heads and $0 if Tails

and then second you will be offered a choice between these two wagers:

• B: $1 if Heads and $1 if Tails
• B′: $0 if Heads and $3 if Tails.

You will first choose A over A′ and then B over B′. This is true regardless of whether you use the independent multi-shot decision procedure where you ignore previous wagers or the cumulative method where you compare the expected utilities of the sum of all the unresolved wagers. The net result of your choices is getting $2 no matter what. But if you chose A′ over A and B′ over B, you’d have received $3 no matter what.

Stepping back, classical expected utility with consistent credences has the following nice property: When you are offered a sequence of choices between wagers, with the offers not known in advance to you but also not dependent on your choices, and you choose by classical expected utility, you won’t choose a sequence of wagers dominated by another sequence you could have chosen.

Level Set Integrals with in my above case (and I strongly suspect more generally, but I don’t have a theorem yet) do not have this property.

I wonder how much it matters that one does not have this property. The property is one that involves choosing sequentially without knowing what choices are coming in the future, but the choices available in the future are not dependent on the choices already made. This seems a pretty gerrymandered situation.

If you do know what choices will be available in the future, it is easy to avoid being dominated: you figure out what sequence of choices has the overall best Level Set Integral, and you stick to that sequence.