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)?