Utility and the infinite multiverse

If we live in an infinite universe, then when we look at total values and disvalues, total utilities, we will always run into infinities. There will be infinitely many persons, of whom infinitely many will provide instances of flourishing, after all. Now one might say: "So what? Our individual actions only affect a finite portion of that infinite sea of value and disvalue."

But this may be mistaken. For if there are infinitely many persons, presumably there are infinitely many persons who have a rational and morally upright generally benevolent desire. A generally benevolent desire is a distributive desire for each person to flourish. It is not just a desire that the proposition <Everyone flourishes> be true, but a desire in regard to each person, that that person flourish, though the desire may be put in general terms because of course we can't expect people to know who the existent persons are.

Now, if you have a rational and morally upright desire, then you are better off to the extent that this desire is satisfied (some people will think this is true even with "and morally upright" omitted). Thus, if you have a rational and morally upright general benevolence, then even if some men are islands, you are not. Whenever someone comes to be better off, you come to be better off, and whenever someone comes to be worse off, you come to be worse off. So if infinitely many people have a rational and morally upright general benevolence, whenever I directly do something good or bad to you, I thereby benefit or harm infinitely many people. And no matter how small the benefit or harm to each of these generally benevolent people, it surely adds up to infinity.

St. Anselm thought that our sins were infinitely bad as they were offenses against an infinite God. If we live in a multiverse, those of our sins that harm people also harm infinitely many people.

One might object that the generally benevolent person will only be infinitesimally benefitted or harmed by a finite harm to one person in the infinite sea of persons in the multiverse. That may be true of some very weakly benevolent people. But there will also be infinitely many generally benevolent people whose general benevolence will be sufficiently strong that the benefit or harm will be non-infinitesimal. After all, one can imagine a person who, if faced with a choice whether she should gain a dollar or a stranger she knows nothing about should gain a hundred dollars would always prefer the latter option. Such a person counts benefits and harms to other people at at least 1/100th of what such benefits and harms to herself would count as. And so if I deprive anybody of a hundred dollars, each such a generally benevolent person will, in effect, be harmed to a degree equal to a one dollar deprivation. As long as there are infinitely many generally benevolent people with at least that 1:100 preference ratio, the argument will yield that a non-infinitesimal harm to anybody results in an infinite harm. And plausibly there would in fact be infinitely many people with a 1:1 preference ratio, or maybe even a 2:1 preference ratio (they would rather that others benefit than themselves).

So we cannot avoid dealing infinite utilities if there are infinitely many persons. For each of our nontrivial actions will affect infinitely many persons, since infinitely many persons will have rational and morally upright desires that bear on the action.

Moreover, even denying the existence of an infinite multiverse, or of an infinite universe, won't get us off the hook. For even if we don't think such an infinitary hypothesis is true, we surely assign non-zero epistemic probability to it. The arguments against the hypothesis may be strong but are not so strong as to make us assign zero or infinitesimal probability to it. And a non-zero non-infinitesimal probability of an infinite good still has infinite expected utility.

Interestingly, too, as long as overall people flourish across an infinite multiverse, each such non-infinitesimally generally benevolent person will seem to be infinitely well off. Such are the blessings of benevolence in an overall good universe.

The above argument will be undercut if we think that one only benefits from the fulfillment of a desire when one is aware of that fulfillment. But that view is mistaken. An author who wrote a good book is well off for being liked even if she does not know that she is liked.

Even more on infinity and probability

Imagine a sequence of blindfolded electrically charged people, at positions 1,2,3,... on a line in some coordinate system. Let f be a permutation of the natural numbers with the property that f(n) is even if and only if n is divisible by four—this permutation maps the even numbers onto the numbers divisible by four and the odd ones onto the numbers not divisible by four. Suppose the person at position n has electric charge f(n). You're one of the people. And that's all the empirical data you have.

Question 1: What is the probability that your electric charge is even?

Obvious Answer: The people at positions on the line divisible by four have even electric charge. So the probability that you have positive electric charge equals the probability that your position is divisible by four. But every position has exactly one person on it, and so the probability that your position is divisible by four is 1/4. Hence that's also the probability that your electric charge is even.

Inobvious Answer: Instead of mentally arranging people by position, arrange them by electric charge. There is exactly one person per natural number arranged by charge. And so the probability that your number is even is 1/2.

The point here is that P(charge is even)=P(position is divisible by four). When we focus on the arrangement by position we are inclined to assign 1/4 to the right hand side, and hence we assign it to the left hand side, too. When we focus on the arrangement by charge we are inclined to assign 1/2 to the left hand side, and hence we assign it to the right hand side, too.

Which is right?

Maybe we can say that one of the two orderings is more relevant for calculating probabilities. I suspect that anybody who takes this route will take the positional arrangement to be that one.

But is that really right? Imagine an angel that is assigning positions and charges to an infinite number of people subject to the rule that the person at position n gets charge f(n). The angel might start by first holding an infinite lottery where each person first gets given a position number, and then will use that position number to calculate the charge f(n) for the person. Or the angel might start by holding an infinite lottery where each person first gets given a charge number m, and then the position number is calculated as f⁻¹(m). In the former case, our ansewr might seem to be 1/4, while in the latter it seems to be 1/2. We have no idea which the angel is going to do if the information listed is all we have, nor any idea whether it is going to be an angel, or a natural process, or whatever. Maybe then we should average the two probabilities, and get (1/2+1/4)/2=3/8 as our probability? But that doesn't seem right, either.

I suspect the right answer is that in this scenario there just is no answer to the question. And if that is right, then where there is a simultaneous infinity of cases in a reference class—as in some multiverse scenarios—there are no probabilities.

But what if instead of spatial arrangement we have temporal arrangement? Then I have an intuition that the temporal arrangement takes priority over the charge arrangement for the calculation of probabilities (and would even take priority over the positional arrangement, I guess). I don't know if I should keep or abandon this intuition. It might offer an important disanalogy between space and time.

Coinstantiation

One of the fundamental concepts of bundle theory is a coinstantiation relation between properties. Interestingly, it may be possible to reduce coinstantiation to instantiation and entailment. Specifically, a bundle theorist may say that the Ps (some plurality of properties) are coinstantiated if and only if there is a property Q such that (a) Q entails each of the Ps and (b) Q is instantiated.

Dutch Books and probabilistic inconsistency

It is often said that if your credences are probabilistically inconsistent, e.g., because you assign probability 0.6 to p and 0.6 to its negation ~p, then you are subject to a Dutch Book, namely a bookie can present you a sequence of betting deals such that by your lights you will want to accept each one, but if you accept them all, then you are certain to lose money no matter how things turn out.

While this is often said, and there is indeed a theorem that roughly says the above, it's not exactly true when it's put as above.

Take the above case where you assign 0.6 to p and 0.6 to ~p. The standard way to construct a Dutch Book would be something like this. If you assign 0.6 to p, then you'd be happy to pay $5.50 for a ticket that wins $10 if p is true. And since you assign 0.6 to ~p, you'd be happy to pay $5.50 for a ticket that wins $10 if p is false. So if you're offered both bets, you'll be happy to accept, but then no matter whether p turns out to be true or false, you'll have paid out $11 but only win $10, a sure net loss of $1.

But the thought that you'll be happy to pay $5.50 for the ticket that wins $10 if p is true can be questioned. The justification for the thought goes like this: You will value the $10-if-p option at its expected value of (0.6)($10)=$6, calculated with your probability assignment. Hence, you will be happy to buy the $10-if-p option for any amount less than $6. And ditto for ~p.

However, this is not the only way to think about the case. The question whether to accept the first deal, namely to pay $5.50 for the chance to win $10 if p is true, can be thought of as the choice between the accept and reject moves in this game

	p	~p
accept	$4.50	−$10
reject	$0	$0

Now the natural way to evaluate the value of the accept line is: (0.6)($4.50)+(0.6)(-$10)=−$3.30, since you assign 0.6 to p and 0.6 to ~p. And of course the value of the reject line is (0.6)($0)+(0.6)($0)=$0. So the reject move is the best one. And of course the same goes for the evaluation of the second deal offered by the bookie. So if you evaluate the choices according to the above methods, you will in fact reject both of the bookie's deals.

In fact, if you adopt the above way of calculating whether you should accept a deal or not, then in the case where there is just one proposition whose truth or falsity is at issue, and you assign equal positive probabilities to its truth and to its falsity, then you will come up with the very same decisions as the consistent decision theorist who assigns 0.5 to p and 0.5 to ~p. Since the consistent decision theorist is not subject to a Dutch Book, neither are you.

So what just happened? Well, what happened is that there are two ways of figuring out whether to pay $5.50 for the ticket that wins $10 if p is true. The standard way is to calculate the value of the ticket, using the obvious calculation (0.6)($10) = $6, and then compare that to the price $5.50 of the ticket. Basically, we are comparing two values: the value of the ticket and the value of a sure $5.50. We are, further, assuming that the value of a sure $5.50 is, well, $5.50. But the latter assumption can be questioned when the probabilities are inconsistent. For while you might say that the value of a sure $5.50 is just (1.0)($5.50)=$5.50, you might also break up that sure $5.50 according to the two options at issue, namely p and ~p, and calculate the value of that sure $5.50 as (0.6)($5.50)+(0.6)($5.50) = $6.60. (Of course, that value looks wrong, but we shouldn't expect things to look right with inconsistent probabilities!) And now we ask whether it's worth giving up that sure $5.50 for the ticket, and we will say that it's not, since the ticket's value is $6 while the sure $5.50 is worth $6.60. This calculation is equivalent to the one implicit in the game-based calculation above.

Here's a more formal way to look at it. When you're evaluating the value of a betting portfolio B that has only finitely many values, a natural thing to do is to break up the sample space into a partition E₁,...,E_n with the property that B takes a constant value V(B,E_i) on each of the E_i. Then the value of B is naturally given by the formula:

• V(B,E₁)P(E₁)+...+V(B,E_n)P(E_n).

If the probabilities are consistent, then it doesn't matter which partition is chosen for the calculation, as long as the value of B is constant on each element of the partition. But when the probabilities are not consistent, then in general the value depends on the choice of partition. The standard calculation makes the following stipulation:

1. Let E₁,...,E_n be the coarsest partition with the property that B takes a constant value on each E_i.

But that is not the only reasonable stipulation available. Here is another:

2. When comparing the values of bets B₁,...,B_k, let E₁,...,E_n be the coarsest partition with the property that each of the B_i takes a constant value on each of the E_j.

The second stipulation leads to results equivalent to those coming from thinking about things in terms of the table I gave earlier. This stipulation does mean that the comparative values of two bets will in general depend on what other bets they are being compared to, and hence we do not satisfy independence of irrelevant alternatives. But things like that shouldn't surprise us given that we're reasoning with inconsistent probabilities!

Moreover, the above is not a complete get-out-of-Dutch-Book card for inconsistent reasoners. There still will be probability assignments subject to Dutch Books. But it will not be the case that every inconsistent assignment is subject to a Dutch Book.

Further, there is an interesting practical question. We have good reason to think that real agents have inconsistent probabilities. When they make decisions on the basis of inconsistent probabilities, we can ask: What should they do, given that their probabilities are inconsistent? Should they decide using the standard method that partitions the sample space according to rule (1) or should they partition it via rule (2)? There is some reason to think that rule (2) is actually the better one for inconsistent reasoners—after all, it less often leads to Dutch Books!

Low-probability explanations

Here is a plausible principle:

1. If p explains q₁ and p explains q₂, then p explains the conjunction of q₁ and q₂.

Now suppose that p says that persons x₁,x₂,...,x₁₀₀ were the buyers of tickets to a fair lottery, with each buying one ticket. Let q_i be the proposition that person x_i did not win. Suppose that in fact x₁₀₀ won. Then p explains q₁ with a perfectly fine 99/100 stochastic explanation. And by the same token p explains q₂, and so on up to q₉₉. So by (1), p explains the conjunction of q₁,...,q₉₉. But the probability of that conjunction being true given p is only 1/100. So we have a stochastic explanation despite a low probability.

One can even rig cases where one has a stochastic explanation despite zero probability if (1) extends to infinite conjunctions.

Two arguments for extended simples

A simple is something that lacks proper parts. An extended simple is a simple that occupies a region of space that is more than a point.

1. If I am not simple, then I think with a proper part of me.
2. I do not think with a proper part of me.
3. So, I am a simple.
4. I am extended.
5. So, I am an extended simple.
6. So, there is an extended simple.

The thought behind (1) is that if I am not simple, then my brain and/or my soul are going to be parts of me in the true ontology, and surely if the true ontology contains them, then I think with them. The thought behind (2) is that if A is a proper part of B, and I think with A, then A is a better candidate than B for being me. And (4) follows from the fact that I am 182 cm tall.

While I am inclined to accept (6), I find the argument for (2) weak. I would find it stronger if one could conclude from the fact that I think with A that A thinks, but I don't see that that follows.

Maybe a better argument:

7. No particle occupies just one point.
8. All particles occupy space.
9. Some particles are simple.
10. Something that occupies space but does not occupy just one point is extended.
11. So, there is an extended simple.

The thought behind (7) is that in real life no particle has a wavefunction that is concentrated at one point.

Here, I am actually not sure of (10).

Some valid arguments from absurdity

Here are some curious forms of argument that I want to play with. First:

1. Doctrine D is so absurd that no one could believe D while fully realizing its absurdity, except by a miracle.
2. Someone believes D while fully realizing its absurdity.
3. So, a miracle has occurred.

Given the human capacity for believing the unbelievable, it is going to be hard to support (1) for any interesting D (except maybe: p and not p).

Let's try this:

4. Doctrine D is so absurd that no one could reasonably believe D while fully realizing its absurdity, except by a miracle.
5. Someone reasonably believes D while fully realizing its absurdity.
6. So, a miracle has occurred.

In arguments of this sort, the difficulty has shifted to (5). But we might try the following. Start by observing that a person doesn't become unreasonable simply by having a trivial belief that isn't reasonable. But to center one's life one a belief that isn't reasonable might be enough to render one unreasonable:

7. If at least one of the beliefs central to x's life is not reasonable, then x is an unreasonable person.
8. x is not unreasonable.
9. One of the beliefs central to x's life is D.
10. x fully realizes the absurdity of D while believing D.
11. So someone reaosnably believes D while fully realizing its absurdity.

The conclusions of the above arguments were that a miracle has occurred. Can we conclude that D is true? Well, we would have to look at our best explanation of the miracle. If it involves God, then we have reason to think D is true. Here's an argument that avoids the detour through miracles.

12. Doctrine D is so absurd that no reasonable person would hold D as a belief central to her life while fully realizing D's absurdity unless she knew D to be true.
13. Some reasonable person held D as a belief central to her life while fully realizing D's absurdity.
14. So, somebody knew D to be true.
15. So, D is true.

I think the big difficulty with arguments of this form in the cases most familiar to me, namely with D a doctrine from the Christian tradition, is that people who are paradigm examples of rationality, like Thomas Aquinas, do not take the doctrine to be really absurd.

The draft

Suppose Belgium is being attacked by a vicious enemy who is particularly targetting civilians—especially children—in a terroristic campaign. Currently, Belgium has an all-volunteer army. However, experts with excellent predictive track records estimate that conscripting 200,000 men for about a year will save almost as many lives, mainly those of children. These 200,000 draftees would be subject to the rigors and hardships of a tough year-long military campaign. Surprisingly, however, due to recent improvements in personal armor, the campaign is expected to result in fewer than 100 deaths of draftees.

There is nothing morally objectionable about the government having such a draft and those called up for it would have a moral duty to serve. Note that the projected death-rate expected from the campaign is about 50 times lower than the US military death-rate in WWII. Such a low death-rate makes this draft close to obviously right.

Now compare this to Judith Jarvis Thomson's arguments—like the famous violinist one—for abortion. In the Belgian draft case, in pregnancy and in Thomson's cases, people lose significant aspects of their ordinary freedoms and capabilities, and do so for the sake of saving the lives of others. I think the draft case underlines that Thomson's cases underestimate the degree to which we can be legitimately morally required to make significant sacrifices to save the lives of others.

Notice, too, three differences between the draft and violinist cases. While the particular people saved by the draft in my story are primarily children, and hence not the draftees themselves, the practice of instituting a draft in such dire wartime circumstances is one that all can potentially benefit from. If I am to be drafted and save the life of some child and I am considering running off, I should reflect that it's just a matter of my luck that the invasion happened now rather than when I was a child and when others would have been drafted to protect me. I need to do my bit or else I will be a freerider. It is not so in the violinist case. I am not a famous violinist. People are not at all likely kidnap anybody to provide life support for me! The pregnancy case here is like the draft case, but even more so. For we all not merely potential beneficiaries of the practice, but actual beneficiaries, since we all came into existence through pregnancy.

Second, in the draft case there is a not insignificant chance that the child whose life one's being drafted will save will be one's own child, while the violinist is a stranger. But in the case of pregnancy the child is almost always one's own (the exception is in cases of surrogate pregnancy). Again, the pregnancy case is more like the draft case, and even more in that direction.

The third difference may seem to play in a different direction, however. Both the pregnancy and the violinist cases involve direct use of one's internal organs. But in the draft, one's womb and one's kidneys are not being drafted—it is the use of external organs, like hands and legs, that is required of one. While there may be a small difference along these lines, I think the difference is not particularly significant. The soldier fights not just with hands and legs, but also with the brain, and is required to do so. To have one's kidneys get used, as in the violinist case, is no more invasive of one's person than to have to obey orders, to have to focus with one's brain and mind on the tasks that one's commander requires one to focus on. The loss of autonomy on a military campaign is, if anything, greater than in the pregnancy and violinist cases.

Note, too, that the draft argument gives support for two claims. First, it supports a moral claim: It is one's duty, on pain of freeriding, to do one's bit for saving lives. Second, it supports a policy claim: It can be both permissible and reasonable for the state to require this of one.

Immutability and split brains

The traditional Christian view that God is unchanging has been accused of being a fruit of Greek ideals of perfection (and what's wrong with that?). Here I want to motivate this view by thinking about our mental life.

But our conscious states are divided between times in much the way that the two centers of consciousness of a split-brain patient are divided from each other. My present state of consciousness only includes shadowy reminders of what I was aware of five minutes ago and vague premonitions of what I am about to be aware of. My temporality makes me like a patient split into untold numbers of centers of consciousness associated with different times (perhaps in a continuous way, with overlapping between close-by centers, since many of our mental states themselves persist over short amounts of time). We are deeply internally disunited--our "transcendental unity of apperception" is quite limited. Such deep internal division and disunion is surely not what the perfect being would experience (at least not in his proper nature—an Incarnation might make for such an experience, and the above reflection should make us grateful that he took up this deeply divided existence for our sake). This is not a matter of some "Greek ideal" of perfection. It is simply the intuition that mental division within oneself is an imperfection.

The above argument presupposes eternalism. But presentism only introduces even greater limitation in our mental life by making the future and past conscious states not be ours.

So we have good reason to think of God's mental life as all-encompassing, of God living an infinitely rich mental life all at once, as Boethius said. But God is a mind and surely all of his mental states are conscious. This gives us good reason to think God is unchanging.

The importance of the future

It would be bad for me to permanently cease to exist in five minutes. But why? Suppose first a metaphysics of time on which there is no future, namely Growing Block or Presentism. On such a metaphysics there is no such thing as my future life, so how could it be bad for there to be a cessation of it?

Since the only tenable alternative to Growing Block and Presentism is Eternalism, the view that the past and future are real (oddly, there are no Futurists who think the future is real but deny the reality of the past), Eternalism is true.

Now, given Eternalism, we have a choice for three visions of our persistence through time. On one vision, Exdurantism, we are instantaneous stages that do not persist through time at all—at most we have temporal counterparts at other times. This does not fit with the intuition of my radical incompleteness should I cease to exist in five minutes. The second vision is Endurantism: I am wholly present at each time at which I exist. But then if the present moment is real, and eternally will be real, and I wholly exist at this present moment, then the intuition about the deep incompleteness I would have were my existence to permanently end in five minutes is undercut. So that can't be right either.

What remains is a family of views on which we are strung out four-dimensionally. The most common member of the family is Perdurantism: I am four-dimensional but have three-dimensional stages localized at times. A less common view is that I am four-dimensional, but not divided up into stages. Both of these views do justice to the idea that my existence is deeply incomplete, in something like the way it would be if I were missing an arm, should I cease to exist in five minutes.

As far back as I thought much about time (probably going back to age 10) I was an Eternalist. Until a couple of years ago, I was an Endurantist. Then I started being unsure whether Endurantism or a stageless four-dimensional view is right. The above argument strongly pushes me towards a four-dimensional view, and since I don't believe in stages, a stageless one.

Moreover, the above may help with a puzzle I used to have, which was how a B-Theorist should think about the badness of impending evils (especially death). How can a B-Theorist make sense of the badness of being closer and closer to something bad? But that may primarily be a problem for the Endurantist, since the Endurantist thinks we are three-dimensional beings wholly located in the here and now (as well as in the there and later, of course).

Hope

If there are ten lottery tickets, and I hold one, I shouldn't hope to win, but I should simply assign probability 1/10 to my winning. Anything beyond the probabilities in the way of hope would be irrational. Likewise, if I have probability 9/10 of winning. Then I can have confidence, but this confidence should no more be a hope than in the former case. It's just a confidence of 9/10.

But if my friend has fallen morally many times but promises to do better, I shouldn't simply calculate the probability of his doing better using the best inductive logic and leave it at that. I should hope he will do better.

What makes for the difference? In the case of the friend, he should do better. But it is, of course, false that I should win the lottery. Indeed, the outcome of my winning the lottery is in no way normatively picked out. I can appropriately hope that the lottery will be run fairly, but that's that.

If this is right then it seems hope is of what should be. Well, that's not quite right. For if I have done something so terrible that my friend is under no obligation to forgive me, I can still hope for her supererogatory forgiveness. So, perhaps, hope is of what should be or what goes over and beyond a should.

If this is right, then this neatly dovetails with my account of trust or faith. Faith has as its proper object a present state of affairs that should be, such as a testifier's honesty and reliability, or perhaps—I now add—a present state of affairs that goes beyond a should. Hope has as its proper object a future state of affairs that should be or goes beyond a should. Both of these flow from love.

If this is right, then in order for there to be appropriate hope in things beyond human power—such as a hope that an asteroid won't wipe out all life on earth—there must be shoulds, or beyond-shoulds, that go beyond human power. This requires an Aristotelian teleology or theism.

Despair

1. If there is no hope of an afterlife, all is hopeless.
2. If all is hopeless, ultimate despair is the right attitude.
3. Ultimate despair is not the right attitude.
4. So there is hope of an afterlife.

I will argue for 1 and 3. If there is no hope of an afterlife, any redeeming value we might hope for is overshadowed by the ultimate evil of both the end of our individual lives and of the human race. But despair is not the right attitude, since despair makes it impossible for us to live our moral lives, both in terms of the motivation to pursue the good and in our duty to comfort others. Despair saps our motivation. And faced with ultimate hopelessness, any comfort we might offer to others is insincere and dishonest. In despair at ultimate hopelessness, we could only live the good human life through self-deceit and the deceit of others. But that is not right. So ultimate despair cannot be the right attitude as it makes the good life impossible.

So there is hope.

Deep Thoughts XXXV

Meeting the minimum requirements is always good enough.

[This is a variant on XXXIV. There are times when we say things like "The minimum is not good enough." When we do that, what I think happens is that we have a context shift. "The minimum" is understood relative to one set of ends or norms while the "good enough" is understood relative to another. One kind of a case is where you're competing for a job. Meeting the minimum required qualifications is good enough for being hirable in principle (if it's not, the minimum requirements were incorrectly stated), but is not good enough for beating the competition. Another kind of case is where someone is being evaluated in a number of areas (or with respect to a multiplicity of assignments). In each area, there is a minimum requirement. Meeting that requirement is good enough for not failing according to that requirement. But there may be a second, meta requirement to exceed the minimum in most of the areas. (There cannot coherently be a requirement to exceed the minimum in all areas. For if there were such, then the "minimum" in each area would not be a minimum requirement but a maximum disqualifier.) In any case, when we keep the context constant (and as a rule in natural language context in short sentences stays constant), "The minimum is not good enough" is a self-contradiction.]

A simple consequence argument

Say that p and q are nomically equivalent provided that the laws of nature entail that p holds if and only if q does.

Assume:

1. If q is not up to you, and p is nomically equivalent to q, then p is not up to you.

Suppose determinism. Let L be the laws. Let t₀ be 1000 years ago. Let p be a proposition reporting something you do. Let q be the disjunction of all the nomically possible states of the universe at t₀ that evolve under L in such a way as to make p true. Then, plausibly:

2. p and q are nomically equivalent.

For given the deterministic laws, if p is true, then a thousand years ago the universe must have been such as to have to evolve to make p true.[note 1] And conversely, the laws entail that if it was such, then p is true.

Finally, observe that events a thousand years ago aren't up to you:

3. q is not up to you.

We conclude that p is not up to you. So no actions are up to you if determinism holds.

Substance causation, agent causation and time

Aristotelians about causation think all causation is substance causation. Events are causes only derivatively. What does the real causing are substances. This should make Aristotelians very sympathetic to the use of agent causation in the theory of free will. And insofar as the theory of agent causation is just that the agent is the cause of free actions, the Aristotelian who believes that we are substances[note 1] is surely going to agree that we are the causes of our free actions, and we are both agents and substances, so the agent is the cause of her free actions.

So far so good. But there is more to agent causation in regard to free will. Typically, agent causalists invoke agent causation to solve problems such as the randomness problem for libertarians. Agent causation is what makes an action be genuinely one's own action rather than a random blip. But the Aristotelian's embrace of substance causation is too broad. For not only does the Aristotelian think that her free actions are caused by her, she also thinks her non-free actions are caused by her, and even things like the circulation of the blood, which isn't an action at all, are caused by her. Moreover, since she is an agent, she thus thinks all of these things are caused by an agent. But if agent causation metaphysically lumps free actions with non-free ones, and doesn't distinguish them metaphysically from the circulation of the blood, then agent causation can't do the job it's designed for. The Aristotelian believes in agent causation, of course, and may do so with good metaphysical reason, but this agent causation cannot be used to solve the problems that the free will theorists want it to solve.

This line of thought might lead some Aristotelians about causation to accept a version of Cartesian dualism on which we are souls. For then one might hold, contrary to Aristotle, that only our free actions are caused by us and that the circulation of the blood and so on is not caused by us, because we are immaterial beings whose only direct effects are in whatever the equivalent of the pineal gland on this theory will be. This is not in the Aristotelian spirit, though, and it leads to unhappy ethical conclusions (bodies as akin to property).

I think there is something else one should say here. One shouldn't say that agent causation just is causation by an agent. Rather, agent causation is causation by an agent qua agent. You cause your free actions qua agent and you circulate your blood qua mammal, though of course you are both agent and mammal. It is a bit odd to say that you don't perform your non-free actions qua agent, though. After all, how can there be an action without an agent? Aren't all actions, free or not, the actions of an agent qua agent? Maybe. But maybe the distinction is still of some help, for maybe the kinds of mere randomness we want to rule out with the distinction isn't an action at all when looked at more closely.

There is another issue around here. There needs to be more to substance causation than the simple structure substance x causes event E. For paradigmatic substances persist over a long time, but many of their effects happen only at particular times in their existence. And there is an explanation of why the substance causes an effect at one time or another. For instance, I caused oatmeal to be assimilated to me earlier to day because I was hungry. The explanation includes not just the substance, but a state of a substance (and maybe other substances—but that's for another day). I caused the assimilation of my breakfast not only qua agent, but qua hungry agent. Likewise, I circulate the blood not just qua mammal, but qua mammal with a brain stem that sends such-and-such electrical signals to the heart.

Apart from considerations of free will, then, Aristotelians should say that the structure of substance causation is something like: substance x qua in state S causes event E. If we have an Aristotelian constituent ontology, then the state will be a mode (an essence, a necessary accident or a contingent accident) of the substance, and the causation relation will be a ternary relation between the substance, the mode and the event.

But now that we have all of this detail in place, we can go back and ask whether we still get benefits of an agent causal theory in regard to free will. That's not so clear. For instance, when I qua hungry agent caused my breakfast to be assimilated to me, the work distinguishing this from non-actions like circulation is being done by my state of hungry agency. It is because this state is involved in the causation—and not just involved, but involved in the right way (my being a hungry agent could cause me to grow a tail if I was rigged the wrong way)—that I am acting. But event causalists can say something exactly parallel. What distinguishes my eating the breakfast from my circulating the blood is that the former is caused by the event of my being a hungry agent qua my being a hungry agent.

So I do not know that Aristotelian agent causalists can claim to do better than event causalists. In fact, for certain ends they might well want to join cause with the event causalists.