The "more"

Consider such pairs of terms as:

• good — holy
• impressive — awe-full
• immoral — sinful
• promise — vow
• puzzle — mystery
• fearsome — spooky

The second term in each pair implies something of the first. In fact, in many (though not all—the last pair is a clear exception) cases, the second term implies the first in a superlative way. However, there is something "more" to the second of each of these terms, something qualitatively different. Moreover, these pairs are analogous to each other—there is an analogy between the "more" in each case.

Thesis: None of the second terms in the above list would have application if naturalism were true. Something might still seem mysterious, but in fact it would be just be very puzzling. It might still appear that a graveyard is spooky, but in fact it is at most fearsome, and if so, only accidentally (e.g., if there is a vicious dog there).

So if naturalism were true, our experience of the "more" in the second term of each pair will always be mistaken. But that would be really puzzling—how could there be an experience type that is always mistaken? So if the thesis is true, then we have good reason to think naturalism false.

I am not here offering an argument for the thesis—I am here just presenting it as something that seems very clear to me.

Science and theology

It is sometimes said that when science and theology conflict, this is because we are dealing with bad science or bad theology or both bad science and bad theology. This may be in fact true of a number of apparent conflicts between science and theology.

But even if this is in fact true, one shouldn't elevate such an observation into a necessarily true principle. Here is one reason to think this. We learn from history that good science is often wrong. (Can one say the same about theology? That may depend on whether one restricts to the theology of a true religion, and on how speculative one allows theology to be and still count as "good".) Unless science and theology have completely logically disjoint subject matter, so that no proposition of science can possibly entail or be incompatible with a proposition of theology, it seems quite possible to have a case where a proposition p is such that (a) p is good science, (b) p is false, and (c) not-p is good theology.

Objection 1: Science and theology have completely logically disjoint subject matter, and hence it is impossible for a coherent proposition from one field to entail or be incompatible with a proposition from the other.

Response: This is false. For instance, Christian theology holds that the tomb of Jesus of Nazareth does not contain the body of Jesus of Nazareth. This proposition and its negation are certainly the sorts of propositions with which historical sciences like archaeology deal. For another example, Jewish and Christian theology holds that the cosmos was created a finite amount of time ago. This theological proposition entails the claim that the cosmos has only finite age, a claim within the competency of cosmology (Aristotelian cosmology denied the claim; Big Bang cosmology affirmed the claim; some recent cosmologies deny the claim again).

Objection 2: Only true conclusions of science count as good science.

Response: This is implausible. Newtonian physics was good science par excellence, but false. Relativity theory and quantum mechanics were (are?) both good science, but we now know that they are not both true, since they conflict. But if this is true, then by the same token we should stipulate that only true conclusions of theology count as good theology, and then the claim that there can be no conflict between good science and good theology becomes tautologous. That said, it may be that some who make the no-conflict claim do mean it to be tautologous. Tautologies can still be useful at highlighting things—and, besides, one can't dispute them, which is certain a good thing.

Crime and punishment

Consider this valid argument:

1. If you deserve F from me, then F is owed[note 1] by me to you. (Premise)
2. If I owe F to you, then F is good for you. (Premise)
3. Therefore, if you deserve punishment from me, then punishment is good for you. (By 1 and 2)

Are the premises true? Where F is a reward or praise, (1) is true. There is some plausibility to the idea that the structure of punishment mirrors that of praise, and if so then (1) is true at least in the case where F is punishment, which is all I need for the argument.

Premise (2) has something plausible about it. How could I owe you a negative debt—that would be a case of your owing me something?

Here is another argument. Start with the following assumption:

4. It is wrong to intentionally impose an overall harm on another when nobody has a non-Cambridge benefit from this harm. (Premise)

Now suppose George, Jeff and Philippa are the only persons in existence (this is a per impossibile supposition since God exists necessarily), and suppose that they are persons who have no afterlife (death is the end of existence). Suppose George murders Jeff. Then it is appropriate for Philippa to punish George. Moreover, it is appropriate for her to do so on retributive grounds—she has strong reason to punish George even if George poses no danger to her and even if George is unlikely to repent of the crime due tot he punishment. Punishing George imposes a harm on George, and does not benefit Philippa (unless punishing George is good for independent reasons, in which case she is benefited by doing a virtuous action, virtue being its own reward; however, this benefit cannot be one that is cited in justification of the action, since that would be viciously circular). But the punishment is not wrong. Hence, George must also be receiving a benefit from the punishment, besides the harm.

I do incline to the view that retributive punishment is non-instrumentally good for the person punished. I am suspicious of the first argument—it's too easy—and the second might be question-begging against many opponents. But I wanted to put these arguments out there.

Presentism

On one of the best presentist accounts we have, namely that of Trenton Merricks, statements that some proposition p was or will be true are to be understood as embeddings of p in the context of a was or will modal operator, which modal operators are analogous to modal operators like M (possibly) or L (necessarily) or in a work of fiction or ought to be the case. Moreover, even if p is the sort of proposition to normally have a truthmaker, was(p) and will(p) do not have a truthmaker. Call this "modalist presentism."

Here is a problem for modalist presentism. There are a number of contexts in which we stand in the same kind of relation to a proposition about the past or the future as to an analogous proposition about the present. One kind of case I've already discussed in another post, the case of induction: we treat claims about past, present and future on par with respect to induction. A different set of cases are provided by certain non-first-person attitudes (this idea comes from Parfit). If my child is to undergo a painful medical procedure this afternoon, I will be pained at his undergoing the painful experience. Suppose that I am today out of causal contact with my child. I do not think it should matter much to my attitude right now towards the child's experience whether the experience has just occurred, or is now occurring, or is about to occur. And even if there is a difference, there is a common core of compassion in all three cases. Similarly, if I have heard that a friend will today receive a teaching award, I will be glad for his sake. Supposing I am unable to attend the ceremony, it will not matter vis-à-vis my gladness whether he has received the award five minutes ago, or is receiving it now, or will received it in five minutes.

The non-presentist has a way of explaining and justifying the common core of the inductive and emotional attitudes: in all cases, the attitude is a response to the reality of some situation. The feeling I have towards my child's actual pain, whether past, present or future, is different in kind from the feeling that I have towards facts of the form Q(my child is in pain) where Q is some modal operator like M or in a work of fiction. (The case of L is different, but that is because Lp entails p.) Likewise, I treat past, present and future occurrences on par for inductive purposes, and recognize the difference between these and possible or fictional occurrences. In fact, we might even say that a good test for whether I take a situation to be real is whether the situation enters into my inductive and emotional attitudes in these kinds of ways.

But for the modalist presentist, my child's having suffered pain is related to my child's presently suffering pain in somewhat way that my child's possibly suffering pain is related to my child's actually suffering pain. So now we have a problem for the presentist: to explain why it is that there is a pattern of attitudes that are equally appropriate towards situations within the scope of was and will operators as towards present situations, without adverting to the reality of these situations.

Here's a different way of formulating the worry, one that will affect even non-modalist presentists. It seems that what makes it appropriate to have the same attitude of grief or joy at various true propositions, and to engage in inductive reasoning about such propositions, is that these propositions have a truthmaker homogeneity: they are all made true by similar kinds of things. But the presentist denies truthmaker homogeneity between reports of past, present and future pains, as well as between reports of past, present and future raven blackness. The present-tense reports have ordinary sorts of truthmakers, like black ravens or people suffering. The past and future tense ones either have no truthmakers (Merricks) or have truthmakers of a significantly different sort (Bigelow, Crisp) from the present tense ones.

It might be thought that while the presentist has trouble explaining and justifying the lack of difference in these kinds of attitudes, the eternalist has trouble explaining and justifying the difference in first-person attitudes. I care a lot about whether a painful experience is past, present or future. But this is not a problem for the eternalist. For the justification of an attitude often lies not just in the objective features of the situation towards which one has the attitude, but also in a relation to the situation. That a situation is earlier than, simultaneous with or later than an attitude can affect whether the attitude is appropriate or not. And this indexical difference seems to matter a lot more in the case of situations that involve one oneself.

A tension about cooperation with evil

It seems pretty clear that we have strong, though perhaps at times defeasible, reason to avoid cooperating in evil activities. Here is something, however, that has struck me, after thinking about material in Wojtyla's The Acting Person (he is explicit about the tension) and correspondence with Mark Murphy. There is a tension between this presumption against cooperating in evil activities and the apparent fact that there is a non-instrumental value in all genuine interpersonal cooperation. There are ways to reduce or remove the tension, but it strikes me as quite an interesting tension. Does the fact that an instance of cooperation is in a bad activity somehow subvert the goods of cooperation?

Two remarks on Thomson's violinist argument for abortion

Thomson's violinist argument for abortion is based on an analogy between pregnancy and being coerced to serve as the life-support system for a violinist. In the course of the argument, Thomson says that pregnancy is the only case in which society (remember she is writing before Roe vs. Wade) requires a member to undergo a sacrifice of the magnitude that pregnancy involves.

My first remark is that this is simply false. There are two counterexamples to this: the draft and taxes. In the case of war, some members of our society are drafted. Being drafted seems pretty clearly at least as great an imposition as being required to continue pregnancy. It typically involves one's life being put under the control of higher officers in respect of just about every small detail, whereas only a few pregnancies require quite as much modification of one's life (cases where bed-rest is required for the length of the pregnancy are similar in this respect, though even then one is free to decide what activities to engage in while in bed, such as reading, writing, listening to the radio, etc.) The danger to life from the draft can be, depending on the conflict, significantly greater than that from pregnancy. Moreover, in being drafted, one becomes put under the orders of a hierarchy that can, and sometimes does, order one to engage in actions that are highly likely to result in one's being severely wounded, captured and tortured, or killed. (I expect that if I were to have to choose on grounds of self interest, I'd choose pregnancy over serving in the U.S. army in WWII, though I need to go on second and third hand data in both cases.)

The case of taxes is less clear, but still not implausible. Let's suppose Jennifer pays out 25% of her income in taxes. The imposition involved here may not seem grave when put in financial terms. But if we consider that in effect about nine years worth of work is commandeered over a 35-year career, this seems greater. Moreover, I suspect many people would willingly undergo a pregnancy in exchange for a lifetime exemption from taxation, and this would not be irrational in regard to self-interest. If this is right, then the imposition of taxation is comparable to that of pregnancy.

So, yes, our society does impose significant sacrifices on some members for the sake of others. It would be difficult, moreover, to imagine a society that did not have a draft when in danger of being overrun by the enemy, or that did not have taxation.

A second thing I find interesting about Thomson's argument is that as far as I can tell, abortions on account of the imposition represented by pregnancy and childbirth as such are relatively rare. With the notable exception of cases where the pregnancy itself constitutes a risk to maternal health and cases where the pregnancy reveals a relationship that the woman believes she needs to keep secret, standard reasons for abortion have to do more with not wanting the child to be born than with not wanting to be pregnant. In other words, most of the problems that lead women to abortion are such that the problem would not be solved by sci-fi technology that instantaneously grows the child to full term and beams her out into her mother's lap. The problem isn't with the pregnancy, but with the having of a child. But Thomson's argument defends abortion on the grounds of the imposition that pregnancy and childbirth as such make on the woman.

Now supposing that Thomson is right that the imposition of pregnancy and childbirth is indeed a morally sufficient reason for having an abortion. Then we would expect the challenges of pregnancy and childbirth themselves to be among the major reasons women cite for having an abortion. But apart from the cases where the pregnancy endangers the mother's health, the challenges of pregnancy and childbirth do not seem to figure among the major reasons for abortion. Granted, this may be because women are afraid it would sound self-centered to cite this as a reason. But since women seem willing to report that having a child "would change life in a way [they do] not want" or that they want to "establish [a] career" first, there does not seem to be a total taboo against citing self-centered reasons.

Moreover, Thomson's argument, if it were sound (and I think it is not), would only establish that there is a right to expel the fetus from the womb, not that there is a right to kill the fetus. But to satisfy the typical reasons why women have abortion, a right to kill the fetus would be needed. And Thomson's argument gives us no reason to think there is such a right.

Evolution and scientific irrealism

Consider the following two statements:

1. We do not have good reason to believe evolutionary theory to be true.
2. Scientific irrealism holds.

Now claim (2) entails that science does not give us good reasons to believe propositions to be true. Moreover, the following claim is uncontroversial:

3. All the good reasons for believing evolutionary theory to be true are scientific in nature.

Thus, (2) together with the uncontroversial (3) entails (1).

But here is an oddity about discourse in our society: There is a lot more outrage against scholars who assert (1) than against scholars who assert (2).

Is there a justification for such a differential attitude?

An explanation for the differential attitude is that those who assert (1) frequently are motivated by religious considerations, while those who assert (2) are rarely motivated by religious considerations (unless they accept occasionalism, like many Muslims, or they are led to (2) by way of (1)). But unless one has a good argument for why it is inappropriate to accept or deny a scientific claim on religious grounds, this explanation of the differential attitude is no justification. Certainly it isn't be a necessary truth that it is inappropriate to affirm or deny scientific claims on religious grounds, unless necessarily God doesn't exist: for if God exists, then he in principle could reveal facts that are of purely scientific interest, or facts of religious interest that entail facts of scientific interest.

Maybe, though, the explanation is like this. If someone asserts (1) by itself, we assume that she doesn't hold (2) (just as someone who says that Elbonians are not human is assumed to think non-Elbonians are). But in fact the only good reason for holding (1) is (2). However, simply the fact that someone believes something for a bad reason surely doesn't justify the kind of outrage that is involved here. After all, one might believe (2) for very bad reasons indeed.

Personally, I deny (2). As for (1), my views are rather complex—I accept common descent and natural selection as a major force, I accept that Behe-Dembski style arguments fail to establish Intelligent Design, but I am also convinced that we do not know that every event in the evolutionary history of every animal was naturalistic.

Two kinds of mathematical intuitions

Mathematicians have two kinds of intuition. A speculative intuition occurs when they think about a problem, perhaps think quite a lot, and conclude that the problem has answer A, even though they how no idea how to prove this. "It just looks like A is the answer." I do not know how reliable speculative mathematical intuitions are. I suspect that they are not very reliable. In particular, I think they rarely if ever justify belief. Certainly, I did not acquire belief in an answer on the basis of speculative intuitions when I was a practicing mathematician.

However, there is also such a thing as pedestrian intuition. This tells the mathematician: "Clearly, p." The "clearly" is not speculative. The content of the intuition is not just that p is true but that p can be easily proved from what preceded. John Fournier, my mathematics thesis director, once gave me the following advice on papers submitted for publication: when there are two obvious steps in a row in a proof, you can omit one, but not both.[note 1] When a mathematician sees that something follows, even if she does not actually go through the proof of the fact that it follows, that pedestrian intuition is, I think, very reliable. It may even be that had the mathematician written down the proof, the proof would have contained some minor mistakes. For this intuition does not seem to be based on having the proof in one's mind. Rather, it seems to be a direct non-inferential grasp of the easy provability of p.

One small piece of evidence for the reliability of pedestrian intuition is the incredible reliability of mathematical publications. Errata are extremely rare in mathematical journals.[note 2] I suspect this is not just because of the refereeing process, but because this highly reliable intuition was guiding the mathematician in writing the proof. In fact, I think the epistemic weight of the result proved in a mathematics paper goes beyond the validity of the published proof. The published proof may indeed contain a minor slip here or there. But what makes these slips be minor is precisely that one can intuitively see what should be in their place. My last mathematics paper was published when I was significantly out of practice. It went back and forth between me and the referee several times, and the referee was rightly exasperated by the amount of mistakes in the proofs. However, all the mistakes were easily fixable: the intuition was exactly right, in a pedestrian way, despite the logical gaps in the proofs.

This is surprising. One might think that a proof with logical holes has no value at all—it is like tracing your ancestry to Charlesmagne with only two gaps in the chain (this isn't my comparison). But somehow the reliability of the pedestrian intuition goes beyond the proof written down.

What explains the extremely high reliability of pedestrian intuition in a well-trained mathematician? One possibility is that it is a highly developed pattern-matching skill. In the past we've seen p-type claims following from q-type claims, and we can see that the present case fits into the pattern, and so p follows from q. This explanation fits well with the fact that experience seems important for this kind of intuition. But I am not sure this would be sufficient to give the intuition the kind of reliability it has. Pattern-matching would, I doubt, have the right kind of reliability. In typical cases of writing down a proof of a new result, the case at hand is unlikely to be exactly like past cases.

Or could it be that there is a process involving a mental representation of a proof, but a representation not directly available to consciousness? If so, what is interesting is that this is just as reliable as, or even more reliable than, consciously going through the steps of a proof (in fact, I suspect that the reliability of consciously going through the steps often or always depends on the non-conscious process occuring side-by-side). This is kind of neat and reminds me of the speculations central to Peter Watts' novel Blindsight. Moreover, if this is right, then I think it should challenge internalist epistemologies that require justifications to be conscious. In these mathematical cases, the justification can be made conscious, but the making-conscious does not seem central, since the non-conscious reasoning is more reliable than the conscious reasoning.

It is an interesting question how the two kinds of mathematical intuition connect up with kinds of philosophical intuition. I do find myself with a quite reliable intuition in philosophy akin to the pedestrian sort of mathematical intuition—an intuition as to what conclusions can be made to follow from what kinds of assumptions. In fact, this is probably just the same intuition at work, though I find it is a bit less reliable in philosophy than in mathematics. (I think I have at least three times been significantly deceived by such an intuition, and in a number of other cases have needed to add plausible ancillary assumptions to make an argument go—though on reflection that probably can happen in mathematical cases, too, which slightly weakens what I said in previous paragraphs.)

There is, however, a second kind of intuition: an intuition that pointless torture is wrong, or that we are not identical with our left big toes, or that identity is non-relative, or that the good is to be pursued and the bad avoided, that nothing can be causally prior to itself, or that every contingent truth has an explanation. I am inclined to class this intuition as different from both the pedestrian and the speculative mathematical intuitions. This intuition is of variable strength, unlike pedestrian mathematical intuition which is pretty uniformly very strong. Sometimes, this kind of philosophical intuition gives us certainty, as in the case of the good being to be pursued, and sometimes it merely inclines us in favor of a proposition. The range of strengths here makes it different from speculative mathematical intuition which, I think, never justifies belief, while this kind of philosophical intuition does justify belief.

Or maybe we need to split this second kind of philosophical intuition into two kinds. One kind is speculative, and this is akin to speculative mathematical intuition. I am, let us suppose, inclined to think electrons are not conscious, but this intuition is not sufficient to compel or justify belief. Another kind is self-evidential which presses belief on us, and I suspect justifies it as well. This kind is more like the highly reliable pedestrian mathematical intuition in respect of the way it compels belief (the reliability question is a different matter on which I want to remain silent), but is unlike the mathematical case in that it is substantive and not merely logical in nature.

Deep Thoughts VIII

Only those who have lived can die.

Another argument for thirding in Sleeping Beauty

As usual, a fair coin is flipped on Sunday, without you seeing the result, and then you go to sleep.

Experiment 1 (standard Sleeping Beauty):
Tails: You get woken up Monday and Tuesday. Your memory is erased each time, and you don't know whether it's Monday or Tuesday when you wake up.
Heads: You get woken up Monday but not Tuesday.
Question: What should your credence in heads be when you wake up?

Experiment 2:
As soon as you have fallen asleep, a second coin is tossed. If it is heads, "Monday" is written down on a hidden blackboard in the experimenter's office, and if it is tails, "Tuesday" is written down on that board. You never see that board.
Tails: You get woken up Monday and Tuesday. Your memory is erased each time as in Experiment 1.
Heads: You get woken up on the day whose name is written in the experimenter's office, but not on the other day.
Question: What should your credence in the first coin's being heads be when you wake up?

I now claim (i) in Experiment 2, the answer is 1/3 regardless of how biased the second coin is, and (ii) it follows from (i) that the answer is 1/3 in Experiment 1.

Claim (ii) is intuitively clear. It shouldn't matter whether the heads wakeup day is Monday or Tuesday.

The harder to argue for claim is (i). Here goes. I am now awake. I give a new rigidly-designating name to today. Maybe the way I do it is I pick a bunch of letters at random to form the name (I neglect the probability that on multiple wakeups I'll choose the same name). So, let's say I have named this day "Xhfure". Let A be the following event: The name of the day written on the experimenter's blackboard refers to Xhfure. Note that A is a contingent event and has prior probability 1/2. Let H and T be the events of the first coin being heads or tails respectively. What is the most specific evidence I now have? I submit it is the following: H or (T and A). Let this evidence be E.

So, now I ask: What is P(H|E)? This is an easy calculation. P(H and E) = P(H) = 1/2. P(E) = P(H) + P(T)P(A) = (1/2) + (1/2)(1/2) = 3/4. Thus, P(H|E) = (1/2)/(3/4) = 1/3.

Indicative conditionals

On the material conditional interpretation, the propositional content of the indicative conditional "If p, then q" is p→q, i.e., (not-p or q).

I claim that this is basically the right interpretation if "If p, then q" expresses a proposition whose truth-value is mind-independent (except for any mind-dependence in p and q themselves). You can take this as evidence that the material conditional interpretation is right—that is how I take it—or that English indicative conditionals do not express a mind-independent proposition.

The argument is simple. Suppose that p and q concern non-mental matters, and suppose that w is a world p→q holds, i.e., p is false or q is true or both. Then there is a world w* which is very much like w, except that it contains two persons, A and B, conversing about p and q, neither of whom has any false or misleading or unjustified beliefs, and neither of whom has any beliefs giving significant evidence for any of the propositions p, q, not-p and not-q. We could then imagine A learning that either p is false or q is true or both, and that then the conversation turns to the subject of p and q. I claim that it would then be appropriate for A to say: "Well, I don't have any idea which if any of p and q is true, but I now know that if p holds, so does q." This seems quite right. Moreover, in saying this, A would not be saying anything false. Therefore, if "If p, then q" expresses a proposition, it expresses a true proposition in w*. But if the proposition it expresses is mind independent, it is also true in w, since the two worlds differ only in respect of mind-dependent stuff.

Hence, p→q entails that if p, then q. The converse is easy. If p→q is false, then p is true and q is false, and it is clear that then if p, then q isn't true. Therefore, necessarily, p→q holds iff if p, then q does. Hence, the material conditional gets the truth conditions for the indicative "if... then..." right.

Could it be that there is still a difference in meaning? The only way I could see that would be if "If p, then q" said something additional, something entailed by p→q, but nonetheless added on to it. But I just cannot see what that could be, unless it be something mind dependent.

But perhaps there is a difference here like that between "p or q" and "q or p"? Maybe there really is a difference in the proposition expressed by these claims, even though neither adds anything to the other. If there really is a difference in the propositions expressed by "p or q" and "q or p", then I guess there might be a difference between those expressed by "p→q" and if p, then q. But if so, that difference is not very significant, it seems. Basically, the two say the same thing. Of course, even if there is no difference in proposition, there may be pragmatic differences.

What about standard counterexamples to the material conditional interpretation? For instance, could I say about a batch of cookies that I know to be poisoned
(*) "If George eats these cookies, he won't feel sick"
simply because I know that George won't eat them? Well, I think such counterexamples at most challenge the claim that the indicative conditional expresses a proposition, not the claim that if it expresses a proposition, the proposition it expresses either is or is basically the same as a material condition. Suppose that I don't know that the cookies were poisoned, but Patricia tells me: "An omniscient being either told me that George won't eat these cookies, or that he won't feel sick, but I can't remember which." It seems perfectly appropriate for me to utter (*), then. Suppose I later learn that the cookies are poisoned and that George won't eat them. Do I have any reason to say that I was mistaken when I uttered (*)? Surely not. I can say that what I said was misleading, but not that it was false. Whether (*) is appropriate to say depends on mind-dependent stuff. But if (*) expresses a proposition, then that proposition is mind-independent. Consequently, the intuitions about the appropriateness of saying (*) should not be taken as evidence about what propositional content (*) has if it has any.

"To make a choice, you need choices"

The title of this post is a remark I heard Nuel Belnap make in the question period after a talk on free will (quoting from memory).

Here, then, is a valid argument for a kind of Principle of Alternate Possibilities:

1. It is not possible to rationally deliberate when one knows one that fewer than two options are possible. (Premise)
2. One deliberates knowledgeably if and only if one knows all the deliberatively relevant facts. (Premise)
3. It is deliberatively relevant which options are possible. (Premise)
4. Therefore, if one rationally and knowledgeably deliberates, then at least two options are possible. (By (1)-(3))

(1) and (2) seem quite secure. But the opponent of Principles of Alternate Possibility may dispute (3), even though it seems very plausible to me.

In any case, (3) is clearly true in some cases. If I'm deliberating between three rescue operations, which can save, respectively, one family member, two strangers, or three family members, learning whether the third option is actually possible would, surely, affect rational deliberation (if it is possible, then it is the best choice; if it is not possible, then we have a hard choice between the first and second options). So there are at least some cases of deliberation where knowledge of what options are possible is deliberatively relevant. This isn't enough to yield (4), but it is enough to yield a weaker claim such as that rational and knowledgeable deliberation in certain kinds of real-world cases requires more than one option to be possible. If one adds the assumption that in these cases rational and knowledgeable deliberation does in fact occur, one concludes that in these cases more than one option is possible. Moreover, "possibility" here must be more than just metaphysical possibility—it must be some kind of causal possibility. (Learning that one of the rescue operations is logically impossible should affect deliberation; but learning that one of the rescue operations is causally impossible is just as relevant.) And hence, most likely, we do get something that is relevant to disputes with determinists.

A Molinist theodicy for infant death

I was reading St. Gregory of Nyssa's "On Infant's Early Deaths". There, St. Gregory provides a two-fold theodicy for early deaths of infants. Those early deaths that are by the hand of man will have the evildoer be punished by God. (It is not clear how much this is a theodicy, unless one sees punishment as a good—as strands in the Christian tradition do.) More interesting is St. Gregory's somewhat tentative hypothesis as to natural deaths of infants. He says that

it is reasonable ... to expect that He Who knows the future equally with the past should check the advance of an infant to complete maturity, in order that the evil may not be developed which His foreknowledge has detected in his future life, and in order that a lifetime granted to one whose evil dispositions will be lifelong may not become the actual material for his vice.

While St. Gregory does not expressly distinguish between middle knowledge and foreknowledge, the idea, which he expands on, is clear: God can see that some infants if left alive would become great evildoers, and so he ensures that they do not survive to become such evildoers. St. Gregory's analogy to a host at a banquet knowing the "peculiarities of constitution" of the guests, as well as above his mention of "evil dispositions" apparently in the infant does suggest that this isn't all about simple foreknowledge (I doubt he intends a compatibilist reading either).

In case you're interested why God allows some evildoers to live a long sinful life while he stops some infants in light of knowing that they would become evildoers, St. Gregory says about the ones that God stops in infancy that "it is not unreasonable to conjecture that they would have plunged into a vicious life with a more desperate vehemence than any of those who have actually become notorious for their wickedness."

Molinism is useful. It's too bad that I don't think it's true.

An argument for a Principle of Alternate Possibilities

Say that George chooses to do A knowledgeably provided that the beliefs on the basis of which George chooses to do A are in fact knowledge. In a paradigmatic case of deliberation (this sentence can be taken to be stipulative of what I mean by "paradigmatic case of deliberation"), the beliefs on the basis of which George chooses include counterfactual claims of the form "Were I to do A, F would happen" and "It is not the case that were I not to do A, F would happen."[note 1]

I now claim that: If George chooses to do A knowledgeably and in a paradigmatic case of deliberation, then it can happen that he failed to choose to do A.

Here is the argument:

1. It is false that were George not to do A, F would happen. (Premise: by definition of "knowledgeably" and since only truths can be known)
2. F actually happened. (Premise: since George does A and knows that were he to do A, F would happen)
3. Whatever happens, can happen. (Premise)
4. If C cannot happen but D can happen, then were C to happen, D would happen. (Premise)
5. Suppose it cannot happen that George does not choose to do A. (Premise for a reductio)
6. F can happen. (By (2) and (3))
7. Were George not to choose to do A, F would result. (By (4) and (6))
8. Thus (7) is true and false. (By (1) and (7))
9. Thus, (4) is false, and so it can happen that George does not do A.

One term that has not been defined is "can happen". On any plausible reading of "can happen", all the premises will hold in a case of knowledgeable and paradigmatic deliberation, with the possible exception of (4). Thus, for any plausible reading of "can happen" that makes (4) true, we get a PAP.

In particular, on any account of counterfactuals that makes p's entailing q entail that were p to hold, q would hold as well, (4) will be verified where "can happen" expresses logical possibility. This gives us a PAP with logical possibility, though only in the case of knowledgeable and paradigmatic deliberation. Still, that's something. After all it entails that if the laws of nature are necessary and determinism holds, then knowledgeable cases of paradigmatic deliberation are impossible.

I don't know what other senses of "can happen" make (4) true.

Arguments like this provide a general template for generating relatively weak versions of PAP. Are any of the versions of PAP that the argument provides sufficiently strong to yield some kind of incompatibilist doctrine? Here is the best I can do. Say that D can happen provided that D is compatible with the laws of nature and the initial arrangement of matter in the universe. Then (4) restricted to cases where C describes a wholly non-initial arrangement of matter is not completely implausible. Given materialism (which of course I deny, but many compatibilists accept), George's not doing A will be a wholly non-initial arrangement of matter, and the argument implies that George's not doing A is compatible with the laws of nature and the initial arrangement of matter in the universe, assuming George is acting knowledgeably and paradigmatically deliberatively. So we do get an incompatibilistic conclusion, but under heavy assumptions.

What is kind of neat about the above considerations is that they do not involve freedom directly, but only deliberation.

Frankfurt counterexamples and compatibilists

Frankfurt counterexamples to the Principle of Alternate Possibilities (PAP) have worried libertarians. However, they should have also worried compatibilists. Traditionally, compatibilists have accepted PAP, but given it a counterfactual spin (see my previous post). Suppose Jones freely chooses to push button A. On the standard Humean analysis, this implies that were Jones to have chosen not to push A, he would not have pushed A. But a fairly crude Frankfurt case will provide a counterexample to this. Imagine Black stands by with his neuroscope and has a firm plan that if he sees Jones choosing not to push A, he will make Jones push A. Then it is true that were Jones to have chosen not to push A, he would still have pushed A.

Hence, Frankfurt cases are also counterexamples to the Humean version of PAP, and indeed are better counterexamples to it than to the libertarian PAP (standard Frankfurt cases are known to beg the question against many libertarians, since they require a sign that is nomically connected with the action in a way that many will not accept).

PAP is very plausible. So it is an important task not just for the incompatibilist but also for the compatibilist to find a version of it that survives Frankfurt counterexamples. Here is my hypothesis: A plausible PAP that survives Frankfurt counterexamples will still be sufficient for incompatibilist arguments once one plugs in a non-Humean analysis of "could have". If this is right, and if I am right that everybody needs a PAP, then Frankfurt examples do not in the end weaken the incompatibilist's case—just as before Frankfurt examples the question was whether the Humean analysis of "could have done" was right, so too this is the question after Frankfurt examples, once one correctly formulates PAP.

My own preferred PAP is flickery and fits well with the above remark: If x freely does A, then x could have failed to freely do A. Actually, it may be that the libertarian is in a better position than the compatibilist when it comes to formulating a PAP. For flickery PAPs like the above don't fit well with the Humean analysis of "could have done". Would the Humean want to say that "x could have failed to freely do A" means "were x not to have willed to do A, then x would not have freely done A"? But that's just a tautology and does no justice to the intuitions behind PAP.

In summary: Everybody who believes in free will—compatibilist or incompatibilist—needs PAP. Frankfurt examples affect both the compatibilist and the incompatibilist. It is a bit easier for the incompatibilist to find a replacement for PAP that survives the examples, but the replacement-finding task is one that both compatibilists and incompatibilists need to engage in. But the real question, as before Frankfurt, is how to understand "could have done" conditions.