Christian apologetics

A correspondent sent me a link to this really nice apologetics site with links to articles by good people (like John Earman and Fred Freddoso) on topics like miracles.

Intentions

Here is the thesis I will argue for: that x intentionally kills y does not entail that x intended that y die.

I need a relevance principle for intentions:

(RPI) If x intends that p in an action A, then x takes the epistemic conditional probability of p on A to be higher than the epistemic conditional probability of p on some relevant alternative (such as refraining from A).

Now suppose that George is falling past Fred's balcony. Under the building there is a net spread out. George's fall is such that he is virtually certain to miss the net unless his path is modified, and it is virtually certain that he'll die if he misses the net. Fred has always wanted to kill George. It's not that Fred has wanted George dead, but Fred wanted to take revenge on George, to be the cause of George's death. Fred has a baseball bat. If he hits George on the head, George's downward path will be modified and George will land on the net. There is no other intervention within Fred's power that can stop George from hitting the ground. If Fred hits George on the head with the bat, George has a 90% chance of dying from the blow, and a 1% chance of dying from landing on the net. Fred knows all this. He hits George on the head, and George dies from the blow.

Fred has intentionally killed George. But by RPI, Fred did not intend George's death, roughly because the action of hitting George with the bat did not increase the conditional (epistemic) probability of George's death.

Clearly, Fred intended that George should die of Fred's blow. Therefore, that one can intend that George die of Fred's blow without intending that George die.

This shows that there isn't going to be any plausible entailment principle for intentions, even if entailment is going to be understood along the lines of any plausible relevant logic (for the entailment from George dying of Fred's blow to George dying had better be relevant). Interestingly, it is not even true that he who intends the conjunction intends the conjuncts. Suppose that if I do nothing, p has probability 0.7 and q has probability 0.7, but the probability of the conjunction is only 0.1. But if I perform A, then p has probability 0.6, as does q, and the conjunction of p and q has probability 0.55. I want the conjunction of p and q, and I don't care about each conjunct (maybe I get a payoff if the conjunction holds, but I get nothing for each conjunct on its own). I know all this. So I perform A. I do not intend p, since I lowered the probability of p. Likewise, I do not intend q. But I do intend their conjunction.

In particular, this implies that in the Principle of Double Effect, the condition that one not intend the evil has to be expanded. Consider this weird case. If a peanut is eaten and Fred is killed, ten innocent people are saved. If the conjunction does not hold, ten innocent people die. Double Effect advocates (like me) will not permit me to wave a magic wand that simultaneously causes Fred to die and the peanut to be eaten (maybe by Fred who is allergic to peanuts?). However, note that Fred's death is not intended here, either as an end or as a means. Only the conjunction of Fred's death and the ingestion of the peanut is intended.

The correct way to expand the condition that one not intend the evil is tricky, and what I sketch in this paper still seems to me to be the best way to go.

"Unexpected" and "unplanned" pregnancies

The process of conception is very chancy, with a randomly timed act of intercourse having a significantly less than one in ten probability of conception and with the conception probability peaking at around 1/2 for an act occurring at around ovulation. Any couple who knows these facts, absent some further information (such as a private revelation from God) cannot rationally expect a pregnancy to result from a sexual act, nor can the couple rationally be said to plan the pregnancy in a sexual act, for it is presumptuous to have something so chancy be one's plan. Thus, if a couple is rational and knows the probabilities, a pregnancy's resulting from a particular sexual act will always be an unexpected and non-planned consequence, though perhaps a hoped for and intended one.

However, the probability of conception for regular sexual activity over a longer period of time, say a year, is higher, and better than even. If something has a better than even probability, then it can be expected. Nonetheless, unless that probability is pretty high, say 9/10, which over the period of a year it is not, then it still is presumptuous to talk of the outcome as planned.

Thus, pregnancy is too chancy an event for it to be rationally planned, though of course it always can be planned for—even very low probability events can be rationally planned for. The standard loose distinction between planned/unplanned pregnancies, and to a lesser degree that between expected/unexpected pregnancies, can be replaced by a distinction between pregnancies hoped for and not hoped for, intended and not intended. (Note that "unhoped for" is not the same as "not hoped for". We use "unhoped for" in the case of events that are evaluated by the subject in a positive way, but a pregnancy need not so be. Likewise, Ryan Wasserman has argued that "not intended" is not the same as "unintended".) Of course, it may be that this is what people have all along meant by the words "planned", "unplanned", "expected" and "unexpected", but in a conceptually confused way. But in a matter as important as this, conceptual clarity is needed.

Augustine on evil

The problem of evil that Augustine struggled with so mightily was neither the inductive problem of evil that so exercises contemporary philosophers of religion nor the deductive argument from evil that the ancients worried about. Augustine's problem of evil was a metaphysical paradox generated by four plausible claims:

1. Evil exists.
2. Everything that exists is God or created by God.
3. God has not created evil.
4. God is not evil.

Unlike the ancient and modern problems, this isn't a deductive argument against the existence of God. Nor was Augustine, as far as I can tell, ever drawn to a fully atheistic solution. The Manichean solution was to revise (2) to say that everything that exists is a God or created by a God, and to similarly modify (3) and (4): there is a God who has not created evil and there is a God who is not evil.

Augustine's famous solution was to deny (1). Evil is but a privation of good. Granted, this does not mean that evil is a lack of good, but a lack of a due good. Hence, a claim that some evil has occurred is ontologically reduces to a claim of the form: (a) a good g does not exist, but (b) g is due. To my knowledge, Augustine does not say quite enough about what grounds (b), but what grounds (b) is not the evil in question, since (b) hold even if g existed. Claim (a) is true not in virtue of a truthmaker but in virtue of there not being a falsemaker. To make all this go, we need to also say something about what "g" stands for—presumably, a definite description of some good.

Augustine in his solution was not addressing either the deductive or the inductive problem of evil. That he was not addressing the inductive problem is obvious. That he was not addressing the deductive problem is also clear from the fact that a crucial premise in the deductive problem of evil, viz., that God is omnipotent, is not present. We need not, thus, think that Augustine's solution tells us anything very helpful with regard to these two problems. However, the fact that it was this problem that Augustine found difficult, and not the deductive or inductive, may be significant. Why was he unmoved by the arguments from evil? He does, of course, address these arguments, but it is not a matter for existential struggle. His response is basically that if we do black deeds, God will use us to paint the mustache in the cosmic painting that he is painting. It is a kind of sceptical theist move, based on the fact that we are in no position to see the whole picture.

Entailment Thesis for truthmakers

The Entailment Thesis for truthmakers is that

1. If x makes p true and p entails q, then x makes q true.

Mulligan et al. have the thesis, but it is surely false. For consider the following very plausible claim:

2. If x is a fundamental entity—one such that facts about its existence do not reduce to facts about more fundamental entities—then x is a truthmaker for the proposition, p, that x exists, and every truthmaker of p is either identical with x or contains x as a part.

Now, let N be a fundamental necessary being, e.g., God, or maybe the empty set. Plausibly, N is not a part of Fred the electron. Now: let p be the proposition that Fred exists, and let q be the proposition that N exists. Then, by (2), Fred is a truthmaker for p, p entails q, but Fred is not a truthmaker for q.

Light pollution

When out observing at my sort-of dark location, I realized that when Scripture says that the heavens declare the glory of God, Scripture is not talking of the few pretty sparkles in a light-polluted modern city sky. The image presupposes a sky aglow with stars, with a glorious Milky Way stretching across it. My observing location is only an approximation to that, but is still pretty glorious. It's interesting how understanding certain texts requires that one know what certain created things look like, and first-person experience (or a really good simulation, like a good planetarium) is needed.

It was indeed a good night for naked-eye viewing. Two or three open clusters in Auriga were naked-eye, the Double Cluster was really obvious, and I might have even caught a glimpse of M 33 with averted vision, but I am not sure. I also got to try out my home-made travel telescope under decent skies. It nicely framed the M 31/M 32/M 110 galaxies in an about 1.7 degree field of view. And the Orion Nebula was really wonderfully detailed through my 13".

A theistic argument against (worldly) states of affairs

By "worldly states of affairs (WSOAs)", I mean existing states of affairs, say of the Armstrong variety. These are not the Plantingan more abstract states of affairs that exist whether or not they are actualized. I've sometimes called the WSOAs "concrete states of affairs", but as Jon Kvanvig has pointed out to me, that's inaccurate, because the worldly states of affairs include some concrete ones, like my writing this post, and some abstract ones, like two plus two being four.

1. If WSOAs exist, there are some intrinsically evil contingently enduring WSOAs, such as my being sinful.
2. It is wrong to freely and directly sustain in existence something that is intrinsically evil.
3. God freely and directly sustains in existence everything that contingently endures.
4. God does no wrong.
5. Therefore, WSOAs do not exist.

A variant on the grounding objection to Molinism

Premises:

1. If there are any Molinist counterfactuals, there are ungrounded true contingent propositions.
2. Propositions reporting divine beliefs are grounded.
3. If p is a contingent truth (i.e., true proposition), then either God's belief is explained constitutively or causally by p, or p is explained constitutively or causally, or there is some third truth that explains both p and God's belief constitutively or causally.
4. An ungrounded truth cannot be explained causally.
5. An ungrounded truth cannot explain causally.
6. When a truth p explains q constitutively, something that grounds p grounds q.
7. God believes every truth.

It follows from (6) that an ungrounded truth cannot explain or be explained constitutively. It follows then (2)-(5) that no ungrounded contingent proposition is believed by God. It then follows from (7) that no ungrounded contingent proposition is true. It then follows that there are no Molinist counterfactuals.

Premise (3) is a way of working out the idea that God's beliefs are knowledge and cannot be merely contingently related to what makes them true.

[Edited. This is an improved version of the argument. -ARP]

St. Anselm on the magnitude of sin

St. Anselm believes that the least of our sins puts us in an infinite debt to God and is infinitely bad. Anselm's own argument for this thesis is uses some implicit premises. Here is my best reconstruction:

1. (Premise) To sin is to oppose the will of God.
2. (Premise) If it is not permissible to do A in order to preserve a good G, then A is at least as bad as the loss of G.
3. (Premise) It is not permissible to oppose the will of God "even to preserve the whole of creation", even "if there were more worlds as full of beings as this", and even if "they increased to an infinite extent".
4. (Premise) The badness of the loss of the whole of creation if the whole of creation consisted of planets as full of beings as Earth and increased to an infinite extent would be infinite.
5. (Premise) If something is at least as bad as an infinite bad, then it's infinitely bad.
6. To oppose the will of God is at least as bad as something infinitely bad. (2, 3 and 4)
7. To oppose the will of God is infinitely bad. (5 and 6)
8. Every sin is infinitely bad. (1 and 7)
9. (Premise) To do something infinitely bad puts us in infinite debt.
10. Every sin sin is infinitely bad and puts us in infinite debt. (8 and 9)

Probably the most obvious thing to worry about is the conjunction of (2) and (3). Premise (2) appears to be a consequentialist claim. Premise (3), on the other hand, is a premise that the Christian tradition does indeed endorse, but the Christian tradition is not a consequentialist tradition (witness St Augustine on lying and St Paul's insistence that we do not do evil that good might come of it). Thus the argument brings together premises that originate in two competing moral theories, and it is unsurprising that when you do that, you can derive surprising things from their conjunction.

But this is too quick. For there is a lot of plausibility to the consequentialist intuition that Anselm invokes in (2). When one thinks about Augustine and Kant on lying, it "feels right" to say that they value honesty over life. On the side of Kant at least, this is mistaken. Kant's objection to lying isn't that honesty is a greater good than life, because Kant's ethics is not centered on the good (at least not in a way that would make this statement work). So perhaps it is right to affirm the consequentialist intuition in (2) as well as the deontological intuition in (3). And if one does that, then one gets the view that certain actions are infinitely bad.

However, this approach is mistaken. For one does not do justice to both consequentialist and deontological intuitions by supposing that wrong actions are infinitely bad. For consider this situation: If you don't kill an innocent person, a hundred other people will each kill one innocent person. (How can you set this up? One way is statistical. You know that if a certain temptation T is given to people, one percent of people will commit a murder. So you're told that if you don't kill one person, temptation T will be offered to 10,000 people.) Clearly the hundred murders are worse than one murder, and yet it's wrong, according to the deontologist, to kill one innocent person. Moreover, this case is directly a counterexample to (2).

One might try to get out of this counterexample by denying that infinities can be compared. But if one does that, then one can no longer say things that mortal sin is worse than venial sin, and the like. Besides, one does want to be able to compare infinities. If I had a choice between preventing one stranger from committing one murder of a stranger and a hundred strangers from committing one murder apiece, obviously I should prevent the latter.

A different kind of objection to the argument would be that in (2), "at least as bad" should be read as "not less bad" (I am worried about cases of incommensurability). But if one makes the same replacement in (5), it is far from clear whether (5) remains true. For it may be that something is infinitely bad in an aesthetic way (say, an infinitely long bad novel) and something else is finitely bad in an incommensurable way (say, a toothache of finite length); the latter is not less bad than the former, but it does not follow that the latter is infinite.

Nonetheless, even though St Anselm's argument for the infinite badness of sin fails, I think there are alternate ways to make the thesis plausible. But that's a subject for another post (hopefully over the next couple of days).

Evil and eternal life

(Cross-posted on prosblogion.)

Let's say I climb Mt. Everest, and then enjoy a delightful view from the top. But as I climb the mountain, I undergo various horrendous sufferings. And after I get back down, I have to undergo extremely painful surgery. Suppose that, so far, the overall value assessment is negative. If that's all that is involved, then climb wasn't worth it. The view was nice, and the good of achievement was nice, but, by far, it just wasn't worth it.

But let me add a little more to the story. I did this when I was 20. I am not permanently traumatized by the suffering, and indeed by the time I am 30, my memories of the hideous pains are no longer unpleasant. But I continue to have memories of the beauty of the climb and of the camaraderie, memories of the grandeur of the epic struggle, and these memories continue to be fairly pleasant. Moreover, the feeling of accomplishment, of having overcome the pains, is nice to have. I then live on for fifty more years, continuing to have pleasant memories of that climb.

While the goods achieved at the time of the climb were not worth the suffering, when combined with the value of half a century's worth of memories, even when these memories are not particularly intensely pleasant, they may be worth it. Suppose you say the contrary. Well, then, replace the fifty years with five hundred or five million. Eventually, the cumulative value of enjoying these memories will overshadow the bads which were confined to one decade of one's life (the climb, plus about ten years during which the memories of pain were painful). (This of course reminds one of Parfit's Repugnant Conclusion. But I think there is nothing repugnant here.)

What this shows is that given a long enough life-span, our evaluations of whether some activity was worth doing can change as a result of the values of memories and of retrospective awareness of achievement. Of course, in principle, they can change in either direction. A pain might have been such that it by itself would have been worth it for the sake of an achievement, but if in fact the memories of the pain continue to be painful while the memories of the achievement fade, then it's no longer worth it.

Observe also that while it would be possible to have the pleasure of the memories of having climbed Mt. Everest without having ever had the pains, that pleasure would then be an empty pleasure, and hence either devoid of value or of much lesser value.

Suppose that in fact we live forever. There is no good argument to the contrary that doesn't presuppose the non-existence of God (here we can insert a discussion of arguments for materialism and of arguments against resurrection based on the need for causal continuity), so someone who offers an argument from evil against the existence of God cannot rely on the denial of the claim that we live forever. The above remarks show that remembering over a significant length of time can act as a value-multiplier, and when the length of time is long enough (and in particular when it is infinite), this can completely swamp the original assessment.

Moreover, memory is not the only such effect over an infinite life-span. A small change in character when prolonged over a very long time can make an enormous difference. Suppose that climbing Mt Everest, in my story, made me slightly more considerate. We might well question whether this was worth all the suffering. If I were to live in this more considerate way for five minutes, it perhaps wouldn't be worth it (Socrates will disagree). But again we have value-multiplication--if the difference remains over a sufficiently long interval, the increase in value, summed (actually, integrated) over that time, will swamp the pains of gaining it. In fact, that small difference, over an infinite amount of time, will make for an infinite good. Moreover, if virtue leads to virtue, we might here have compound interest at work.

Of course, God could produce the better character directly and maybe he could induce in us false memories. But the value of that infinite good having been produced in the right way may very well be quite high. (One thinks that the value of a good G's having been produced in the right way is proportionate to the value of G.)

These value-multiplication processes can be selective. Thus, God might very well ensure that our memories of pains not be painful to have (to do that God would need to heal traumas, etc.), while ensuring that our memories of goods be pleasant. Nor would there be anything dishonest in God's doing this. In fact, I think most of us have plenty of memories of pains where the memories aren't themselves painful, and this is no defect in this.

If this is right, then selective value-multiplication processes working in an infinite afterlife might very well, and in quite understandable ways, swamp the kinds of value assessments we get from this-worldly considerations. This possibility, which indeed is not merely a possibility but a fairly high likelihood if God exists, might not entirely undercut inductive arguments from evil, but I think it blunts them quite significantly.

And if one is worried that this undercuts our own reasons to prevent evils, all I can do is point one to this older post of mine.

Is sex a basic human need?

Start with these premises:

1. A (human) community is obligated to supply those of the basic needs of its members that can be met, unless perhaps these members have freely consented to not having these needs met.
2. It is not permitted to require anybody to have sex, absent a free promise from the requiree.
3. If a community is obligated to provide A to x, then it is permitted for the community to require one or more of its members to provide A to x.
4. There is at least one community where there is at least one individual who (a) is capable of sex; (b) does not have sex with anyone; (c) has not consented to the state of affairs in (b); and (d) nobody has promised anything that entails having sex with this individual.
5. Basic needs are the same for all members of all (human) communities.

Conclusion:

6. Therefore, sex is not a basic need.

Note 1: What if we replace "sex" with "companionship" or "friendship" or "the provision of food"? Then I think we should deny the analogue of (2).

Note 2: Plausibly, someone who sees sex as a basic need is thereby likely to see it as a right and entitlement, and hence to have a resentment towards the persons who do not fulfill that basic need when they "so easily could", as he or she might say. There is, thus, very good reason for society to attack the idea that sex is a basic need.

Note 3: In the above, I was thinking of basic individual needs. Might not sex be a basic need for the species as a whole? Yes, it is. But as the species is larger than the community, just as not every member of a community is individually obligated to provide for every basic need of the community, so too not every community is obligated to provide for every basic need of the species. Moreover, apart from God (see Note 4), there is no authority that coordinates what basic needs of the species each community needs to meet.

Note 4: The quantifiers in (2) are restricted to fellow human beings or at least to fellow creatures. God has the authority to command a particular couple to marry, and to consummate the marriage.

Beings of reason

Extend English by adding a new kind term "ersoh", and allowing quantification over ersohs. Now the following stipulations generate a semantics for ersohs as well as for a relation "horsesucceeds":

1. Every ersoh horsesucceeds a unique horse.
2. Every horse that dies at a time after which there are at least three minutes (i.e., at a time such that time does not come to an end in less than three minutes after the horse's death[note 1]) is horsesucceeded by a unique ersoh.
3. If e horsesucceeds h, then e exists forever (if time has no end) or until the end of time (if time has an end) from the moment three minutes after the death of h.
4. An ersoh e₁ in w₁ is identical with an ersoh e₂ in w₂ if and only if the horse that e₁ horsesucceeds in w₁ is identical with the horse that e₂ horsesucceeds in w₂.
5. If P is a physical-property predicate (e.g., "has mass of 2kg") that it makes sense to apply to a physical object at particular time, then e satisfies P at t if and only if (a) e exists at t and the horse h that e horsesucceeds satisfies P at t*, where t*=f(t,t_d,t_b) where t_d is h's time of death, t_b is the beginning of h's existence, and f is some specified one-to-one function[note 2] that maps times from t_d+3min to times between t_b and t_d.
6. The only basic predicates that an ersoh satisfies are is an ersoh, horsesucceeds h and P where P is handled as in (5). All other basic predicates are unsatisfied by every ersoh. More complex predications to ersohs are to be reduced to these in some Tarskian way.

I may have omitted something needed for a complete semantics of ersoh-talk. If so, add it, keeping to the spirit of the proposal. The point is that we can easily generate a complete semantics for a language that supposes ersohs.

Now, surely, there are no ersohs in a strict sense of "are". But we can meaningfully talk about them in a way that reduces to talk about horses.

Here, then, is one of my major philosophical intuitions: Any entities talk about which reduces to talk about other entities have the same ontological status as ersohs. They don't really exist. Hence, if reductionism about persons is true, then in a strict sense of "are", there are no persons.

But what is this "strict sense"? Well, the above gives an ostensive definition of it: the basic entities are, while ersohs aren't.

[Minor typos fixed.]

Mereological universalism and artifacts

One reason to believe in mereological universalism is that mereological universalism lets one's ontology include artifacts tables and chairs, without the weird consequence that what entities exist depends on what people have thought. For given any bunch of parts, there is a possible world where that bunch of parts was thus placed by a person with a unified purpose, and hence that bunch of parts is an artifact. But whether that bunch of parts thusly arranged is an object should not depend on what went on in the mind of that person. So, either the bunch of parts is an object in both the world where it is an artifact and the world where it is not, or it exists in neither world. Therefore, if artifacts exists, mereological universalism is true.

Here are some problems for this combined view—the view that accepts mereological universalism as a way of making sense of artifacts.

1. Hermes in the stone: In our world, the sculptor has made the marble statue of Hermes; in w₂, he hasn't, and there is just the block of marble. But if our world's Hermes is identified with a mereological sum of bits of marble, he exists in w₂ as well. (Moreover, he exists in our world even before he was sculpted—this consequence can be avoided by an appropriate four-dimensionalist move.) It is not the case that the artist has caused the Hermes to come into existence. So the approach only does justice to some of our intuitions about artifacts. (This problem can be eliminated by supposing a five-dimensional mereological universalism, where the "fifth-dimension" is worlds.)

2. suppose now that our most fundamental ontology does not include bits of matter. Instead, what we have are fields. It now is no longer clear that mereological universalism by itself yields the existence of artifacts. One might try to generalize mereological universalism to the situation by letting the parts be something field-points, where a field-point can be represented by a triple <x,F,v> where x is a spacetime point, F is a field type (e.g., electromagnetic), and v is the actual value that F has at x. Artifacts then would be four-dimensional mereological sums of field-points. But do field-points really exist? The abstract triples that represent them maybe do, but the field-points themselves are not identical with the triples because the triples are necessary beings, and hence so would their mereological sums be. Moreover, which field-points get included in the chair? This, I guess, is a species of a standard boundary problem like the one Unger uses to argue for his non-existence, but it seems to me even more problematic in the field setting. Suppose, for instance, that on a particle model the object's particles would have some wave-functions. The wave-functions may well be non-zero everywhere in space, though their values are very small outside a small region. So it seems that there is a sense in which an ordinary object should be thought of as existing almost everywhere in some sense, but particularly concentrated in some area. But the field-point-sum object can't exist everywhere, even if the associated wavefunctions are everywhere non-zero, because then there would only be one field-point-sum object—the one consisting of all the field-points there are—and all artifacts would be the same.

A hypothesis about marriage and friendship

Hypothesis: A society where romantic relationships and marriages are seen as primarily about emotional union between two adults is likely to be a society where non-romantic friendships are emotionally more anemic.

If this hypothesis is correct, then there is reason to promote a more embodied view of marriage not just for the sake of marriage, but also for the sake of friendship.

Epistemic normativity

Back when I was a graduate student, I learned explicitly from Nagel's The Possibility of Altruism that states of myself that are worth promoting (respectively, avoiding) are worth promoting (avoiding) as found in others, and for the same reason. This simple fact, the implicit grasp of which is largely constitutive of our moral maturation, has a rather important consequence:

1. If my own belief that p is something that is worth my promoting, then your belief that p is something that is worth my promoting as well, and for the same reason.

This has obvious practical consequences for evangelization, participation in public debate, etc.

But (1) also has a very interesting theoretical consequence. My reason for promoting my belief that p is no different in kind from my reason for promoting your belief that p. But my reason for promoting my belief that p may well be what is normally considered a purely epistemic reason. Now, it is clear that I need not have a purely epistemic reason to promote someone else's belief that p (sometimes her believing p will help me epistemically, because she will use her intellect to help me; but this need not be the case). There will be cases where the only reason I have to promote someone else's belief that p is a moral reason, grounded in the value of the other's possession of the truth. But by (1), the reason for my promoting my own belief that p must then be of the same sort, namely moral or prudential. And indeed, moral, because prudential reasons are just a special case of moral reasons where the beneficiary is ourselves; the lesson of Nagel is that there is no difference between the two qua reasons. Because we can always tweak a case so that I derive no epistemic benefit from your believing p, it follows that I only have a moral or a prudential reason to promote my believing that p.

It follows from the above argument that epistemic reasons are a species of moral/prudential reasons.

However, there is a powerful objection. It could be granted that reasons to promote or bring about a belief in oneself are always moral/prudential. However, one might object that epistemic reasons are not reasons to promote or bring about a belief in oneself. Beliefs are not something one brings about in oneself—they are something one catches, like a cold, as the phrase goes.

This objection is mistaken. Sometimes when we see the overwhelming evidence for p, we immediately believe p. But sometimes we suffer from doxastic akrasia, and we need to push ourselves to believe—e.g., by forcing ourselves to think p, against long-standing habit. And while this may not be the normal case, it is very plausible that if R is an epistemic reason for my believing p, then R is a reason to promote my belief that p.

Moreover, we can imagine a scenario where my brain is so constructed that to come to believe anything that I previously disbelieved, I need to entertain the belief while stomping my left foot. And were my brain so constructed, the epistemic reasons would be reasons for entertaining-plus-stomping actions.

Immoral contracts

Disclaimer: Being neither a legal philosopher nor a lawyer, I ask that the following be taken with a grain of salt.

Start with this argument as background:

1. There is never an on-balance reason to do something immoral.
2. It is immoral to press someone to do something immoral.
3. Therefore, there is never an on-balance reason to press someone to do something immoral.

Now, let's stipulate that a contract is performance-immoral if one of the contracted actions is immoral. There are other ways a contract could be immoral, of course. It could, for instance, be that one party contracts to do some work ignorant of the prevailing payscale while the other party severely underpays. But such a contract would not be performance-immoral—it would not be immoral to do the work and it would not be immoral to pay the money.

Now, add this observation:

4. Enforcing a contract is at least partly constituted by pressing the parties to perform the contracted action.

This is consistent with the fact that contemporary American civil jurisprudence tends not to force performance, but only requires monetary compensation. For it is, nonetheless, the case that such requirements when they go beyond merely refunding moneys paid exert pressure to perform, and indeed the institution of the enforcement of contracts is intended to exert such pressure.

Finally, let us add a very weak and uncontroversial liberal premise:

5. The exertion of pressure by the state on a citizen is only permissible given an on-balance reason to exert that pressure.

It follows from (1)-(5) that

6. It is not permissible for the state to enforce a performance-immoral contract.

While there used to be a common-law doctrine of immoral contracts that said this—so, for instance, you couldn't sue a concubine that you had made an advance payment to but who refuses to live with you—I am told that in the case where the immoral action is legal, the doctrine is no longer a part of current American jurisprudence. Be that as it may, if the argument is sound, it clearly ought to be.

This doctrine of the unenforceability of performance-immoral contracts would have some interesting and far-reaching consequences. For instance, if you're a pornographer, many of your contracts would end up being unenforceable. This would not destroy the pornography industry, but would make it significantly harder for larger pornographic businesses to operate. (That said, despite the value of small businesses, I do not know whether small pornographic businesses are preferable to large ones.)

Another interesting consequence of the argument would be the conditional that if same-sex sexual activity (SSSA) is immoral, then the state is not permitted to recognize a same-sex marriage (SSM). For a marriage is, among other things, an agreement to engage in a shared life of a sexual nature.[note 1] But if SSSA is immoral, then to engage in a shared life of a sexual nature with someone of the same sex is immoral. And for the state to recognize a contract always involves a measure of enforcement at least by means of public opinion. Thus, the recognition of a SSM would be an enforcement of a performance-immoral contract, and that is not permissible to the state. Of course, this is all predicated on the assumption that SSSA is immoral, an assumption that the proponents of SSM will not grant. However, the conditional that if SSSA is immoral, then SSM ought not be recognized is itself an interesting conclusion, since people like John Rajczi have argued that even if SSSA were immoral, the state ought to recognize SSMs.

I think the best way to challenge my argument is to challenge the conjunction of (3) and (4) by using Double Effect kind of reasoning. The pressure in (3) is either intended or not. If the pressure in (3) is not intended, then (3) is false. For it is permissible to do things that put pressure on others to act immorally, if the pressure is not intended to do that. For instance, by asking someone to whom we've lent money for our money back, which we may well have a right to do, we might put some pressure on them to steal the money. So the pressure in (3) must be intentional. But then for the validity of the argument, the pressure in (4) must also be intentional. However, one might argue that the state's enforcement of contracts is not intended to press for performance. It is, instead, intended to press for the disjunctive state of affairs of performance or compensation.

I am not sure about this response. But it does seem that if we agree with this, then we should distinguish, strictly speaking, the state's recognition of a contract from the state's enforcement of it. The enforcement consists, then, in pressing for performance or compensation. But the recognition presses by means of public opinion—contract-breakers are not well thought of—for performance. There is, I think, some reason to distinguish recognition from enforcement. We should not recognize a contract with a graphic designer to draw a square circle—the contract is null and void on grounds of impossibility. However, we could press for performance or compensation. If this is right, then the argument would show not that it is wrong for the state to enforce a performance-immoral contract, but that it is wrong for the state to recognize one.

Thus the state could still enforce contracts between pornographers and their printing or DVD pressing shops, without recognizing these contracts. However, if SSSA is immoral, the state still could not recognize SSM, though it could enforce marriage-like contracts between persons of the same sex. But by calling it a marriage, it would be recognizing such contracts, and this the state has no right to do if the contracts are performance-immoral. This could make it possible for one to have a principled reason to disallow SSM while allowing the state to enforce the contractual aspects of "same-sex unions". (This post is also an experiment: will everyone be put to sleep by the stuff on contracts before they get to the sex stuff.)

Aliens in the heavenly Jerusalem?

If Christianity is correct, there is at least a moderate probability that there are embodied intelligent persons other than humans. If so, will some of them be in the heavenly Jerusalem, too, available for us to interact with? I think that the value of unity between creatures gives a plausible affirmative argument. Over a finite amount of time, it might make sense that different intelligent species be sequestered, as inter-species communication has many difficulties. But given an infinite amount of time, it seems plausible that such contact would be appropriate. The heavenly choir, thus, may well include an intelligent gas cloud (not literally a gas cloud: a being of body and soul, whose body is composed of a gas cloud) slowly changing colors in a meaningful way, and chatting with St Thomas about divine simplicity.

Of course all such possibilities for wonder pale beside the simple wonder of union with God.

Science and theism

Suppose I am a theistic scientist, and I come up with a simple and elegant theory that fits the data. You ask me:

1. But what reason do you have to believe that the theory is true?

I am likely to answer:

2. There is a good God who created a world exemplifying genuine values like simplicity and beauty.

Indeed, if there is a good God, it is more likely that a simple and elegant theory that fits the data is true than if there is no God at all. Whatever one thinks about induction and inference to best explanation, it seems exactly right to say that:

3. If (2) is true, its truth significantly raises the probability that a simple and elegant theory that fits the data is true.

But now imagine two scientists, one a theist and one an atheist, and they have together come with a simple and elegant theory that fits the data. It may very well be the case that the theist should assign a probability of 0.6 to the theory—after all, there may be other simple and elegant theories that fit the data that they have failed to discover, and which fit well with the world being the sort that is created by a God who loves lawlike simplicity. But if (3) is true, the atheist scientist's credence in the theory should be significantly lower. It seems likely, then, that if the theist assigns 0.6, the atheist scientist may very well need to assign something below 0.5.

If this is right, then you will have cases where a theist and atheist scientist agree on the scientific evidence, but the theist weakly assents to the theory but the atheist is more skeptical of the scientific theory.

In general, assuming rationality on both sides, we would expect atheists to be significantly more sceptical of scientific claims than theists who, in turn, should be bolder theorizers. But I think we do not observe this. Hence, on one or both sides, there is some irrationality—or else I am wrong about (3).

"Serious" intellectual work

This morning, I had a look at a recent mathematics paper that I am a coauthor of. I was struck by how complex it is. The reasoning in a mathematics paper is extremely elaborate and complex. In philosophy, we tend to think that an argument with, say, twenty steps is very elaborate. But here the proof involves eleven lemmas, each of which has a proof consisting of several, and at times quite a large number of, steps, many of which are quite elaborate. I can see how one can look at a philosophy paper and a mathematics paper, and think: "The mathematics paper, that's really serious intellectual work. The simplicity of even the most complex philosophical arguments, with the exception of ones in philosophical logic, shows the lack of intellectual seriousness of the philosophical enterprise." I think it is not uncommon for scientists and mathematicians to have this attitude towards philosophy.

I think this attitude is mistaken. Anecdotally, writing good mathematics papers is not harder for me than writing good philosophy papers. Writing a mathematics paper takes me significantly longer than writing a philosophy paper. There is a lot more detail. But how long it takes to write a paper is not a good measure of intellectual difficulty or seriousness. Typically (though not always—I think the paper I was looking at is a counterexample) the main difficulty is coming up with the basic idea for the paper. The difficulty in coming up with the basic idea for a good mathematics paper is not very different from that of coming up with the basic idea for a philosophy paper. In both cases, one may spend years thinking about a problem, trying out solutions that fail, and finally the idea may just come—or it may be a series of progressive refinements. Once the idea comes, wrapping it up can be challenging, and in the mathematics case it may involve more tedium (or not—the tedium is different, in the one case there is tedium in getting all the details of the proof right, while in the other case there is a tedium in relating one's result to a vast literature). Of course, one might find that the details aren't as simple as they seemed once one works through them—but this can happen equally in a mathematics and a philosophy case.

Moreover, even in the mathematics case, the length and complexity of a proof is not the mark of intellectual quality. If one could find an elegant, quick proof—that would be all the more appreciated by the community.

Grandfather paradox

Suppose I went back in time and tried to shoot my grandfather before my father was conceived. Then either I would hit or I would miss. If I hit, absurdity results. What is less discussed in the literature is that if I miss, absurdity also results. Suppose that I miss due to sloppy aiming. (This is the case most favorable to my argument. But I think a similar story can be told for other causes of missing.) Then, my sloppy aiming is explanatorily prior to my grandfather's survival. But my grandfather's survival is explanatorily prior to my existence, and hence to my sloppy aiming. Hence, we get an explanatory circle, which is absurd.

More on the deflationary account of diachronic identity

[Cross-posted from Matters of Substance.]

First, the easy version of the deflationary account. Here is a question about diachronic identity: What makes it be the case that:

1. Some F0 at t0 is diachronically identical with some F1 at t1.

Deflationary answer:

2. There exists an x such that x is an F0 at t0 and x is an F1 at t1.

Observe that (2) does not make use of "diachronic identity" in its statement. Moreover, all of the conceptual ingredients that (2) uses are ones that any substantive account of diachronic identity (the memory or bodily continuity theories in the case of persons are paradigms) will also have to use in analyzing (1): being an F0 at t0, being an F1 at t1, quantification and conjunction (I have a hard time imagining any substantive account of diachronic identity that somewhere doesn't presuppose conjunction!) So, (2) is simpler, and if it is conceptually circular, so is any substantive account.

Now, the somewhat harder version, the question of analyzing diachronic identity wffs. Question: What makes it be the case that:

3. x at t0 is diachronically identical with y at t1.

Deflationary answer:

4. x exists at t0 and x exists at t1 and y exists at t1 and x is synchronously identical at t1 with y.

Since we all need synchronous identity, and it does not seem to be posterior to diachronic identity, it seems fair to presuppose it in an account of diachronic identity. The result seems to be an account of diachronic identity much simpler than any substantive account.

If one is worried that "x exists at t" presupposes diachronic identity, consider this. What is it to exist at t? Here are some standard proposals:

• Presentism: At t: x exists.
• Perdurantism: a part of x is located within the spacelike hypersurface t.
• Eternalist endurantism: x is wholly located within the spacelike hypersurface t.

None of these proposals seem to presuppose diachronic identity. Now, the last two proposals require an analysis of being located or wholly located in a region R. But this could be just a matter of instantiating a primitive located-at relation to R, or a matter of having R if regions just are properties (I am fond of--though I do not endorse--the proposal that regions are properties, with containment being entailment, and that to be in a region is to have the region as a property), or a matter of being appropriately related to other entities by the nexus of spatiotemporal relations.

In any case, substantive accounts of diachronic identity do not clarify what it is to be located in a region of spacetime or what it is to exist at t. Substantive accounts of diachronic identity explain what it is for an object that is located in one region to exist in another region, but that still doesn't explain what it was for the object to be located in the first region. In fact, there is something really weird about substantive accounts of diachronic identity here. It would be very strange to claim to have a good account of what it is for a person who is queen of country x to also be queen of country y (for general non-identical x and y) without that account also being an account of what it is for a person to be queen of x (for a general x). Surely we all need an account of what it is for a person to be a queen of x, and once we have that, the account of what it is for the queen of country x to also be the queen of country y is just a matter of applying that account twice (and using synchronic identity to take care of the definite articles). But like the queen-identity theorist, the substantive diachronic identity theorist has an account of what it is for, say, a person who occupies R1 to also occupy R2, without having an account of what it is to occupy R1. And once we have an account of what it is to occupy R1, we get for free an account of what it is to occupy R1 and R2, at least if we have synchronic identity.

Maybe the simplest way to summarize the deflationary account is this. It is no more mysterious how it is that x at t0 is identical with y at t1 than it is how it is that x who is the Queen of England is identical with y who is the Queen of Canada.

However, the above arguments presupposed that we're dealing with entities facts about which do not wholly reduce to facts about some other entities. In the case of wholly reducible entities, my arguments fail. The reason for that is that in the case of a wholly reducible entity, what it is to exist at t will be reducible to facts about some other class of entities. For instance, for a reducible x to exist at t will not be a matter of x's instantiating some primitive located-at relations. In that case, the conceptual baggage of "exists at t" might be the same as the conceptual baggage of the substantive account of diachronic identity, and so the deflationary account may be incorrect. (I think of wholly reducible entities as akin to wholly stipulative meanings. In the case of words with wholly stipulative meanings, we might not expect deflationary accounts of truth and meaning to apply--we might want the stipulations to be expanded out, like abbreviations, before the deflationary account is applied.)

If I am right, then someone giving a substantive account of what diachronic identity for Ks consists in is committed to Ks being reducible.

Deep Thoughts XXV

Every effect has a cause.

[Cf. Deep Thought VI.]

Deep Thoughts XXIV

One can try without succeeding.

Deep Thoughts XXIII

One cannot succeed without trying.

Truth supervenes on being

Truth supervenes on being (TSB) holds that any two worlds that differ in the truth of a proposition differ in what exists. Here's a fun thought: Suppose divine believings are entities, and that they essentially have the property of being divine believings and they essentially have the content they do. Suppose God exists necessarily. Then TSB holds trivially, because any two worlds that differ in the truth of a proposition also differ in what beliefs God has. It's hard to run this argument given divine simplicity, though.

More on the correspondence intuition

Introduce the notion "SatCorr", where SatCorr(p,T) iff p is a proposition, T is a partial theory of truth, and T satisfies the correspondence intuition in respect of p. I think the following are true:

1. If SatCorr(p,T) and SatCorr(q,T), then SatCorr(p or q,T), SatCorr(p and q,T) and SatCorr(not p,T).
2. If T says that singular existential propositions are made true by and only by the the objects they report the existence of, and p is any singular existential proposition, then SatCorr(p,T).

A consequence of (1) and (2) is that the correspondence intuition does not require truthmakers for all truths. For if we accept (1) and (2), any theory like T in (2) will automatically satisfy the correspondence intution for conjunctions, disjunctions and negations of singular existential propositions—even if it does not provide truthmakers for these.

Spatiotemporal position

Here is a regulative principle for metaphysics: As much possible, treat spatiotemporal position on par with other properties, like wisdom, mass, momentum, fearsomeness, beauty, tallness, charge, etc. (I leave it open whether spatiotemporal position is a relational property or not.)

Basic entities and predication

Suppose that trope theory is correct. Then what it is for x to have a given property P is to have a trope, say P_x, associated with it. But suppose now that x is a reducible entity—one facts about which reduce to the existence and functioning of other entities (e.g., x might be a table—table-facts reduce to facts about particles and societies). In that case, it is surely not the case that what it is for x to have P is for x to have associated with it P_x. For if x has P_x associated with it, then x is no longer reducible. For consider the fact that x has P. For this fact is the same as the fact that x is associated with P_x. But that x is associated with P_x does not reduce to facts about how, say, the components of x are arranged. For the latter facts are constituted by association with certain tropes of the components; but the fact we are interested in involves P_x. The only way x's having P could reduce would be if facts about the existence of P_x somehow reduced to facts about other things. But then P_x wouldn't really be a trope. The point of tropes is that they are ontologically basic—facts about them don't reduce.

Therefore, if trope theory is correct, then it does not apply to cases where we predicate something of a reducible entity. This, I think, gives one good reason to say that the reducible entity does not really exist in the same sense of "exist" that the other entities do. After all, if predication means something different in its case from what what it means in the other cases, it seems plausible its entitihood is not univocal with theirs.

I ssupect that the same argument might work with other theories of predication as well. If so, then reducible entities don't really exist in the full sense of the word.

Correspondence theory of truth

A correspondence theory of truth is sometimes presented as making sense of our intuition about the correspondence between true statements/beliefs/propositions and the world. However, Correspondence Theory(tm) holds more specifically that every true proposition corresponds to something in the world. And that is surely not intuitive. Certainly, Aristotle who said that to speak truly is to say of what is that it is and of what is not that it is not did not think that negative propositions corresponded to something that is. There is no widely held intuition that the proposition that there are no unicorns is made true by a thing. In fact, the idea that it is is counterintuitive, as are particular fleshings out of it. This is not a decisive count against it, but it seems that the Correspondence Theorist(tm) may have engaged in a bait and switch—done justice to the letter of the correspondence intuition but not in the way that that intuition called for, while committing us to a highly counterintuitive thesis.

Suppose Aristotle were right that all statements can be classified into the positive and the negative, and that the positive ones are made true by something that is, and the negative true are true because there is nothing that makes their negations true. Surely that would fully satisfy our correspondence intuition, though it would not be a Correspondence Theory(tm).

A theory of spacetime

I am not saying this theory is correct—it's too platonic for my taste. But it's suggestive. There are special properties called "locators". Moreover, as it happens, the collection of all locators forms a topological space (one can think of the open sets as corresponding to certain distinguished properties of locators). This space we can call the Receptacle. The Receptacle partitions into topologically connected subspaces. Each of these we can call a spacetime. Thus, a spacetime is a maximal connected set of locators. Some spacetimes have an additional structure, say a metric or manifold one.

The points of a spacetime are simply the locators that make it up. They are, thus, Platonic entities. An entity x occupies a point P if and only if x has the property P. Occupation, then, is simply exemplification. A spacetime is said to be actualized if and only if some point in it is occupied.

Question: Wherein do locators differ from other properties, like mass-properties (having mass x grams), that also have a topological (and even metric) structure?

A theory of personal identity with no counterexamples

This is likely equivalent to Merricks' proposal—I still need to think about whether it is—but I like it. Question: When is it the case that the same person is located at spatiotemporal location y and at spatiotemporal location z? Answer: When and only when there exists an x such that (a) x is a person, (b) x is located at y, and (c) x is located at z. Note that the answer does not use the concept of identity, and all the concepts it uses are ones that substantive theories of personal identity also presuppose.

Vagueness

A guiding intuition in much of my thinking in metaphysics is that no vague fact is to be taken metaphysically seriously. I don't have an account of the seriousness, though. Still, the intuition has some nice consequences. Psychological theories of personal identity make diachronic identity vague—but diachronic identity should be taken seriously, so the theories are false. Materialism makes it vague where there is intentionality (because it makes all interesting macroscopic properties vague), hence materialism is false.

The problem of animal pain

Supposedly intense pains that non-human animals undergo provide significant evidence against theism. Why? Well, the thought is that, if he existed, God could have done things better. But how?

Suggestion 1: He could have made something that has the same motivational effects that pain has but that doesn't hurt.

Response: It's not clear that this is possible—it may be that the qualia of pain reduce to motivational effects and cognitive content. But let's grant it's possible. Now we can ask: Do we have good reason to think God hadn't done this? After all, if the pain-replacement, call it shpain, had the same motivational effects, we would observe the same kinds of aversive responses to shpain as to pain. Maybe we wouldn't expect certain kinds of whimpering. But a dog's whimpering is not quite like human whimpering. I think the reason we see the two as species of the same behavior is because both are associated with similar triggers and similar motivational states. But if the objection to theism that we are evaluating is that God instead of creating pain in animals should have created shpain, then we need evidence that animals experience pain instead of shpain, and if I am right about why we see whimpering as a pain behavior, the whimpering does not provide such evidence.

Maybe we can get some evidence for animals having pain rather than shpain by looking at neurological similarities between humans and animals. This may, however, presuppose the supervenience of the mental on the physical, which is controversial. Furthermore, we do not know enough about how pain systems in the brain work. We know that in addition to similarities between human and non-human brains there are differences. Given that shpain and pain have similar triggers and similar motivational results, on the hypothesis that animals have pain rather than shpain, we would expect a lot of neurological similarity and some difference between animal brains and our brains—and that's exactly what we observe.

Suggestion 2: God could have miraculously prevented pain in those cases in which the motivational role of pain is not important to the animal's flourishing, say when the animal is certain to die.

Response: Let's consider the hypothesis that he has, in fact, done so, and see how strong the disconfirming evidence is. It is plausible that God's miracles would be calculated to produce a particular effect and would be in some way minimal as deviations from the ordinary operations of nature. The reason for that is that there is a great value in the ordinary operations of nature. If so, then what we would expect as a miraculous intervention would be a minimal deviation—one sufficient to relieve the pain. Now, the pain has certain neural correlates. A minimal miraculous intervention might well keep most (if materialism is true) or all (if dualism is true) of these correlates intact. And in particular it might very well be that pain behaviors continue because of the remaining correlates. Now, granted, the fact that we still observe the pain behavior is some evidence against the hypothesis that God has eliminated pain in these cases by being evidence against the hypothesis that God has eliminated pain in a way that eliminates pain behaviors. But unless it was very plausible that the latter is how God would eliminate pain, the evidence against the hypothesis that God has eliminated pain behaviors is not that strong.

Suggestion 3: God could have made a world where animals don't need pain or anything like it, because conscious non-human animals are never endangered by anything.

Response: To evaluate this would require the evaluation of a different argument from the argument from animal pain—the argument from the red-in-tooth-and-claw nature of our world, bracketing the question of pain. I think it is plausible that animal death is not an evil in itself—animals do not naturally have immortality. But death is an ultimate kind of danger, and if so, then the plausibility of the suggestion is decreased. Maybe we could imagine a world where nobody dies before reproducing, but that would be a world where it would be hard for evolution to work, and evolution is valuable.

Conclusions: The problem of animal pain only becomes a problem when one adds some reason to think that God could have done better here. There are three suggestions to that effect. On the first two, the theist can make the reasonable response that we do not have very strong reason to think God hadn't done that allegedly better thing. On the last one, we have a broader problem than that of animal pain.

Verificationism and idealism

I just realized (thinking about Quine's description of verificationist reductionism in "Two Dogmas") that there does not seem to be any difference between verificationism and idealism.

Real numbers

For a long time I've been puzzled—and I still am—by this. Our physics is based on the real numbers (complex numbers, vectors, Banach spaces—all that is built out of real numbers). After all, there are non-standard numbers that can do everything real numbers can. So what reason do we have to think that "the" real numbers are what the world's physics is in fact based on?

I think one can use this to make a nice little argument against the possibility of us coming up with a complete physics—we have no way of telling which of the number fields is the one our world is based on.

Color perception

Here's another data point towards a theory of perception. My son, 4, is colorblind (or color perception deficient or whatever the right term these days is). He was looking at the dark red flowers on his mom's blouse, and said they were black. He was told they were red, and he accepted that—he is very accepting of the fact that colors aren't what they seem to him as. I then asked him if they looked red to him after he was told they were red. He was very definite about an affirmative answer to this question.

Neonates' cries influenced by native language

This is rather neat.

Curry sentences

Curry sentences are of the form:

1. If (1) is true, then p,

where I shall stipulate the "If ... then ..." to be a material conditional, and where p abbreviates something not paradoxical. If p is false (in an unparadoxical way—maybe, p is "snow is red"), (1) is paradoxical because it provides an argument for p. Now, it is clear that whatever we say about (1) we should also say about:

2. If not-p, then (2) is not true.

Now, go back to my old favorite, the contingent liar paradox. There are many versions. One of them is this. Let D be some definite description of a sentence which picks out different sentences in different worlds. Then consider:

3. The sentence satisfying D is not true.

Paradox ensues in worlds where D picks out (3). Now, consider:

4. The contingent liar (3) is unparadoxical if D picks out a first-order sentence that is unproblematically true or unproblematically false, in which case (3) has the opposite truth value to that of that sentence.

Then, consider this:

5. The following sentence is not true: "1=1" if p and (5) if not-p.

By (4), sentence (5) is unparadoxically true if p. We ought to, however, say about (5) exactly whatever we say about:

6. "1=1" is true if p, and (6) is not true if not-p.

Thus, we ought to say that (6) is unparadoxically true if p. But we observe that the first conjunct in (6) is trivially true, at least if p is not itself paradoxical. So, surely, we ought to say about (6) exactly what we say about:

7. Sentence (7) is not true if not-p.

Thus, (7) is unparadoxically true if p.

But we ought to say the same thing about (2) as we say about (7), and about (1) as about (2). So, the Curry sentence (1) is unparadoxically true if p. And if p is false, it is a liar sentence, and a contingent liar sentence if p is contingently false. All this means that the Curry paradox is not very different from the contingent liar.

Sex solely for pleasure

Is there an intrinsic morally significant difference between having sex solely for one's pleasure and having sex solely for money? To sharpen the question, let's ask: Is there a morally significant difference between having sex solely for one's pleasure and having sex for money which one intends to use solely as a means to one's pleasure?

Both are cases where the sex is engaged in solely for hedonistic ends, but in the one case the pleasure is achieved more indirectly. Still, in both cases there is some indirectness. Sex, in and of itself, need not be pleasurable. In both cases, it seems to be engaged in as a mere means to pleasure. The difference, however, is that in the one case, the pleasure is the pleasure of this very sexual act, while in the other case, the pleasure is a different pleasure (e.g., the pleasure of driving a nice car, or the pleasure of sex with someone else whom one wishes to seduce in an expensive way). So, in the case of sex solely for one's pleasure, the pleasure is more closely tied to the sex, and it may even be a mistake to talk of the pleasure as a distinct end. If so, then there is a significant—and perhaps morally so—difference between the two cases: in the money case, sex is engaged in purely instrumentally, while in the pleasure-of-sex case, the end is too close to the sex to call the sex purely instrumental.

This distinction, however, imports into the original question something that wasn't there. Granted, there is a difference between sex solely for the pleasure of the sex, and sex for the sake of money which one wants for the sake of some other pleasure. But in the case I originally specified, I did not suppose a case of sex for the sake of the pleasure of the sex; I supposed a case of sex for the sake of pleasure simpliciter. And when one's end is pleasure simpliciter, then one's action plan involves a fungibility of means: one looks around for the ways to get a lot of pleasure, considering whether it is more convenient to get pleasure by proving a new theorem, or having sex, or eating cake, or volunteering at a shelter—or by having sex for money and then using the money to buy a pleasure. Insofar as one is having sex solely for the sake of pleasure, one is prima facie indifferent between these options except insofar as they produce different levels of pleasure with different degrees of convenience.

And if so, then it does not seem that there is a significant moral difference between sex solely for money solely for pleasure and sex directly solely for pleasure. In particular, it follows that if we think that non-marital sex for money is always wrong, we will conclude that non-marital sex solely for pleasure is always wrong; and if we think that marital sex for money is always wrong, we will likewise conclude that marital sex solely for pleasure is always wrong. (To be honest, I think some cases of marital sex for money—say, when one is starving and one's spouse refuses to provide food except on condition of sex—are more defensible than marital sex solely for pleasure.)

However, there is a difference between sex for the pleasure of the sex and sex for money. Sex for the pleasure of the sex is not solely hedonistic. The hedonist as such does not care what she is taking pleasure in, convenience, consequences and intensity being kept constant. Insofar as one cares about what one is taking pleasure in, one is not a pure hedonist. In a case of sex for the pleasure of the sex, the sex is not present purely instrumentally. Here, we also should distinguish sex for the pleasure of sex from sex for the pleasure of the sex. The pleasure of sex can be achieved apart from sex, say by direct neural input. The pleasure of the sex can only be achieved through the sex. It may be that there is little moral difference between sex for the sake of the pleasure of sex and sex for the sake of money. After all, one could have sex for the sake of money in order to get the pleasure of sex—perhaps one is saving up for a neural sexual pleasure implant. But there is a moral difference between sex for the sake of the pleasure of the sex and sex for the sake of money. Say that a sophisticated hedonist is someone for whom not only the intensity, convenience and consequences of a pleasure matters, but the kind of pleasure also matters. Maybe the sophisticated hedonist wants to have a variety of kinds of pleasure, or maybe she has arbitrarily chosen some pleasures over others. In any case, the person who has sex for the sake of the pleasure of the sex is neither a pure hedonist nor a sophisticated hedonist, for she not only cares for the kind of pleasure, but also that which it is had in.

One is unlikely—perhaps it is even an impossibility—to value the pleasure of the sex without non-instrumentally valuing the sex. There may well be people who have sex solely for pleasure. For instance, if Sally wants to have some pleasure and goes through all the options and chooses the one with the best balance of intensity and convenience, and that happens to be sex, she may be having sex solely for pleasure. But such cases are, I think, rare. The pure case of someone who wants to have sex for the sake of the pleasure of sex is less rare. Such a case would require the person to be indifferent as to the gender, age, appearance and species of the sexual partner, except insofar as this impacts convenience, consequences and the pleasure received. Maybe some people do have such an indifference—the only reason, for instance, why they prefer their partners to be of their own species is that they find bestiality to lack something of pleasure.

There is a further kind of distinction we should draw at this point, a distinction between having sex for the sake of the pleasure of the sex—of this particular sexual act with this person at this time—and having sex for the sake of the pleasure of this sort of sex. Thus, the person who cares about the appearance of their sexual partner (typically) seeks the pleasure of sex with a good-looking person. The number of people who have sex for the sake of pleasure is probably small, the number of people who have sex for the sake of the pleasure of sex is probably also small, but the number of people who have sex for the sake of the pleasure of sex of a certain sort (where the sort is either specified by specifying the kind of sexual act or the kind of partner or both) is probably larger. And this, too, I think is not very different morally from sex for money. After all, one might well be having sex for money for the sake of the pleasure of sex of the preferred sort. And I think this is morally objectionable, and apt to make an object of the partner.

On the other hand, sex for the sake of the pleasure of the sex requires or at least tends to require valuing the sex with this person at this time non-instrumentally (actions are individuated by agent, time, patient, etc.) And that's different.

The Christian tradition has unanimously condemned sex for the sake of one's own pleasure. But it is not clear that this condemnation of hedonistic sex applies in the case of sex for the sake of the pleasure of the sex—for in that case, the intended end, "the pleasure of the sex", is partly constituted by the sex itself, and hence the sex is engaged in for the sake of the pleasant good of the sex, rather than for the sake of pleasure alone. And if the sex is intrinsically unitive, this may well be sex for the sake of pleasant union, which is a species of sex for the sake of union, which in turn is taken to be permissible by the tradition. Of course, this is very speculative, and the tradition is authoritative while my interpretation of it is not.

The paradox of Shakespeare's last words

Let p be the proposition that the last thing asserted by Shakespeare in his life is not true. This is a perfectly good proposition, and it is one that we can easily assert. Moreover, it is a proposition that Shakespeare could easily have asserted many times—but only if these times weren't the last moment of his life. Suppose in our world, w₀, Shakespeare asserted p at time t₁. (For all we know, he did!) Surely there is a world, w₁, which is just like our world, but where Shakespeare is killed instantly after t₁. In w₁, then, Shakespeare did not assert p, since p is something that it is logically impossible for Shakespeare to assert as the last assertion of his life. But of course, in w₁, Shakespeare uses the exact same words at t₁ as he does in w₀, and seemingly with the same intention.

So, what are we to make of this? On pain of contradiction, we must hold that in w₁, Shakespeare fails to assert p in his last moment. If we think that words plus intention suffice to determine a proposition asserted (and even if we don't, we can perhaps stipulate a sense of "asserted" in which that is true, and make sure that that's the sense in p), it follows that what intentions one has can depend on what will happen later or that one's "words" include contextual features such as whether one dies shortly thereafter or when one utters them. In other words, we get a temporal externalism about intentions, or else a very weird notion of "words".

And we get an argument from this liar paradox against open futurism. For in w₀ at t₁, it is open whether Shakespeare will die right after t₁ or not. But if he dies right after t₁, he is not intending p. But it is true at t₁ that he is intending p. Hence, it is true at t₁ that he does not die after t₁, which contradicts open futurism. Or, to put it differently, according to the open futurist, there is no fact at t₁ as to what Shakespeare intends at t₁.

Let's make the open futurist even more uncomfortable. Suppose at t₁, you say:

1. One day, I will open my mouth and utter a noise that does not express a true proposition.

This is a perfectly ordinary locution, and one that all of us can reasonably make in light of our fallibility, unless we're expecting to die shortly. Surely you've said something, indeed something most likely true. But this is not the case if open futurism is true. For it is open for you next to say:

2. I just uttered a noise that did not express a true proposition

and then die. Our options are: (a) take (1) to be true and (2) to be either false or nonsense; (b) take (2) to be true and (1) to be either false or nonsense; and (c) take both (1) and (2) to be nonsense—i.e., to fail to express a proposition. There seems to be no reason to prefer (a) to (b) or (b) to (a). So we should go for (c). But if we take (c) as the right solution, and open futurism is true, then we have to say that whenever (1) is uttered, there is not yet a fact about whether it expresses a proposition. This is really weird. Not that it's not weird without open futurism. But it's less weird.

Fun with substitutional quantification

Stipulate that "x strongly believes p" iff x believes p and it is not the case that x believes not-p. Consider the argument:

1. For anything that Freddie believes, there is a possible world where Sally strongly believes it.
2. Freddie believes the negation of Sally's deepest held belief.
3. Therefore, there is a possible world where Sally strongly believes the negation of Sally's deepest held belief.

Isn't it fun to derive an impossibility from two propositions whose conjunction is possible?

We learn from this that if we are to read (1) substitutionally, we need a substitutional quantification in which we are only allowed to substitute names. In that case, (3) does not follow from (1) and (2), because if "Xyzzy" is the name of the negation of Sally's deepest held belief, then instead of (3) all we get to conclude is:

4. There is a possible world where Sally strongly believes Xyzzy.

But there is no contradiction here, because in the relevant possible world, Xyzzy isn't the negation of Sally's deepest held belief. But still, wasn't (1)-(3) fun?

Is quantification substitutional?

Consider:

1. Possibly, something exists which could not be referred to with a linguistic expression.

If quantification is at base substitutional, then (1) is false. But the negation of (1) is:

2. Necessarily, everything can be referred to with a linguistic expression.

Call this "referential universalism". Now, there presumably are worlds where there is no language. Could there be entities that could exist only in such worlds? If so, then, most likely (2) would be false (some such individuals could be referred to in a cross-worldly way by appropriate definite descriptions, but there is little reason to think they all could be). So, referential universalism is not particularly plausible.

The substitutionist could affirm that referential universalism is a trivial truth. In English, some names, like "Alex", ambiguously refer to multiple entities, and are disambiguated contextually. Presumably, there is an extension English* of English which has the name "Ting" that is much more ambiguous—it can refer to anything at all. Thus, "George loves Sally" is appropriately translated by "Ting loves Sally" as well as by "George loves Ting", in different contexts. But then (2) is a trivial truth—"Ting" can refer to anything at all.

It is a fine question how to allow for ambiguous reference and remain a substitutionist. One way is not open: take substituents to be pairs consisting of an ambiguous referring term and a referent. For if one did that, one is doing objectual quantification over referents. So, probably, what one needs to do is to substitutionally quantify over pairs <e,c> where e is an ambiguously referring expressing and c is a description of a context (it can't just be a context as then we'd be objectually quantifying over contexts). But then our substitutionist becomes committed to the highly non-trivial truth:

3. Necessarily, everything is such that in some context there is a linguistic expression that unambiguously refers to it.

Now, maybe it will be said that I haven't offered an argument against (2) or (3). True. But I now make this move. Look: (2) and (3) are trivially true when read substitutionally. Our understanding of (2) and (3) as non-trivial truths shows that we do not, in fact, read their quantifiers substitutionally, and hence substitutionism is false.

None of this affects the claim that there is a perfectly good substitutional quantifier--only the claim that all quantification is to be understood in terms of it.

Experiences and presentism

That x is having a certain kind of conscious experience at t is not just a claim about what is happening right at t. If mental processes are in some way correlated with physical processes, then this follows from the fact that it does not really make sense to talk of the instantaneous state of the physical process (think, for instance, of wave phenomena or classical momenta—these are defined in terms of what happens at other times). But even without this correlation, this is plausible. Thought experiment: imagine seeing a red circle for a tenth of a second with no after image and no memory (the memory is wiped instantly). You see an obvious flash. Shorten the amount of time you're seeing the red circle. Eventually, you don't see it at all.

But if presentism is true, isn't this really weird? It would be really weird if my present conscious state were partly constituted by past-tensed states of affairs. The eternalist (or even growing block theorist) can talk of a temporally extended conscious state. That's not a problem. But the presentist can only talk of the present conscious state together with some (dodgy) past-tensed states, like having seen a red circle a quarter of a second ago. Of course, folks who think that beings coming out of swamps at random couldn't be conscious even if they had souls will not be bothered by this.

Why can't the past change?

If you're a B-theorist, it is no puzzle that the past can't change. It can't change because we are always in the same world, and so neither the past, nor the present nor the future can change. Today, let us suppose (I think correctly) that it is the case that on Wednesday it was raining. Could it tomorrow be the case that it wasn't raining on Wednesday? Not at all—for the very same world, the very same events, that make propositions true today is the one that we evaluate against tomorrow. The fact that the past can't change, thus, is a matter of mere logic—it just follows from the truth conditions for sentences.

But what if you're an A-theorist? So, you think that things will be objectively different tomorrow. Indeed, you already do think that some things about Wednesday will objectively change. For instance, while today (Saturday) Wednesday is objectively three days in the past, tomorrow it will objectively recede one more day into the past. So in fact we already have a change, but a change that the A-theorist doesn't mind. (Though she should.)

In any case, logic alone doesn't do the job. One way to see this is that some A-theorists actually think the future changes. Thus, today, it is false that either I am at Mass on November 8 or that I am absent from Mass on November 8. But come November 8, this disjunction will be true. But the clever tricks that open futurists use to make sense of an open future could be used, equally well, to make sense of an open past. (The parallel holds for B-theory. The B-theorist is committed to the claim that the future cannot change. This sounds fatalistic, but we must distinguish the ability to change the future from the ability to affect the future.)

In the setting of my earlier post on A-theory, the claim that the past cannot change corresponds fairly closely (and in fact exactly, if we assume a closed past) to the claim that the earlier-than relation is transitive. If today, a world where it rains on Wednesday is is past, tomorrow that world will also be past. So in the setting of that post, the explanatory challenge to the A-theorist is why the earlier-than relation E is transitive. The A-theorist who takes E to be fundamental can only say that it is a brute fact that it is necessarily transitive.

There may be A-theorists who can meet the challenge, however. Suppose that you think that there is a TimeShift operator which shifts tensed propositions time-wise. Thus, if p is the proposition that it is sunny, TimeShift(+1 day, p) is the proposition that in a day it'll be sunny. Suppose, further, we take worlds to be maximal consistent collections of propositions, or maximally specific consistent propositions. Then the TimeShift operator can also operate on worlds, and we can define E(w₁,w₂) to hold iff there is a t<0 such that w₁=TimeShift(t,w₂). Then it really is a matter of simple logic that E is transitive, and we have a perfectly good explanation of why the past cannot change.

Note, however, that an open-futurist cannot take this explanation. For her, the fixeity of the past remains a surd.

If this is right, then Tom Crisp is mistaken in taking the earlier-than relation between abstract times (which are just worlds in my terminology) to be primitive. An A-theorist should not say it's primitive—it needs explaining. Or at least I remember him taking it to be primitive, but my memory isn't so good.

The changing past

A decade ago, the end of World War II was 54 years in the past. Right now, the end of World War II is 64 years in the past. If A-theory is true, these are genuine properties of WWII, and it has changed in respect of them. But something in the past cannot change. So A-theory is false.

The A-theorist's best answer to this argument is, I think, that this is a mere Cambridge change. A mere Cambridge change is when an object does not change in respect of intrinsic properties, but something else around it changes, which makes appropriate the application of a different predicate to it. The classic example is that x may grow shorter than y without changing in height—simply because y grew taller. The change in x was Cambridge and that in y was real.

A mere Cambridge of an object x change requires something else, a y, that really changes, where x's change consists in x having a description that makes reference to x's unchanged and y's changed qualities. Let us try to see how to do this for WWII.

Option 1: WWII has the unchanging property of ending in 1945. But 1945 has a changing property—it once was future, then was present, then was past, eventually being 54 years in the past, and now being 64 years in the past. So WWII, or WWII's end, undergoes a Cambridge change in virtue of 1945 (or a specific date in 1945) undergoing a real change. But the idea that 1945 should undergo a real change is at least a bit problematic, I think. It is plausible to say that 1945 is in the past, and so it shouldn't be able to really change. The alternative seems to be to makes times be something abstract—but the idea of abstract entities really changing is also troubling. So one would need to make 1945 be an enduring concrete entity. That's weird.

Option 2: WWII has the unchanging property of ending, say, 15,000,001,945 years after the beginning of the universe, but the universe has a changing age. When we say that WWII ended n years ago, we mean that the year that WWII ended, say 15,000,001,945 cosmic era, is equal to the age of the universe minus n. So, the end of WWII doesn't change, but the age of the universe does. This seems to work, but leads to further puzzles. What kind of an enduring entity is the universe? What is this property of age that so inexorably grows?

Option 3: WWII has the unchanging property of ending in 1945, but there is an objectively changing fact—the fact of which time is present. And in virtue of the latter changing fact, which does not consist in a change in any entity, 1945 undergoes Cambridge change. This view requires a relaxation of the account of Cambridge change—it doesn't require entities to change. (One might try to say that propositions reporting what time is present change in truth value. But that had better be true in virtue of something else.) I think the idea of change that does not happen in virtue of anything's changing is dubious.

A-theory

Here is the right way to see A-theory (this is particularly accurate as an account of Tom Crisp's presentism). There are infinitely many possible worlds, one of which, w₀, is actual. Which world is actual changes with time: tomorrow, say, w₁₇ will be actual (a world encodes everything that is objectively the case—but the A-theorist thinks there is an objective difference between how things are today and how they will be tomorrow). Of course, w₀ and w₁₇ are not unrelated: at w₀ it is true that tomorrow* w₁₇ will be actual, while at w₁₇ it was true that yesterday* w₁₇ was actual (here, "tomorrow*" and "yesterday*" are narrow-scope versions of our usually wide-scope terms).

Moreover, there are three crucial relations that can hold between worlds: S and E.

We say that S(w₁,w₂) if and only if w₁ and w₂ are simultaneous—i.e., it is the same time in both of them. When I say that it might have been the case that right now I am writing a post on growing-block theories, this implies there is a world w simultaneous with the actual world w₀ such that at w, I am writing such a post. This relation is an equivalence relation—it is reflexive, symmetric and transitive.

The earlier-than relation E(w₁,w₂) holds if and only if at w₂ it is true that w₁ was actual. However, it is important to see that the S and E relations are not of a kind. S holds between the actual world and many, many worlds that have never been, are not, and never will be actual. E only holds (in some order) between the actual world and worlds that have been or will be actual. The relation E is transitive. Moreover, no two worlds related by S are related by E. In particular no world is earlier than itself..

Socrates was sitting if and only if there is a world w₁ such that E(w₁,w₀) and at w₁ Socrates is sitting.

The relations S and E probably have to be taken to be primitive.

If E(w₁,w₂) then I will say that w₂ is in w₁'s future and w₁ is in w₂'s past.

We can now precisely characterize closed-future and closed-past views. We have a closed future (past) if and only if the collection of worlds that the actual world is earlier (later) than the actual world is totally ordered by E. It is a consequence of this that no two worlds later (earlier) than the actual world are simultaneous. Everybody, I assume, believes in a closed past. Closed-futurist A-theory, then, is the view the collection of all worlds can be partitioned into disjoint subcollections, in one of which subcollections are all the worlds that aren't E-related to any world (these are the worlds that have no past or future), and each of the other subcollections is totally ordered by E.

Open futurists, on the other hand, think that there are two future worlds that are not E-related—in fact, they typically think there are two future worlds that are simultaneous.

Presentism then adds the further claim that at a world w, only those things are existent that are presently* existent. While A-theory is a theory of the structure of time, presentism is a theory of the ontology of each world. They neatly complement each other, because the presentist has an elegant answer to the question of what it is for an object or event to exist at a time:

1. x existed at t in w if and only if there is a world w₁ such that (a) it is t in w₁, (b) E(w₁,w) and (c) x exists in w₁
2. x exists at t in w (where w is such that it is t in it) if and only if x exists in w
3. x will exist at t in w if and only if there is a world w₁ such that (a) it is t in w₁, (b) E(w,w₁) and (c) x exists in w.

Our timeline (which is branching if open-futurism is true) is the collection of the actual world and all worlds that are E-related to the actual world.

This formulation shows the problem of how A-theory, divine immutability and omniscience could all be true (after all, doesn't it contradict immutability if God has to keep on updating his beliefs) is the same as the problem of how contingentism, strong aseity and omniscience could all be true, where contingentism is the doctrine that not everything is necessary and strong aseity is the doctrine that God has exactly the same intrinsic properties in all worlds. Moreover, this formulation also shows that an A-theorist who believes in divine immutability is someone who believes a restricted version of strong aseity—restricted to the worlds in our timeline. There is thus a good plausibilistic argument from A-theoretic immutability to strong aseity—why restrict to our timeline?

Where does the B-theorist stand in regard to all this? She insists that at every world it is true that in the past and the future, the very same world is actual. Of course, a different Lewisian "centered" world will be actual in the future. The above is really a matter of formalism, so it does not solve any really hard problems, so it does not solve the problem of how worlds and centered worlds differ.

The formalism does, however, highlight some problems for presentism. Consider the problem of induction for presentists. Normally, only what happens in the actual world is relevant for inductive inferences. We know that most worlds are different enough from the actual world that doing induction over them will mix us up completely. But to have any hope of induction being useful, the presentist has to insist on making use not just of data about what happens in the actual world, but also data about what happens in worlds earlier than the actual. I don't know that the presentist can answer this. Here's another problem. Finding out that I promise something in a world w₁ gives me very little reason to do the promised deed in w₀. But if I also find out that E(w₁,w₀), then I have reason to do this. This seems magical, and unless the A-theorist can give us a good substantive account of the E-relation, this will be unexplained.