Vague pain

I suspect that most theories of diachronic personal identity—the exceptions being the soul, further-unanalyzable-fact and no-diachronic-identity theories—have to admit of cases where there is a person in ten years who is only vaguely identical with me where it is definite that he exists and is a person. (Think of cases where people split, parts of brains get put in other heads, memories get recombined, etc.) Vague identity is a known problem given the indiscernibility of identicals (a problem one can get out of by abandoning classical logic—a heavy price to pay to avoid the three exceptional theories). But now consider the following way of making the problem vivid:

1. In ten years there will be an x who definitely suffers pain but who is only vaguely identical with me. (Premise for reductio)
2. Necessarily, for any given kind and intensity P of pain, if x and y have the same exactly alike, it is definitely intrinsically less bad for x that she only only vaguely suffers P than it is for y that she definitely suffers P. (Premise)
3. Therefore, what will happen in ten years is definitely less bad for me than for x. (By 1 and 2)
4. If y suffers from something definitely less bad than x (on some particular occasion), then x and y definitely differ in their properties. (Premise)
5. If x and y definitely differ in their properties, then x and y are definitely non-identical. (Premise)
6. Therefore I am definitely not x. Which contradicts (1).

I am thinking that (2) is the thing for the opponent to challenge. Maybe (2) slips between intuitions about vagueness in the pain (a vague pain is intrinsically less bad than a definite pain) and intuitions about attribution of the pain. But I think (2) is pretty plausible even if one thinks about this. Suppose that over then next 40 years we have a sequence of persons, x₁,x₂,...,x₄₀, with the last one being definitely not identical with me, and with each only somewhat identical with the previous. It seems clear that I should not be concerned at all in a self-centered way about pains to x₄₀, and that I should be less and less concerned as one goes down the sequence. And it seems that (2) is the best explanation here.

A different way out is to insist that whenever x and y are vaguely non-identical, it is only vaguely true that x and y are non-identical. I think one would end up with a view on which we have vagueness all the way down, so it's only vaguely true that it's vaguely truth that ... x is me (for any finite number of vaguelies). But I don't find this plausible. For one, it seems to me that if one has a sequence like the above one, at some point it should be non-vaguely true that there is only vague identity. For another, presumably it is only vaguely true that it's vaguely true that ... x is not me. But in the latter case, intuitively, x is very close to definitely being not me. And that should be enough for (2).

Quite possibly the previous two paragraphs beg the question against the defender of vague identity. As may the first premise of the following argument, which is nonetheless fun:

7. If you're vaguely in excruciating pain, definitely you are at least in a somewhat bad state. (Premise)
8. If you are definitely in at least a somewhat bad state, you are definitely in existence. (Premise)
9. If vague identity is possible, then it is possible that you are only vaguely x at t and x is definitely in excruciating pain at t and you definitely are not identical with anybody at t other than x. (Premise)
10. Suppose vague identity is possible. (Premise for reductio)
11. It is possible that you are only vaguely x at t, and are definitely at least in a somewhat bad state at t, and you definitely are not identical with anybody at t other than x. (By (7)-(10))
12. It is possible that you are only vaguely x at t, and definitely exist at t, and definitely are not identical with anybody at t other than x. (By (8) and (11))
13. Necessarily, if you definitely exist at t and definitely are not identical with anybody at t other than x, then you are definitely x at t. (Premise)
14. (12) and (13) contradict one another. So we reject (10).

The concept of marriage

I will give an argument that many people in our society are operating with a concept of marriage that differs in a central way from the traditional Western concept of marriage. I will then say a little on the same-sex marriage debate.

Entry into an institution is largely or wholly defined normatively by what participation in the institution makes permissible, obligatory or impermissible. Some of these normative features of institutions are central to the role that the institution plays and some may not be so central.

In the Western tradition, one of the normative features of the institution of marriage is that it bestows on the couple the permission to engage in sexual relations. Moreover, this normative feature has been quite central to the institution of marriage in the West. For instance, this permission to have sex has very often been one of the main reasons for a couple to marry (St. Paul certainly sees it this way). In fact, of the permissions that the institution of marriage bestows on a couple, it is hard to find any others that are of equal centrality. Marriage bestows a permission to call oneself "married", but that is mainly a word. Most of the other permissions, such as those involving taxation, visitation, living under one roof, etc. are clearly much more contingent in the Western tradition.

But presently, many believe that it can be permissible for unmarried people to have sex. Therefore, entry into marriage is presumably not seen by them as the bestowal of the permission to engage in sexual relations. It is hard to deny that this is a change in a central feature of the concept of marriage. In the past, marriage's normative impact in the sexual sphere of activity was that something previously impermissible—sexual relations—became permissible. Thus, marriage significantly expanded the options for sexual activity. In the present day, marriage's normative impact in the sexual sphere is seen by many as a contraction—rather than allowing previously forbidden sexual activity with a spouse, marriage forbids previously allowed sexual activity with others. This is a very significant change in how marriage works. (I shouldn't say that marriage in the past caused no new prohibitions. For instance, it implied a prohibition against flirting behavior with others than the spouse, etc. But in terms of sexual relations, marriage extended the options.)

I suspect that few advocates of same-sex marriage believe non-marital sex is always wrong. Therefore, they are already operating with a different concept of marriage from the traditional one. Moreover, if one sees marriage sexually as primarily constricting of permissions (prohibiting sex with persons other than the spouse), then it is no surprise that one will have less difficulty with the idea of same-sex marriage—after all, what is wrong, one may ask, with a couple voluntarily constricting what is permissible to them? Expanding what is permissible is a more serious issue.

Thus, I think it is very important that those who believe in the correctness of the traditional Western understanding of marriage not overfocus on the same-sex marriage issue. The issue of fornication—and of divorce for that matter—is probably at least equally important.

Pleasure and same-sex sexual activity

1. Each kind of deeply humanly significant pleasure is a way of affectively relating to an independent deeply humanly significant kind of good in which the pleasure is taken. (Premise)
2. There is no deeply humanly significant good in same-sex sexual activity when the couple takes no pleasure in the activity. (Premise)
3. Climactic sexual pleasure is deeply humanly significant. (Premise)
4. Climactic sexual pleasure is a pleasure taken in sexual activity. (Premise)
5. If a kind P of pleasure is a way of affectively relating to an independent kind G of good, and an instance of P fails in this way to relate to an existent instance of G, then that instance is empty. (Definition)
6. It is wrong to deliberately induce an instance of a deeply humanly significant kind of pleasure when that instance is empty. (Premise)
7. If there would be no deeply humanly significant good in an activity were the activity done pleasurelessly, then the activity fails to realize an instance of an independently deeply humanly significant kind of good. (Premise)
8. Therefore, same-sex sexual activity fails to realize an instance of an independently deeply humanly significant kind of good. (By 2 and 7)
9. Therefore, taking climactic sexual pleasure in sexual activity is empty when the partners are of the same sex. (By 1, 5 and 8)
10. Therefore, climactic sexual pleasure between partners of the same sex is empty. (By 4 and 9)
11. It is wrong to deliberately induce climactic sexual pleasure between partners of the same sex. (By 3, 6 and 10)

If this argument is sound, then heterosexual sexual relations intended to induce climactic sexual pleasure are wrong when they fail to realize a deeply humanly significant independent good. What could be that independent good? Well, if it's a deliberate attempt at reproduction, then sex is wrong whenever a couple isn't trying to reproduce. But I think the the pleasure in sex is not affectively associated with a voluntary and deliberate attempt to reproduce—there is too much of the animal in the pleasure. Likewise, the couple is not simply taking pleasure in their loving relationship—they are taking pleasure in sex. (If they were taking pleasure in their loving relationship, the sexual nature of the pleasure would be unexplained, since one can have just as deeply loving non-sexual relationships, or at best explained circularly.) Rather, it is that, I think, there is a completing of a biological whole in uncontracepted heterosexual intercourse, and that is deeply humanly significant. If this completing of a biological whole is what is deeply humanly significant about heterosexual sex, then oral sex, masturbation, and the like are ruled out. Contraception may not be immediately ruled out, but is still wrong since it is contrary to integrity: the couple is acting against the biological union which constitutes the deeply humanly significant good in which the climactic pleasure is being taken.

Sleep

Here is a quick argument that sleep is bad in some respects. Sleep either involves unconsciousness or non-veridical experiences. Unconsciousness is bad, since it is the lack of consciousness, which is a good, and a good due to our nature as rational. Non-veridical experiences are clearly a bad. So, sleep always is bad in some respects.

Whether this argument succeeds or not (I think it doesn't; from our nature as rational beings it does not follow that it is our nature to always exercise rationality), it does raise a question about the value of sleep. Clearly, sleep is instrumentally good. Is it good non-instrumentally, though? And will we sleep after the resurrection of the body? As one of our grad students pointed out, Scripture considers sleep analogical to death. There are also positive portrayals of wakefulness. So when death is no more, will there be sleep? Aquinas thinks not.

Inerrance

Occasionally, the rhetorical question is asked of inerrantists: "What's the use of having an inerrant text, if your interpretation of the text is fallible?" Sometimes this question is asked by opponents of inerrance, and sometimes by those who think that those who accept inerrance don't go far enough—they should also accept an infallible exegetical authority. I've done this myself, as an argument for Catholicism.

But the argument implicit in the question is not a good argument without further work. It would be silly to ask: "Why do you care about having a calculator that makes no mistakes, given that you can punch the wrong numbers into it and read the answer off wrongly?" When using a fallible calculator, there are three sources of errors: the calculator, the data input, and the reading of the output. Surely it is a good thing to be able to eliminate one of the three, even if the other two remain.

Furthermore, there is the following advantage to having an inerrant text: progress in interpreting the text is apt to get us closer to the truth of the matter in the subject the text is about. But if the text is wrong on some point, it might be that the better we interpret it, the further from the truth we find ourselves (if we take the text to be authoritative). It is worth having this feature. We might be currently unable to tell what Scripture requires of us in some matter, but it is not unreasonable to devote significant effort into trying to figure it out—because it is likely true.

But let's go back to the rhetorical question and see if we can make it into any argument that can be defended. First of all, it's not clear how "What's the use of p?" even when met with no answer gives us reason to deny p. What's the use of the moon? I don't know, but my not knowing the use for it doesn't seem to significantly affect my confidence that it's there.

However, inerrance isn't like the moon. Inerrance is very unlikely without a miracle. And we might think that God doesn't work miracles except with good reason. So perhaps we could argue that if inerrance is of no use, God wouldn't bother with it. But that's going to be weak. How could we rule out all uses of inerrance? And in fact, surely there are some. The belief that Scripture is inerrant has inspired many people to obey various good commands in Scripture. Moreover, it is better be inspired by a true rather than false belief. So there is surely some use of inerrance. One might worry that the miracle is too great and the benefit disproportionately small. But I don't see why an omnipotent being can't do a great miracle for a small benefit (God helps me find lost objects sometimes—for all I know, he may even be miraculously transporting the lost objects to me, though somehow it seems more likely that he is simply directing my attention to the objects), nor do I see the benefit as small.

Still, there is, I think, some force in the argument of the rhetorical question. There are four sources of errors in information obtained from a text: errors in the original, errors in copying, errors in reading (decoding of words), and errors in interpretation. If it turns out that there are likely so many errors in interpretation that the benefit of lack of errors in the original is quite small, then there is something to be said for asking why God would have ensured a lack of errors in the original without ensuring an infallible method of interpretation. (If a measurement has two sources of error, one of the order of magnitude 0.001 units and the other of the order of magnitude of 0.020 units, a scientist would be unlikely to try to minimize the first error without trying to minimize the second.) But this would require a further argument that fallible interpretation would be quite unreliable—we couldn't just base the argument on the mere fact that interpretation is fallible. Moreover, I think this wouldn't so much an argument against inerrance, as an argument for an infallible method of interpretation (such as a magisterium or tradition or both).

Is it the case that errors in the interpretation of the Bible are so very common that there is something to the argument? I think it might be. Granted, there may be wide exegetical agreement on certain basic points. But if the point of inerrance is simply to preserve agreement on these basic points, we would not need full inerrance, but a more limited doctrine of preserving the truth in the basics (this point was made by one of our grad students in discussion today). So we might still argue: If we think God valued truth in such a way as to give us full inerrance in Scripture, we have good reason to think that he would also have ensured an infallible interpretative method, since that would serve the same value. This is an argumentum ex convenientia, an argument form well loved by medieval theologians.

So, yes, there is something to the argument in the original rhetorical question, but it would take significant effort to defend it carefully. I haven't put in that sort of effort in this post.

More liar paradoxes

The standard way to run the liar paradox is with truth. But the family of liar paradoxes is wide, and I am trying to find a way of characterizing it. To that end, I am thinking about as many variants as I can. Here is one with desire satisfaction (it's not original to me): Annabelle believes that to have all of one's desires satisfied makes one soft. So, she has a desire to have an unsatisfied desire. One day, as it happens, all of Annabelle's other desires are satisfied. Is this one, too?

We can do this with action fulfillment, too. On Thursday, Patrick tells Annabelle that he will do whatever she asks of him on Friday. On Friday, she asks him to refrain from doing everything that he on Thursday said he would do. Patrick made no other statements on Thursday about what he will do.

These cases suggest that one isn't going to get a solution to liar paradoxes simply by restricting language to remove "truth" from it. For there are just too many concepts that can play the same role as truth does.

By the way, there is a joke I once heard about the sadist and the masochist together in hell. The masochist says: "Hurt me." The sadist says: "No."

Dutch books

There is nothing philosophically new here, but I think this is kind of fun. If you click here, you will get a mathematical equation which you ought to have credence 1/2 in (at least immediately). Why? Because a visit to that link has a 50% chance of displaying a mathematical equation that is true and a 50% chance of displaying one that is false, and it's too complicated to see off-hand which it is (now if you have more time, you can do the calculation, and then revise your credence). So you click there, and you do the rational thing—you assign a credence of 1/2. And then, of course, there is a Dutch Book against you, since in fact the equation is either necessarily (and a priori) true or necessarily (and a priori) false.

If you'd like an equation you should be pretty sure about, click here—you'll have a 90% chance that the equation is true. And if you'd like something to speculate over, click here—you'll have a 10% chance of getting a true equation.

Deep Thoughts XVII

What is not done cannot be undone.

[I am not the first to say this. I Googled it and found I was beaten to the punch by Matti Nykanen. But I like the line enough that I'll say it anyway. Some of my other Deep Thoughts aren't original either, I bet.]

Quiz on freedom

Here is another little foray into experimental philosophy. I would be very grateful if you answered out this very short three-question multiple choice quiz on freedom. It shouldn't take more than about one or two minutes. Feel free to forward the link. I'll eventually post some summaries, when I get enough data.

[The comments on this post are disabled, as discussion might disturb the results.]
[The quiz was down for two hours or so, due to a bug in the perl code, but is now back up.]

Liar-like dizziness without truth

Can one run the liar paradox without the concept of truth?

Suppose I write on my board: "At no point today do I believe anything written on this board", and know that nothing else will have been on the board today. Now there is no problem of inconsistent truth assignment: there is no logical contradiction in the sentence on the board being true (in which case I don't believe it) and there is no logical contradiction in the sentence in the board being false (in which case I do believe it). But while there is no contradiction, there is dizziness as I try to figure out whether to believe what is on the board.

The dizziness results from two plausible principles:

1. I should avoid false beliefs.
2. If the evidence conclusively points to p, I should believe p.

Principle (1) prohibits me from believing what is on my board. For I know ahead of time that were I to believe what's on the board, I would be believing something false. The case somewhat resembles the surprise exam. For, it seems that knowing myself, I may know that I won't violate norm (1) in this regard. I also know that not violating norm (1) entails not believing what's on the board. But then I know p, and I know that p entails q, but I don't know q even though I am, plainly, thinking about q. That is, surely, at least a very unstable situation.

Perhaps, though, (1) is mistaken. Maybe it's rationally acceptable to believe something even when one knows that the belief would be false, when the belief is self-referential? Is the norm that I should refrain from believing something when I know that believing it would be the having of a false belief, or is the norm that I should refrain from believing something that I know to be false? I do not know that what is written on the board is false, because I do not know what I will in fact believe. Still, (1) does seem very plausible.

Or is this a case where, whatever I do, I do something irrational?

Or should I say what I say about the liar, and deny that what is written on the board has meaning, even though an exactly similar token would have meaning?

Compatibilism and theism

I am just having fun in this post. I will make claims that seem to have established something interest, but I don't think I'm doing anything interesting. Compatibilism seems to be the doctrine that there is a possible world where determinism holds and some being is free. But God exists necessarily, and God is, plainly, free in every possible world. Therefore, compatibilism is true if and only if there is a world where determinism holds. But there is a world where determinism holds, if by "determinism" we understand the following doctrine: The total state of the world at any given time, together with all the laws, entails the state of the world at all given times. For, it is possible that an angel exists and that every time t, God instantaneously announces all of the history (past, present and future) of the world to the angel (maybe God creates a book that contains that history). Since God cannot lie, it follows that, necessarily, the total state of the world at any given time entails the state of the world at all other times. So, determinism is possibly true, and compatibilism is, hence, true.

Yes, but I've cheated here. While one might incautiously say that compatibilism is the compossibility of determinism with freedom, one really means something like the compossibility of physical determinism with an embodied person's being free. But if that's what compatibilism is, it's still probably true. For either a given form of physical determinism rules out the possibility of extra-physical interventions that deviate from the laws or it does not. If it does rule out that possibility, it is an impossible doctrine, being, apparently, incompatible with God's omnipotence. If it does allow for the possibility of extra-physical intervention, then it is possible for the extra-physical parts or aspects of an embodied being to intervene in the physical order. Since a determinism that allows for such a possibility is possible, and since a determinism that does not allow for such a possibility is impossible, it seems reasonable to take this interenable determinism to be what the doctrine of compatibilism is talking about. And then compatibilism is true.

But maybe I've cheated again. Maybe the question is whether physical determinism is compatible with the free will of purely physical persons. But there the answer is, I think, pretty simple: such a compatibilism is false, because there are no possible worlds containing purely physical persons.

Notice that on all of the above proposed accounts of compatibilism, I've settled the problem (assuming necessary theism or assuming a form of dualism, both of which are doctrines that I can argue for) without saying anything much about responsibility. That suggests that none of the above definitions of compatibilism got at what we really mean by the word.

It's not all that easy to get a definition of compatibilism that escapes the above. Here is a somewhat messy one that might do the trick: It is possible that there is an embodied and free person in a universe with deterministic laws which that person lacks the power to go against. However, this definition might be skewed towards incompatibilism. For the compatibilist may wish to say that one is not free if one lacks the power to act otherwise, but then account for "lacks the power" in a compatibilist way. But if "lacks the power" is understood in a compatibilist way, then the definition of compatibilism is probably not very good. I think the definition is still defensible, but it needs some work.

Basically, what I'd like to have is a definition of compatibilism where neither its truth nor its falsity follows from considerations that don't get at the heart of the real issues with responsibility. And it's not quite as easy as it at first seems to do that.

Liar paradox: Another dead end?

One might (why? I don't know why, but I did think this at some point) think that a distinction between thought and language, together with the idea that the only meaning language has is speaker meaning expressive of a thought, would help with the liar paradox. After all, it seems that the liar sentence is a merely linguistic curiosity, and does not express a thought.

But a variant of the liar escapes this. I am going to describe this variant through a story that seems to make it very plausible that there is a thought being expressed. Frank has two diaries. A blue one for insightful ideas and a gray one for humdrum observations. He feels that his insights haven't been very good lately. He thus thinks to himself, on good empirical evidence, that today is a day on which nothing true gets written down in the blue diary. He then reaches for his gray diary, and writes down this pessimistic thought: "Today is a day on which nothing true gets written down in the blue diary." However, although he had reached for the gray diary, he ended up writing down his thought in the blue one, because he was rather absentminded. So now his blue diary contains the entry: "Today is a day on which nothing true gets written down in the blue diary." Moreover, let us suppose that he writes nothing else in the blue diary today.

What I like about this story is it makes the paradoxical sentence have a genuine use in our language, rather than just being an excrescence in the way the standard liar sentence is.

It seems that what is written in the blue diary expresses a genuine, and even epistemically justified, thought that Frank had. But what is written in the blue diary is true if not true and false if true, according to his intentions. So the move to speaker meaning doesn't help.

If we add the further assumption that what is in the blue book successfully expresses Frank's thought, then Frank's thought is true if not true and false if true. So unless we abandon classical logic, we need to say that Frank's thought was not expressed by what he wrote. But why not? Had he written it in the gray book, it would have expressed the thought. And he wrote the same thing in the blue book. So there doesn't seem to be a mismatch between word and thought—the words seem just the right ones to do justice to the thought. Maybe, though, some variety of future-based externalism is true: maybe what, if any, thought has been thought can depend on what will transpire (e.g., on whether Frank writes something or not). That's a weird idea, but even apart from the Hegelianism that was rampant where I did my PhD, there is independent reason to accept that. E.g., I might dub Kenya's next child "Patrick." And then I might think to myself what seems to be the thought that Patrick will be a girl. But if Kenya doesn't have another child, then I haven't thought anything. But this line of thought leads to the very disquieting conclusion that introspection is not a perfect guide to whether I am having a thought—and that undercuts the cogito.

It seems that in these cases we must go for the least paradoxical claim. Denying classical logic is most paradoxical. So we either need to say that the meaningfulness of the sentence depends on where I happened to write it down, or I have to say that the meaningfulness of the thought depends on future events. Oddly, my present intuitions pull me towards the second, though the first seems less weird. Epistemic akrasia?

Arguments and sincerity

When we write down a complex logical argument, it seems there is a pretty good chance that while writing down the proof, we will write down sentences that express propositions which we do not believe. Some of these sentences will be as part of a conditional proof, and those are not puzzling. But some of the sentences that express propositions which it seems we do not believe will be simply asserted. For instance, in the middle of our argument, we might make a claim that involves some complex logical or mathematical formula, which we then expand out using appropriate manipulation rules. But the expanded out claim may well exceed our mental capacities: we can handle it on paper, but it is just too complex for us to believe, it seems.

If this is right, then sincerity does not require that I believe what I say. (I assume the rules for sincerity do not depend on whether I am writing or speaking.) All that is required is that I believe that what I am saying is true. (What should I say about the speaker meaning in such a case?)

Or so it seems. But here is a curious test case. Politician reads a speech that her speechwriter wrote. She trusts her speechwriter to write only truths. The politician did not read over the speech ahead of time. She enunciates the sentences carefully, but she is distracted and pays no attention to what the text says. I think we would say that she is not being fully sincere. Maybe, though, our standards for sincerity are unfairly high in the case of politicians. Or maybe there are different kinds of sincerity—there is the bare sincerity which is one's duty in speech, and there is something that one might call "real sincerity" which entails conviction (where conviction is belief and more).

On the other hand, there is a different way of looking at the case of the complex sentence in an argument (this is inspired by some things that David Manley said based on his book with John Hawthorne). Maybe we can simply gain access to the proposition by means of the sentence, without having ourselves to understand or even parse the sentence.

Or maybe the things in the middle of proofs should not count as assertions. Perhaps making steps in proof is a mechanical procedure, akin to punching buttons on a calculator and likewise intrinsically devoid of propositional content, aimed at producing empirical evidence of the truth of some entailment. (That the evidence produced by a complex proof is empirical in nature is clear to me, weird as it may sound. One reason is that memory is intricately involved.)

Material conditionals

Say that a proposition p is weakly earthly provided that for every pair of worlds w₁ and w₂ which exactly match one another in respect of all states of affairs localized within a thousand lightyears of earth and all entities and events capable of causally affecting states of affairs localized within a thousand lightyears of earth, p has the same truth value at w₁ and at w₂. It is very plausible that just about all propositions used in everyday speech are weakly earthly. A sentence is weakly earthly provided it expresses a weakly earthly proposition.

Now, suppose that "If p, then q" is weakly earthly. I shall argue that "If p, then q" has the same truth value as the material conditional. First, observe that if the material conditional is false, so is "If p, then q", since otherwise modus ponens wouldn't work.

For the converse, suppose the material conditional p→q is true. Now imagine a possible world w* which is just like our world, but which also contains a one-way causally isolated island universe u, such that events in our universe can affect events in u but not conversely, and where u contains Frizzy, a being that knows the truth values of all weakly earthly propositions (maybe God has told them all to him), and that believes no contradictions. Moreover, Frizzy has the odd property that he always speaks sentences in pairs. First, he utters a claim with no regard for its truth. After that, if the first claim he had uttered turns out to be something he believes to be true, he utters a second claim that he believes to be true; otherwise, he utters another claim with no regard for its truth.

Now suppose Frizzy utters the pair of propositions a and b (in this order), and suppose a and b are propositions Frizzy knows the truth values of. Then, if a is true, so is b. And, hence, it is true that "if a, then b". But now as long as the material conditional p→q is true, i.e., as long as we do not have both p and not-q, it is coherent with the above description of w* that Frizzy utters the pair p and q. So let us suppose that. Then, as noted above, it follows that it is true in w* that "if p, then q". But "if p, then q" is weakly earthly. Hence, if it is true in w*, it is true in the actual world.

What I have shown is that for any weakly earthly indicative conditional, the truth value of the conditional is equal to the truth value of the corresponding material conditional. Moreover, this argument can be run in any possible world (in some possible worlds, of course, the claim is close to trivial because there are no contingent weakly earthly claims). Therefore, necessarily, a weakly earthly indicative conditional holds iff the corresponding material conditional does. Now, assuming indicative conditionals have truth value it would, I think, be very unlikely that there would be something special in this way about weakly earthly indicatives. (The assumption is needed, because if indicatives don't have truth value, there are no weakly earthly indicatives.)

So, we have very good reason to think that either indicatives lack truth value or else indicatives are logically equivalent to material conditionals. I don't know which disjunct to choose.

Knowledge of past and future

We observe B, and have good evidence that 99.999% of the time B was causally preceded by A. We are, I think, pretty likely to say we know that A occurred. On the other hand, if we have good evidence that 99.999% of the time B is causally followed by C, a lot more people will be very cautious in affirming they know that C will occur.

The difference here does not, I think, depend on the mere fact that A is in the past and C is in the future. For, surely, if one is unwilling to say "I know I will fail to win the lottery" before the winner is picked, one will also be unwilling to say "I know I failed to win the lottery" after the winner has been picked but before one has heard who it is. It would be really weird to imagine someone sitting around in a closed room, watch in hand, and then as soon as noon comes, she says: "Now I know I failed to win the lottery", just because the winner is picked at noon.

It could be that this is just another example of widespread irrationality (when I wrote this post, which I am much less sure of now, I think this is what I would have said), but let us not have recourse to that immediately.

I am inclined to think the difference is not based on whether the knowledge claim is in the past or future, nor even on whether the knowledge claim is in the past or future of the evidence, but on the causal connection between the evidence and the event about which the knowledge claim is or is not made. We are, I think, much more willing to move epistemically from effects to causes than from causes to effects. If this willingness is not mistaken, then it follows that there can be probabilistically isomorphic epistemic situations in one of which one knows and in the other of which one does not.

Here is one line of thought on this. Perhaps we are confusing de re with de dicto knowledge. Suppose that Koons is right to say in Realism Regained that if D causes E, then it is possible to have D without E but not possible to have E without D. Then by knowing D de re, we cannot know E de re because many numerically different effects could follow the very same D. But by knowing E de re, we are in a position to know D de re, because no other cause could have produced this very E that we know de re.

And maybe this isn't just a confusion. For it may be that saying that I know that E occurs, or maybe implicates, that I de re know (am acquainted with?) E.

This is related to the scholastic idea that genuine knowledge is knowledge of the forms, and this is always by acquaintance.

A different line of thought on the asymmetry would be that one of our doxastic proper functions is gaining non-probabilistic beliefs about causes from effects, but we simply do not have a doxastic proper function of gaining non-probabilistic beliefs about effects from causes. A theist might even give an explanation of this: God hasn't designed us to gain non-probabilistic beliefs about effects from causes, as that would make miracles be deceptive.

[Corrected to fix typo pointed out in first comment below. Thanks, Tim!]