Deflationism about truth and evolution

I doubt that a deflationist about truth—someone who understoods truth at base in terms of Tarski's Schema (T)—who does not make use of propositions can make sense of the following claim:

1. There was a probability at least 0.01 that somewhere there would evolve beings most of whose empirical beliefs are true.

I don't know if (1) is true or not, but whether it is true or not, it makes sense. Now, as far as I can see, the only good non-propositional deflationist translation of (1) is:

2. There was a probability at least 0.01 that somewhere in the universe there would evolve beings most of whose empirical beliefs b satisfy the condition that there is a sentence S of English such that b is a belief that S, and in fact S,

where the "there is a sentence S" is understood substitutionally.

But one way to see that (1) and (2) differ is this. Let (1a) be a straightforward translation of (1) to Chinese—what a competent translator will produce given (1). Then, (1a) will be synonymous with (1). Now consider the claim:

3. There was a probability at least 0.01 that somewhere in the universe there would evolve beings most of whose empirical beliefs b satisfy the condition that there is a sentence S of English such that b is a belief that S, and in fact S.

The non-propositional deflationist reasons for thinking (1) and (2) cognitively equivalent will also be reasons for thinking (1a) and (3) cognitively equivalent.[note 1] So, our deflationist is committed to the equivalence of (1a) and (3). But now (1a) is just a Chinese translation of (1). As long as the translator did her job, (1a) had better be cognitively equivalent to (1).

So, we conclude by transitivity of cognitive equivalence, that according to our deflationist, (2) and (3) are cognitively equivalent. But they are not. The reason is simple: Chinese and English developed in sufficiently different cultural milieux that there will surely be some concepts in the one language that have no equivalent in the other. (Think for instance of the impossibility of translating the English "nice" to various other languages, or the impossibility of translating the Hebrew "khesed" to English.) As a result, the substitutional quantification over all sentences of Chinese will pick up some sentences that have no English equivalents, and vice versa, and so different claims will be made by (2) and (3). (Indeed, if the probability of the evolution of linguistic beings most of whose beliefs are true turns out to be very, very close to 0.01, then (2) and (3) might differ in truth value, because the probabilities in these two claims will be slightly different.) But once we accepted that (1) and (2) do not differ cognitively, we had to accept that (2) and (3) don't differ cognitively. Hence, (1) and (2) do differ cognitively.

A second way to see that (1) and (2) differ is this: Plainly there could have evolved linguistic beings most of whose beliefs are true but few of whose beliefs can be translated into English. (Think of plasma-based beings most of whose beliefs are about aspects of plasma-based existence that English lacks the ability to express.)

But maybe one will say: "English and Chinese nowadays include the whole language of science, and are highly extensible, etc., so in fact anything an alien could believe is something we could say in either English or Chinese." I don't know about that. But non-propositional deflationism about truth, if true, should be true of all languages. Now, imagine a race of aliens who spend most of their life playing games and philosophizing. They live in a nutritionally rich environment such that they do not need to have as many well-developed empirical and scientific concepts as we do. Their language is highly deprived on the empirical side. For instance, they do not know anything about light or any other form of electromagnetic radiation. But they're superb players of a game very much like chess but played by smell, and they love talking about the nature of language. They have a concept of truth that functions just as ours does. Now, if non-propositional deflationism is true, it is true for these aliens, too. Thus, their equivalent to (1) had better be equivalent to something like (2) or (3), but with the name of their language in the place of "English" and "Chinese". But it is clear that the switch from "English" and "Chinese" to that alien language does in fact change things. In particular, because of the empirical impoverishment of their language, it is harder for their equivalent to (2) or (3) to be correct, because there are fewer empirical beliefs of yet other aliens that can be translated into their language than can be translated into ours.

Miracles

I think it would be valuable if a good philosopher of religion were to carefully look at some of the most carefully checked contemporary miracle reports—namely those involved in Catholic beatification and canonization proceedings. I think it would lend some reality to a largely theoretical discussion. These reports are very well documented, I understand.

Here is a story that I was recently sent that is currently under investigation—it is a story of a man dying from flesh-eating bacteria, healed allegedly by the prayers of Blessed Columba Marmion.

Sentence tokens

It is tempting to identify sentence tokens with certain noises or inscriptions. But this is mistaken, if we want meaning and truth to be a function of the sentence token. For it is easy to imagine a case where a speaker with a single noise says two things, one a truth in language L₁ and the other a falsehood in language L₂, to two different interlocutors. It's kind of hard to come up with examples using actual languages, except of the one word sort. My favorite there would be pointing at a bottle and saying to two people, one a speaker only of English and the other a speaker only of German "Gift", and each ignorant of the other's presence (we can imagine them on either side of a divider). To the speaker of English, one has said that the bottle is a present; the speaker of German has been warned that it is poison. A different kind of example can be produced using ambiguity and context. If I've just been talking with Fred about rivers and with George about finances, and neither was a party to the other conversation, I can say: "I was by the bank yesterday", deliberately telling Fred that I was by the riverbank yesterday and telling George that I was visiting a financial institution. The two claims might be both true, or both false, or one true and the other false.

So if we want sentence tokens to play the role of resolving ambiguity, taking care of indexicals, etc., so that meaning and truth would be a function of the token, the tokens can't be noises and inscriptions. They could be noise (or inscription) and intention pairs, or they could be utterings (maybe in each of my above cases, I deliberately do two utterings with one same noise, just as I might do two mosquito killings with one well-placed slap), or they could be noise and understanding pairs (if we prefer to locate meaning on the side of the listener), or they could be acts of hearing.

Hope from history

Sometimes the Christian may feel depressed over present errors and distortions, supported by intellectual and cultural elites, defended by individual Christians, and sometimes perhaps insufficiently condemned by the elders. It may seem like various battles, such as the ones over abortion, divorce, and Sunday work/shopping (I do not equate the three issues), are lost, even among many of the faithful. Sometimes it helps me to remember past battles that also appeared to be unwinnable but that have been won, mainly to increase hope, though a wiser person than I might also learn lessons from the past victories.

Two past battles seem to me particularly memorable: simony and duelling. They are different kinds of examples. Simony (the charging of money for sacraments), as far as I know, was never strongly supported by anybody but the simoniacs themselves. But nonetheless it seemed to be a vice that for centuries was impossible to root out. Yet now, by the grace of God, we are almost entirely free of it. Duelling was supported by much literature, and by examples in the highest society of people who engaged in this sin without any sign of shame. The situation might well have seemed hopeless, and the defense of the Christian teaching on the sanctity of life would have seemed crazy. Yet, again, while people still fight, the cold-blooded, formalized duel to the death is almost entirely gone, as are its defenders. It's almost a miracle—or perhaps literally it is a miracle.

Also certain kinds of once-mighty ideological enemies of Christianity are no more. An interesting case is the puritanical secularist, whom one now one meets mainly in the pages of Chesterton and in history books. For instance, Gonzales in The Mexican Revolution quotes the revolutionary Saturnino Cedillo (around 1920):

I want land. I want ammunition so that I can protect my land after I get it in case somebody tries to take it away from me. And I want plows, and I want schools for my children, and I want teachers, and I want books and pencils and blackboards and roads. And I want moving pictures of my people, too. And I don't want any Church or any saloon.

Or any brothel, too, I bet. These kinds of secularist revolutionaries seemed to have four enemies: the exploiting classes, the Church, the saloons and the brothels. This sternly moralistic secularist was a formidable enemy in his time: his just opposition to exploitation, drunkenness and prostition did make it harder to fight against him. But he is no more. That is a pity in some ways.

God and the afterlife

The following arguments came out of a fascinating conversation with Sam Calvin. I think neither of us thinks they are conclusive, but they are suggestive and interesting.

Start with this argument:

1. (Premise) If the cosmos is an (axiologically) abhorrent place, then it is not the case that we should trust our moral beliefs.
2. (Premise) We should trust our moral beliefs.
3. Therefore, the cosmos is not an abhorrent place.

The thought here is that we get our moral beliefs from the cosmos that we live in (here the cosmos would be the sum total of what is, including ourselves and, if theism is true, God), and if the cosmos is a truly horrible place—an axiologically abhorrent place—it is not the case that we should trust the faculties by which we generate moral beliefs.

Now:

4. (Premise) If there is no life after death, then the cosmos is an (axiologically) abhorrent place.

The thought behind this premise (and perhaps behind the whole argument that this is a part of) is due to Gabriel Marcel: Think of someone you love, and think what a horror it would be if this person—this very individual—were to cease to exist forever. From this, we conclude:

5. There is life after death. (By 3 and 4)

Further

6. (Premise) If the space of all possibilities is (axiologically) abhorrent, then it is not the case that we should trust our moral beliefs.
7. Therefore, the space of all possibilities is not abhorrent. (By (2) and (6)).

Here, we can use the fact that the cosmos we inhabit is a part of the hypothetically abhorrent space of possibilities, and if the space of possibilities is so nasty, why should we think we're in a nice part of it? Next:

7. (Premise, perhaps only stipulative?) God is defined as that which most ought to exist.
8. (Premise) Necessarily: (if God exists, God necessarily exists).
9. (Premise) If that thich most ought to exist cannot exist, the space of all possibilities is axiologically abhorrent.
10. If God does not exist, God cannot exist. (By 8)
11. If God does not exist, then that which most ought to exist cannot exist. (By 7 and 10)
12. If God does not exist, the space of all possibilities is axiologically abhorrent. (By 9 and 11)
13. God exists. (By 6 and 12)

Irrealism and Tarski

According to Tarski, Schema (T), of which instances have the form:

1. "..." is true if and only if ...,

where the same text is put for the two instances of "...", is compatible with both realism and irrealism, with correspondence theory and coherentism.

Let's explore this claim. Suppose we are irrealists (nevermind that we might then prefer some other term, like "epistemicist") who have some epistemic notion of truth, e.g, a sophisticated version of the claim that S is true if and only if it would be arrived at in the ideal limit of inquiry. Abbreviate the epistemic definition of the truth of S as E(S). I will at times use the the ideal limit formulation for explicitness, but it should really be considered a stand-in for whatever more sophisticated story is to be given.

If we accept both Schema (T) and the epistemic definition of truth, then we have to accept every instance of:

2. E("...") if and only if ....

But (2) gets us into trouble. First of all, if we accept the Law of Excluded Middle (LEM)—that for all p, p or not p—then we have to accept the implausible claim that for all p, E(p) or E(~p). For many values of p, that is simply implausible for any of the epistemic versions of E. Thus, it is not plausible that in the ideal limit of inquiry we will conclude that Napoleon died with an even number of hairs on his head, and it is not plausible that in the ideal limit of inquiry we will conclude that it wasn't the case that Napoleon died with an even number of hairs on his head.

So, our irrealist who accepts (1) will, it appears, have to deny LEM. This shows that Schema (T) is not neutral between realists and irrealists. For while a realist can accept Schema (T) and either believe or not believe LEM, the irrealist is forced by the acceptance of Schema (T) to deny LEM. And if we see LEM as self-evidently true (though that remark begs the question against the intuitionists), then Schema (T) will in fact be unavailable to our irrealist.

Let us consider the irrealism further. Here is an instance of (2) (with the toy version of ideal-limit irrealism):

3. We would in the ideal limit find out that there are conscious beings in the Andromeda Galaxy if and only if there are conscious beings in the Andromeda Galaxy.

This is a startling claim. Moreover, it is a claim that is part of a large family of equally startling claims relating how things are far away and what we would find out. These claims, furthermore, are not merely accidentally true, since the characterization of truth had better not be an accident.

Let's push on further with instances of (2). For instance:

4. The ideal limit of inquiry is never reached if and only if in the ideal limit of inquiry we would conclude that the ideal limit of inquiry is never reached.

But the right hand side of the biconditional doesn't hold: in the ideal limit of inquiry we would not conclude that the ideal limit of inquiry is reached. So, the left hand side doesn't hold. Consequently, we have an a priori argument that the ideal limit of inquiry is reached. But unless one is a theist (who thinks that God has always already reached that ideal limit), it is absurd to suppose we'd have an a priori argument for that—that would yield give an atheist an a priori argument for the claim that we won't all perish tomorrow. The present example is one that cannot be leveled against irrealists who do not engage in any kind of idealization. But I suspect that non-idealizing irrealist views degenerate into relativism.

If this is all right, then in fact the irrealist cannot afford to accept Schema (T), and Tarski is wrong in thinking Schema (T) is neutral.

But non-acceptance of Schema (T) comes with a price, too. We either have to allow that truth of "There is conscious life in the Andromeda Galaxy" does not suffice to show that there is conscious life in the Andromeda Galaxy, or we have to allow that there could be conscious life in the Andromeda Galaxy, even though it is not true that there is conscious life in the Andromeda Galaxy. That is absurd. Of course, as an argument, this is question-begging.

Let's see if we can do better. If the irrealist's use of the word "truth" does not conform with Schema (T), the word "truth" does not match what seem pretty clearly to be central cases of our use of the word. Thus, when the irrealist says that "truth" depends on inquiry, the irrealist is not actually talking of what we mean by "truth", and is not disagreeing with the realist. And assuming that the irrealist doesn't say crazy things like (3) and (4), it is not clear wherein the irrealist is being an irrealist. (I would be quite happy if it were shown that irrealism is impossible.) But if the realist can give a correspondence theory of the concept of "truth" that conforms with Schema (T), then the conformity with Schema (T) would be evidence that the realist is not using "truth" in a Pickwickian sense.

To put the main points differently, epistemicism can be first and second order. First-order epistemicism affirms all the instances of (2). Second-order epistemicism affirms all the instances of

5. "..." is true if and only if E("...").

Now: (a) first-order epistemicism makes sense but is crazy, (b) second-order epistemicism together with Schema (T) leads to first-order epistemicism, and (c) second-order epistemicism without Schema (T) uses the word "truth" differently from how we use it, since our usage is governed, in part, by Schema T. The challenge for the epistemicist is either to deny that first-order epistemicism is crazy, or to show how second-order epistemicism without Schema (T) is talking about "truth".

Infinite conjunctions

Field claims that our desire that we only believe truths can be understood as a desire for the infinite conjunction that

1. I believe "p₁" only if p₁, and I believe "p₂" only if p₂, and ...,

where I go through all the sentences. But one cannot replace a universally quantified desire with a conjunctive desire. Here is one way to see this. Suppose I falsely believe that "Eats jabberwocky sits" is a sentence. If I desire to believe only truths, then this desire together with my false belief explain why it is that I am motivated to ensure first that "Eats jabberwocky sits" is a truth before trying to believe it. (Think here of a case when an authority says "Eat jabberwocky sits", and we have prima facie reason to think that what she is true and hence a sentence, so I then investigate, for instance checking the authority's reliability.) But if what I desire is the infinite conjunction, then it is unclear why my desire has any explanatory bearing on my investigation into whether "Eats jabberwocky sits" is true, since my desire has nothing to do with the sentence.

What Field might try to do is, I suspect, to posit in me a mistaken belief that one of the conjuncts in my desire is 'I believe "Eats jabberwocky sits" only if eats jabberwocky sits', which somehow explains my activity. There are two problems with this. First, it is not clear how it is that the belief that something is a conjunct in something I desire is motivating. But the more serious puzzle is this. The mistaken belief that one of the conjuncts is 'I believe "Eats jabberwocky sits" only if eats jabberwocky sits' is supposed to motivate me. Motivate me to do what? Presumably, to believe "Eats jabberwocky sits" only if eats jabberwocky sits. But that is not an answer, because it is ungrammatical. So there seems to be no way of formulating what it is that I am motivated to do!

One might try to do better as follows. What I am motivated to do is to believe "Eat jabberwocky sits" only if what the (alleged) sentence "Eat jabberwocky sits" says is true. But 'What "p" says is true' is a quantification that Field will want to expand again into an infinite disjunction:

2. ("p" says that p₁ and p₁, or "p" says that p₂ and p₂, or ...).

So what I am motivated to do is to

3. believe "Eat jabberwocky sits" only if "Eat jabberwocky sits" says that p₁ and p₁, or "Eat jabberwocky sits" says that p₂ and p₂, or ....

But how does that motivate me to investigate whether "Eat jabberwocky sits" is true? After all, "Eat jabberwocky sits" does not in fact occur among "p₁", "p₂", .... If anything, I should be directly motivated not to believe "Eat jabberwocky sits", since it does not satisfy any of the conditions. Now, it is true that I believe that "Eat jabberwocky sits" is in the list of all sentences. Let's be more explicit about what I believe in believing that. What I believe is that a sentence of the form '"Eat jabberwocky sits" says that p and p' is one of the disjuncts on the right hand side of (3). This motivates me to believe "Eat jabberwocky sits" only if p, it seems. Well, not quite. For I haven't picked out p. Alright, let's pick it out. Stipulate that p_n is the first sentence in the list of all sentences (e.g., alphabetically ordered) such that "Eat jabberwocky sits" says that p_n. Now it seems that the content of my desire is getting clearer. As a result of my false belief that there is such a p_n, I desire to believe "Eat jabberwocky sits" only if p_n. But that doesn't make any sense unless I can actually spell out what "p_n" is. I can't have a belief with a variable sentence baldly inserted. Besides, how could that desire guide my action when in fact I don't know what "p_n" is?

I might try to do something with definite description in place of "p_n". I desire to believe "Eat jabberwocky sits" only if the first sentence that says what "Eat jabberwocky sits" says. But that's again ungrammatical. OK, so I desire to believe "Eat jabberwocky sits" only if the first sentence that says what "Eat jabberwocky sits" says is true. However, the last clause becomes, once again, an infinite disjunction: I desire to believe "Eat jabberwocky sits" only if "s₁" is the first sentence that says what "Eat jabberwocky sits" and s₁ say, or .... We once again see that we are back where we were.

But of course the above is a bit silly, because I have a very clear belief about what "p_n" is. But if I have such a belief, then what I desire is to believe "Eat jabberwocky sits" only if eat jabberwocky sits. And that's ungrammatical.

This problem shows an interesting problem for deflationist theories of truth. The theorist who says that truth is a property has no difficulty with the sentence "'Eat jabberwocky sits' is true." The sentence is, simply, false: it ascribes to a string of words that do not form a sentence a property that only strings of words that do form a sentence can have. But the deflationist's take on what it is to believe that 'Snow is white' is true is seems to be that it is, simply, to believe that snow is white. And if so, then to believe that 'Eat jabberwocky sits' is true is to believe that eat jabberwocky sits. But that's ungrammatical. So, either the deflationist must make a difference between what it is to believe that 'Snow is white' is true and what it is to believe that 'Eat jabberwocky sits' is true, which seems problematic, or she must give a more complex account of what it is to believe that 'Snow is white' is true. That more complex account is probably going to have to be something like the disjunction: 'Snow is white' is (or says the same as) 'p₁' and p₁, or 'Snow is white' is (or says the same as) 'p₂' and p₂, or .... That does not seem very plausible.

From self-interest to morality

On a familiar Hobbesian picture (whether it was that of Hobbes, I know not), a sovereign is needed to enforce the laws in order for moral behavior to become rational, where rationality is equated with self-interest, and once there is a sovereign, it is rational to strictly adopt morality. Gauthier, instead, thinks we can get by with the fact that by strictly committing ourselves to the moral code, we will likely lose out—we'll get caught.

I do not know that either picture is sufficient to show that it is rational to become moral. For, it seems, a smart person with the executive virtues might instead of adopting morality, will adopt almost-morality, such as a disposition to act morally unless one has a better than 99.9% chance of gaining at least twenty million dollars without getting caught. We can imagine the almost moral financier who goes along, as morally as everybody else, cooperating with others, obeying traffic laws, punctiliously handling her clients moneys—as long as less than $20 million is at stake or as long as the chance of getting caught is 0.1% or higher. It seems that from a self-interest perspective, she might do better than just by adopting morality, though on the other hand Gauthier might point to the psychic costs of monitoring for the possibility of getting $20 million dollars with a chance of getting caught under 0.1%. On the other hand, the wishful thinking might add some spice to the person's life. And maybe the person has a pretty good antecedent chance of eventually being able to work the swindle. So, I think, on Gauthier-like and thumbnail-Hobbes-like considerations, it might sometimes only be rational to adopt almost-morality.

But there is a better way to argue for adopting morality. Say that a view is "serious" provided that there is some evidence for it. On all serious non-religious views, all life's payoffs are finite. On some serious religious views, adopting morality increases the chance of an infinite positive payoff, and on some of these also infinitely increases the size of a possible infinite positive payoff (e.g., by moving one from one level in heaven to another, thereby resulting in greater bliss for eternity). On some serious religious views (there is an overlap between these and the former), adopting morality decreases the chance of a negatively infinite payoff, and on some of these also infinitely decreases the size of a possible infinitely negative payoff (e.g., my moving one down to a lower circle of hell). On some serious religious views, the effect of adopting morality on infinite payoffs is inscrutable. On some serious religious views, there either are no infinite payoffs (e.g., religious views that have no afterlife) or the infinite payoffs are only finitely affected by whether one adopts morality (e.g., reincarnationist views on which everyone eventually achieves the same level of bliss, so that how one lives only affects how many lives it takes to do that).

But on no serious religious views is it the case that the effect of adopting morality decreases the chance of a positive infinity payoff, increases the chance of a negative infinity payoff, infinitely decreases a positive infinity payoff, or makes infinitely worse a negative infinity payoff. Putting the above together, and using some coherent way of handling infinities mathematically, and assuming that at least one of the serious religious views on which there is an increase of a probability of a plus infinity, or an infinite increase of the size of a plus infinity, or a decrease of the probability of a minus infinity, or an infinite decrease of the size of a minus infinity given adoption of morality is a view that has non-zero probability, and assuming that non-serious views cancel out or are overwhelmed probabilistically by serious ones, we get the conclusion that self-interest requires that we should adopt morality, rather than almost-morality or any other alternative.

I do want to consider one objection. According to orthodox Christianity, salvation is a fruit of God's grace rather than something we achieve by our own willed effort. Now, one might argue from this fact that it is not the case that I decrease the chance of God giving me the grace of conversion when I adopt the way of life of the pimp over the way of life of a philanthropist. If so, then whether I adopt morality or not will not affect the chances of infinite (whether positive or negative) payoffs. That's fine. But there is no Christian view on which it is the case that we in fact increase the probability of a positive payoff by adopting the way of life of the pimp. Granted, God loves the pimp, but God also loves the philanthropist. The probabilities that God will offer such-and-such a grace to a person are, on these grace-based views, inscrutable. One might worry that the philanthropist is more prone to self-righteousness than the pimp. But just as, according to Christian doctrine, God loves the exploiter, so too does God love the self-righteous. (Of course he hates the exploiting and the self-righteousness, both for the effect on victims, and for the effect on the vicious person.)

But that objection is only relevant if the above-described Christian view is the only one with non-zero probability. (There are some complicated theological and probabilistic questions about some of the arguments in the previous paragraph—it might turn out to be compatible with a grace-based view of salvation that morality, being itself a fruit of grace, increases the chance of salvation, or prepares the way for the acceptance of grace. Also, once one has received grace, by acting seriously immorally, one rejects grace. While God might offer it again, perhaps we cannot count on it.) And if that is the case, then one has other rational reasons to be moral—reasons internal to that Christian view, such as that by being moral, one acts lovingly towards the God who died for one's sins, and lives more fully as a member of the body of Christ. It does not matter for the argument whether a religious view on which morality improves the chance of an infinite payoff is true. All one needs is non-zero epistemic probability.

A more serious objection is with regard to the content of that morality. But among the serious religious views, first there will be agreement that one ought to be moral, so striving to figure out what is moral and striving to do that will be prudent, and, second, there will be agreement on various, though not all, aspects of what being moral entails. In such a case, it will be more prudent to choose the safer route (thus, if one serious view says that contraception is immoral, and no serious view says that contraception is morally required, then one shouldn't contracept).

Truth and explanation

As some of my previous posts note, one of the contemporary debates over truth is whether truth can be explanatory. If so, then, it is argued, it is a bona fide property, a relational one according to most proponents of this. The form of arguments offered by folks like Kitcher is something like this: Success at a certain activity is best explained by the hypothesis that practitioners have true beliefs about an area of the practice; hence, having one's beliefs be true is an explanatory property. This is an argument that concludes to the property-hood of truth from truth entering into an explanans.

It seems that it might also be possible to go the other way: it seems one can conclude to the property-hood of truth from truth's entering into an explanandum. For instance: Why is it that most of our short-term predictive beliefs are true? Surely it is plausible that we can give a natural selection (either of the genetic sort, connected with belief-forming faculties, or of the mimetic sort, connected directly with particular beliefs or more general ideologies) explanation of the truth of these beliefs. Moreover, the explanation is causal in nature. Now, it is plausible that if we can give a causal explanation of the obtaining of some feature, that feature had better be a bona fide property in a broad (i.e., abundant) snese.

I don't know if this is an independent argument for the propertyhood of truth, though. For our reason to think that a natural selection explanation of the truth of these beliefs is possible is that it is plausible that the truth of these beliefs leads to (biologically or culturally) reproductive success. And this "leads to" is itself explanatory. So it seems that the status of truth as entering into explananda in the selective way is dependent on the status of truth as entering on the explanans side of explanations of fitness.

This leads to an interesting question. The person who believes in the closedness of the natural (in particular, any naturalist) is committed to the correctness in our world of the inference:

1. F is natural; E's occurrence explains F's occurrence; therefore, E is natural.

Should she also accept the following formally similar inference?

2. E is natural; E's occurrence explains F's occurrence; therefore, F is natural.

Laws of nature

It is a really interesting question for someone who believes in lower level laws (e.g., Aristotelian laws grounded in the natures of substances, or in separate laws of nature governing different kinds--electrical, gravitational, etc.--of interaction) how higher level laws like the law of conservation of mass-energy which depend on the appropriate coordination of lower level laws (e.g., in the Aristotelian case, that no entity can increase its mass-energy without some other entity decreasing its mass-energy at the same time) get to be explanatory. One answer is that the higher level laws entail the lower level ones and are ontologically more basic. Aristotelians will deny this, though, and I am not sure we have reason to think so. Certainly, the law of conservation of mass-energy does not by itself entail various electromagnetic laws--other assumptions need to be added. It seems at least possible, and I think plausible, that the lower level laws are in fact ontologically more basic, and the higher level ones supervene on them.

I wonder whether the right answer to that question isn't Leibnizian. The lower level laws (perhaps combined with certain boundary conditions) entail the higher level ones. The explanation of the coordination of lower level laws to produce certain cool results like conservation of mass-energy is that it is good that the lower level laws be such as to result in these higher level laws (which have various positive axiological features, such as elegance), and God does what is good.

There may also be a nice teleological answer, if one can make sense of a teleological dependence between laws. In fact, the theistic answer might have two takes: a more voluntarist one and a more teleological one.

Is truth explanatory?

Rorty (in Lepore, ed., Truth and Interpretation, 1986) claims that the concept of truth does not enter into explanations. Suppose, however, that I observe physicians and magicians attempting to cure diseases. I notice that the physicians are often successful, while the magicians are no more successful than chance. Moreover, suppose that I know nothing about the actual disciplines of medicine and magic. I might, nonetheless, form the explanatory hypothesis that:

1. Physicians are more effective at healing because their beliefs about the causes of diseases are more often true than those of the magicians.

Rorty considers simpler versions of this sort of explanation (he considers the case of a person getting a destination because he knows where it is), and thinks that those are only "promissory notes for explanations", and that the full explanation will say what the contents of the beliefs are, without the need to refer to truth. Thus, Rorty thinks that (1) is enthymematic (that much is obvious—there is a lot of background assumed in (1)), and indeed enthymematic for an explanation that makes no reference to truth. Presumably this expanded explanation is something like this:

2. Physicians are more effective at healing because physician A believes that gout is caused by elevated levels of uric acid, and gout is caused by elevated levels of uric acid, and physician B believes that ..., and ..., and magician X believes that gout is caused by demons, but gout is not caused by demons, ..., and 'A, B, ...' is a list of most physicians, while 'X, Y, ...' is a list of most magicians.

It is a mistake, however, to take (1) to be enthymematic for (2). One reason is that the inference to (1) was an instance of inference to best explanation, and was an inference that one could make without anything like the sort of information involved in (2). A different reason for this is that we lose important explanatory information in passing from (1) to (2). We miss the regularity about physicians' and magicians' beliefs that is expressed by (1), a regularity that is not merely coincidental but itself explained, e.g., by the physicians' employment of the scientific method and the magicians' adherence to a secrecy that makes intersubjective testing impossible.

To take (1) to be enthymematic for (2) would be relevantly like replacing the explanation:

3. About half of the coins I tossed landed heads because the outcomes of the throws are independent random variables, with probability 1/2 of landing heads, and hence it is statistically likely that approximately half of the coins I tossed land heads,

with:

4. About half of the coins I tossed landed heads, because six is about half of ten, and coin 1 landed heads, coin 2 landed heads, coin 3 landed tails, coin 4 landed tails, coin 5 landed heads, coin 6 landed heads, coin 7 landed heads, coin 8 landed heads, coin 9 landed tails and coin 10 landed tails.

First, one can know (3) without knowing anything like the kinds of details in (4), and make an explanatory inference to (3) without making any explanatory inference to (4). Second, (3) contains additional information—information about the statistical facts. Claim (4) is compatible with it just being a coincidence that about half of the coins landed heads, just as claim (2) is compatible with it just being a coincidence that the doctors are better at treating disease, while (1) and (3) are explanatorily richer, making it clear that we are not dealing with mere coincidence.

The point has been made, in a somewhat different way, by Hartry Field. And Kitcher has run a similar argument, too. There is nothing original about the basic argument, but I think the comparison to (3) and (4) is illuminating.

Corollary: Truth enters into explanation of physical facts. But if it enters into explanation of physical facts, then either naturalism is false, or truth is a natural property. The prospects for seeing truth as a natural property are poor—that is something we see from the literature on truth, as well as from the fact that if truth were a natural property, then presumably a liar sentence could be formulated in the (first-order? I think so!) language of science. Hence naturalism is false.

Scepticism, causal theories of reference and the Causal Principle

Suppose we agree that

1. Causal theories of reference have successfully answered the sceptic by ensuring that most of our empirical beliefs refer precisely to the situations that cause the beliefs (cf. Davidson).

Thus, the person whose body is a brain in a vat makes claims about the computer system that produces inputs for the brain, etc. Then, I suspect, we have to say that we know that the Causal Principle (CP) is true—that every contingent event has a cause. For suppose that contingent events could lack causes. Then causal theories of reference have not successfully answered the sceptic, because they are compatible with the Rob Koons' sceptical scenario of someone whose perceptions are all uncaused.

Let's think about what a causal theorist should say in Koons' scenario. For simplicity, assume physicalism. I think some of what I say generalizes to the non-physicalist case, but only some. I think we need some more detail about the scenario. Here are three versions:

2. The apparently perceptual beliefs occur without any cause.
3. Mental perceptual states (states relevantly like our state of being appeared to red-cubely) occur without any cause, and then cause beliefs.
4. Sensory nerve stimulations occur without any cause, and then causal mental perceptual states and beliefs.

I will consider version (2), though (3) and (4) are also interesting. As it stands, the causal theorist has to say that my description in (2) is incoherent. Granted, states that are neurally just like our own belief states occur in the victim. But these states, being systematically uncaused, are not about anything, and hence are not belief states. It seems, then, that on version (2) of the story, the causal theorist has escaped scepticism—it is still true that most of the victim's beliefs are true. But while (2) may be incoherent, there is still a sceptical scenario in the vicinity. For wouldn't it count as a sceptic's victory if the sceptic were to make us conclude that, perhaps, most of the empirical-belief-like mental states we have are not in fact beliefs? We can imagine what it is like. Suppose that an epistemic authority told us: "Yesterday, the borogoves were very mimsy." We would then acquire a neural state that would cause us to say: "I believe that yesterday, the borogoves were very mimsy." This neural state would not be a belief, perhaps, because the sentence is in fact nonsense—it does not express anything—but it would masquerade as a belief. And the scenario that most of the things that appear to us as empirical beliefs are like that would, surely, be a sceptical scenario. It seems plausible that any scenario on which it is not the case that most of those states that are not introspectively distinguishable from beliefs are not correct beliefs (i.e., are not correct or are not beliefs) is a sceptical scenario. If so, then a Koonsian scenario where most of our belief-like neural states are uncaused would be a sceptical scenario, and one that the causal theorist does not have an answer to.

I think the causal theorist's best answer compatible with (1) would be to deny that in the case where the empirical-belief-like states are uncaused that these states would be conscious, or to say that if our minds littered with too many empirical-belief-like states that are not empirical beliefs, then we would not be able to form the concept of an empirical belief. Perhaps that answer works. But I am not sure. One might, for instance, have a lot of empirical beliefs early on in one's life, which are in fact veridical, and these early ones could anchor one's concept of "empirical".

If this line of reasoning is right, then (1) requires an acceptance of the Causal Principle.

The simple life

It is not an uncommon sentiment that life used to be simpler. I suspect that a portion of the sentiment rests on a combination of some of the following factors: (a) a confusion between the simplicity of artifacts and the simplicity of life; (b) a confusion between the simplicity of individual life and the simplicity of the community's life (this might be a special case of (a), if the relevant aspects of the community's life count as artifacts); (c) a confusion between the simplicity of process and the simplicity of product; and (d) a certain lack of imagination.

Here is a two word refutation of the claim that life used to be simpler: "manual transmission". Granted, cars with automatic transmission are more complex, but that is a complexity of artifacts, not a complexity of life (see point (a)). Sure, having to fix a car with an automatic transmission is more complex, but the average person does not have to do that—one can delegate the task to an expert (see point (b)). Or let's go further back. Bows and arrows. Simple? Even sticking to a self-bow, how many of us have actually tried to make one (and don't forget how to make string), much less make a good one?

The average Western worker accomplishes tasks of significant complexity. But the processes by which these tasks are accomplished are often efficiently simplified (see points (b) and (c)). With a few mouse clicks, pages of text slide out of a printer.

One area, however, where it does seem like there is significantly more complexity is the area of law. The average person does need to fill out tax forms subject to laws of dizzying complexity; anybody who deals with various sorts of media runs up against complexities of copyright law; and anybody who has a business of their own has to abide by a myriad of rules. At the same time, it might turn out to be the case that the complexity of our formalized laws does not greatly exceed the informal complexity of custom in past societies.

Pascal's wager and infinity

(Cross-posted to prosblogion).

Some people, I think, are still under the impression that the infinities in Pascal's wager create trouble. Thus, there is the argument that even if you don't believe now, you might come to believe later, and hence the expected payoff for not believing now is also infinite (discounting hell), just as the payoff for believing now. Or there is the argument that you might believe now and end up in hell, so the payoff for believing now is undefined: infinity minus infinity.

But there are mathematically rigorous ways of modeling these infinities, such as Non-Standard Analysis (NSA) or Conway's surreal numbers. The basic idea is that we extend the field of real numbers to a larger ordered field with all of the same arithmetical operations, where the larger field contains numbers that are bigger than any standard real number (positive infinity), numbers that are bigger than zero and smaller than any positive standard real number (positive infinitesimals), etc. One works with the larger field by exactly the same rules as one works with reals. This is all perfectly rigorous.

Let's do an example of how it works. Suppose I am choosing between Christianity, Islam and Atheism. Let C, I and A be the claims that the respective view is true. Let's simplify by supposing I have three options: BC (believe and practice Christianity), BI (believe and practice Islam) and NR (no religious belief or practice).

Now I think about the payoff matrix. It's going to be something like this, where the columns depend on what is true and the rows on what I do:

	C	I	A
BC	0.9X-0.1Y	0.7X-0.3Y	-a
BI	0.6X-0.4Y	0.9X-0.1Y	-b
NR	0.4X-0.6Y	0.4X-0.6Y	c

Here, X is the payoff of heaven and -Y is the payoff of hell, and X and Y are positive infinities. I assume that the Christian and Islamic heavens are equally nice, and that the Christian and Islamic hells are equally unpleasant. The lowercase letters a, b and c indicate finite positive numbers. How did I come up with the table? Well, I made it up. But not completely arbitrarily. For instance, BC/C (I will use that symbolism to indicate the value in the C column of the BC row) is 0.9X-0.1Y. I was thinking: if Christianity is true, and you believe and practice it, there is a 90% chance you'll go to heaven and a 10% chance you'll go to hell. On the other hand, BC/I is 0.7X-0.3Y, because Islam expressly accepts the possibility of salvation for Christians (at least as long as they're not ex-Muslims, I think), but presumably the likelihood is lower than for a Muslim. BI/C is 0.6X-0.4Y, because while there are well developed Christian theological views on which a Muslim can be saved, these views are probably not an integral part of the tradition, so the BI/C expected payoff is lower than the BC/I one. The C and I columns of the tables should also include some finite numbers summands, but those aren't going to matter. A lot of the numbers can be tweaked in various ways, and I've taken somewhat more "liberal" (in the etymological sense) numbers--thus, some might say that the payoff of NR/C is 0.1X-0.9Y, etc.

What should one do, now? Well, it all depends on the epistemic probabilities of C, I and A. Let's suppose that they are: 0.1, 0.1 and 0.8, and calculate the payoffs of the three actions.

The expected payoff of BC is EBC = 0.1 (0.9X - 0.1Y) + 0.1 (0.7X - 0.3Y) + 0.8 (-a) = 0.16X - 0.04Y - 0.8a.

The expected payoff of BI is EBI = 0.15X - 0.05Y - 0.8b.

The expected payoff of NR is ENR = 0.08X - 0.12Y + 0.8c.

Now, let's compare these. EBC - EBI = 0.01X + 0.01Y + 0.8(b-a). Since X and Y are positive infinities, and b and a are finite, EBC - EBI > 0. So, EBC > EBI. EBI - ENR = 0.07X + 0.07Y - 0.8(b+c). Again, then EBI - ENR > 0 and so EBI > ENR. Just to be sure, we can also check EBC - ENR = 0.08X + 0.08Y - 0.8(a+c) > 0 so EBC > ENR.

Therefore, our rank ordering is: EBC > EBI > ENR. It's most prudent to become Christian, less prudent to become a Muslim and less prudent yet to have no religion. There are infinities all over the place in the calculations, but we can rigorously compare them.

Crucial to Christianity being favored over Islam was the fact that BC/I was bigger than BI/C: that Islam is more accepting of salvation for Christians than Christianity is of salvation for Muslims. If BC/I and BI/C were the same, then we'd have a tie between the infinities in EBC and EBI, and we'd have to decide based on comparisons between finite numbers like a, b and c (and finite summands in the other columns that I omitted for simplicity)--how much trouble it is to be a Christian versus being a Muslim, etc. However, in real life, I think the probabilities of Christianity and Islam aren't going to be the same (recall that above I assumed both were 0.1), because there are better apologetic arguments for Christianity and against Islam, and so even if BC/I and BI/C are the same, one will get the result that one should become Christian.

It is an interesting result that Pascal's wager considerations favor more exclusivist religions over more inclusivist ones--the inclusivist ones lower the risk of believing something else, while the exclusivist ones increase it.

It's easy to extend the table to include deities who send everybody to hell unless they are atheists, etc. But the probabilities of such deities are very low. There is significant evidence of the truth of Christianity and some evidence of the truth of Islam in the apologetic arguments for the two religions, but the evidence for such deities is very, very low. We can add another column to the table, but as long as the probability of it is small (e.g., 0.001), it won't matter much.

Praise and relativism

Hartry Field agrees with Putnam that values are non-factual. Of course, there is a fact of the matter about whether x values F, but there is no fact of the matter about whether x's valuing F is correct. This includes epistemic values. Field thinks this is not a problem. One simply relativizes epistemology to an "evidential system". Then, making use of a non-relativistic concept of truth, one defines the reliability of an evidential system. Finally:

if there is any "highest epistemological praise" it will be something like "is justified relative to some highly reliable evidential system" (or "is justified relative to all highly reliable evidential systems", or some such thing). This isn't really an adequate formulation of what "the highest epistemological praise" (if there is such a thing) would be, for (among other things) reliability is not the only feature we want our evidential systems to have; but it gives the general flavor. (Journal of Philosophy 79 (1982), p. 564)

Field is cautious about whether there is any such thing as the "highest epistemological praise". His caution could have two sources: he could be cautious about whether there is such a thing as "high epistemological praise" or about whether there is such a thing as the "highest epistemological praise". I shall take the latter to be his worry. Thus, on my reading, Field thinks there is such a thing as high epistemological praise, and to give it is to say something of "the general flavor" of the claim that a belief is "justified relative to some highly reliable evidential system (jrtshres)".

But now let me raise this question. What makes saying that a belief is jrtshres be a case of praise, while saying that it is justified relative to some evidential system (jrtses—note that every belief has this property) or that it was acquired during a full moon (adafm) are, presumably, not praise?

To answer this question we need to figure out the sense of the word "phrase". I see two prima facie plausible answers. On the first, to praise something is to attribute to it a property that is valued (individually or socially)—this is the relativistic notion of praise. On the second, to praise something is to attribute to it a property that is in fact valuable—this is the objective notion of praise.

Let's start with the second. This clearly has difficulties. Thus, it is easy to imagine (and I remember a claim that there is a code of honor among Russian thieves according to which this is so) a criminal subculture where to say that something was earned through honest work got is not praise, even though it is the attribution of a property that is in actual fact valuable. Similarly, it seems to be genuine praise if I say, misunderstanding the aim of checkers: "Great! You've just managed to get yourself into a position where you have no valid move." Nonetheless, there may be a sense of "objectively correct praise" on which to praise something is to attribute to it a property that one believes to be objectively valuable. But then by engaging in epistemic praise, we are presupposing something incompatible with Field's relativism about epistemic values—we're taking a belief's being jrshrtes to be objectively valuable.

On the other hand, here is a difficulty for the relativistic notion of "praise" as a reading of what Field is claiming. It seems that on a relativistic notion of praise, what is going to be the highest epistemological praise is not that a belief is jrtshres, but that it is justified according to one's own evidential system (on the individual relativist reading—the social case needs a modification in the argument). The evidential systems in Field's paper embody different individuals' evidential values, and so if one praises by attributing properties that one values, then one will be praising compliance with one's own evidential system.

I suppose Field could object that it is possible to see one thing as valuable for one's own beliefs and another as valuable for another's. Perhaps one sees epistemic caution as good in one's own case but values incaution in others, being glad that others explore crazy hypotheses, as that gives one a richer fund of ideas to work with. This example, by itself, is no good, though. Instrumentally valuing something that others do, on account of its benefits to oneself, is not really praise (unless one has an overinflated ego and one equates oneself with God or the universe or something like that). It is not, for instance, praise for the conman to say, once the con is done: "You have made me rich", though the conman values being rich. It would, on the other hand, be more like praise for the conman to say to someone: "You have made yourself rich." As long as we see others as being relevantly like ourselves, it does not seem that we can coherently praise in another what we do not value in ourselves.

Moreover, let's simplify and assume that what it is to value something is to have a certain kind of preference for it. A more sophisticated theory of subjective value will need a more sophisticated version of this argument, but I suspect the basic point will still be possible to make. Then on the relativistic reading, the force of the praise comes down to something basically like one's preference for jrtshes beliefs. But the following statement seems to me to be performatively inconsistent: "I praise you for F, because I prefer F." The relativism in the second clause undercuts the praise in the first. Epistemic praise, however, can be made both of oneself and of another. If made of another, one can hold back on the "because I happen to prefer jrtshes beliefs" clause. But if we praise ourselves in a clear-headed way, then we cannot hold back on it, and we indeed are being performatively inconsistent.

Of course, if to value something is to believe that it is objecitively valuable, the performative inconsistency disappears. But Field cannot take this route.

If all this is correct, we get a more general result: If relativism about values is correct, praise is insincere, manipulative or in some way inconsistent.

Propositions

Certain arguments that I've used myself in the past have presupposed that back-reference to things one's interlocutor said standardly reference the interlocutor's expressed proposition. For instance, if George says "I am hungry" and you say "I believe that", you are not expressing a belief in your hunger, but George's—you are assenting to the proposition that he is hungry. I knew, of course, that there are cases where things aren't quite like that. For instance, you tell me on the phone "It's a cold day", I might say "Not here!" But of course the proposition you uttered includes a rigid reference to the place you uttered it (it's implicitly indexical), and it is just as true there as here. I took these exceptional cases to be "mere exceptions", where one references the sentence rather than the proposition, or cases to be handled by, say, positing a "relocation" operator that acts on propositions.

But I've been thinking about religious dialogue and coming across more cases, and ones that may be fairly important to our communication. Here is one example. My concept of marriage is such that it is analytic that marriage is not just a social status. But let's say you think that marriage just is a social status, and you know what my concept of marriage is. When I say "Fred and Jane got married last Saturday" then I am expressing a proposition that you believe to be false. For the proposition that I expressing is that they entered a marriage—i.e., entered into a marital relationship that is more than a social status. If standard back-reference is to the expressed proposition, then you should say "That's not so!" But instead you will say "Yes" or "That's true" or at most "Indeed, though I understand 'marriage' differently." Moreover, because differences in concept are quite common, this is a pretty normal situation.

It seems, then, that what I refer back to is your words, classified lexicographically (if you said, "Yesterday, Fred was at the bank", meaning a financial institution, it would be misleading for me to agree, when I believed that Fred spent all of yesterday by the side of a river), and with indexicals shifted. The effect of your "That's true" in these cases seems to be basically that of repeating (without plagiarism) my words, with indexical shifts, rather than asserting my proposition.

Perhaps, though, this is just another exceptional case, reflecting the fact that "That's true" in ordinary concepts means "That's close enough in the present context."

If, however, this is more than an exceptional case, then I may have been wrong in this paper of mine when I said we had a duty to use words in our interlocutor's sense.

Life is short

It is a truism that life is short. But this truism is in tension with the very plausible claim that life-long commitments are hard. So which should go?

Or can it be, perhaps, that life-long commitments are hard—for those who have not existentially appropriated the shortness of life? If so, then we would have the following prediction: In societies where individuals are socially isolated from the fact of death, well-kept life-long commitments are more rare (either because life-long commitments are more rare, or because they are kept less well). I suppose this is one of those predictions that it would be really hard to make sufficiently precise to check.

Caves and holes

On the face of it, the ontology of caves is just like that of holes. But there do seem to be some significant differences. A hole is, as it were, pure nonbeing, albeit of a sort that depends on its walls for its existence. But a cave includes the hole and the walls. When we talk of cave walls, we think of them as parts of the cave. But what is the wall? Is it just a veneer of the rock? It seems to me that if you could take a cave and cut it out of the rock, keeping a thin veneer of rock, and put it in space (so the veneer wouldn't collapse under its own weight), the cave would survive. So only a veneer is essential. Is only a veneer of rock part of the cave? No—more is. For the physical properties of the cave—say, the material causes of stalactites—probably include more than a veneer. Besides, if only a veneer of wall is included in the cave, then only a veneer of stalactites and stalagmites would be included. But that's absurd. So, more than a veneer of wall is part of the cave. But how much? This is, surely, vague.

So caves seem to be more ontologically solid than holes, and it seems that we can answer a bunch of questions about them. But like sand sculptures, they depend ontologically on nonbeing—if you fill in the hole (or cover the sand sculpture with sand) with solid rock, it seems the cave perishes. This ontological dependence shows that caves (and sand sculptures) are not substances. If they are at all.

Ponzi schemes

With Madoff getting 150 years in jail, it's topical to say something about Ponzi schemes. So let me make this remark: There are possible worlds where there is nothing wrong with Ponzi schemes. For instance, there is nothing morally wrong with certain Ponzi schemes in certain worlds. What makes Ponzi schemes problematic in our world is that with a finite amount of total wealth (including future wealth), it is not possible to have a system of transactions that do not create wealth, increase the wealth of some, and do not decrease anyone's wealth. But in a world with an infinite number of investors having infinite total wealth, it is possible to have financial schemes that increase the wealth of some, without decreasing the wealth of any, and yet without any wealth being created, simply by shuffling wealth about.

For instance, if the investors are numbered 1, 2, 3, ..., one can have a scheme where 1 gets $1 from 2, 2 gets $1 from 3 and 4, 3 gets $1 from 5, 6, 7 and 8, 4 gets $1 from 9, 10, 11 and 12, and so on. If the transactions are somehow made to be simultaneous, then once the scheme is over, each investor is richer, none is poorer, and no wealth has been created--it's been "sucked in from infinity." Interestingly, this infinitary scheme makes folks further down the chain get more money than people closer to the head of the chain: 1 only gets a dollar, but 3 and 4 each get $3.

But what if the transactions are not simultaneous and sequential? This can still work in finite time if supertasks are possible. But if the transactions are sequential and supertasks are impossible, then at any given finite time in the procedure, some investors are better off, while others are worse off, and only in the infinite time limit has everybody benefited.

Pascal's wager and decision theory

I think Pascal's wager could be seen as a way of destroying most of standard decision theory in the case of many agents. The reason for this is that just about any significant choice one makes will have the property that according to some religious views, that choice affects the probabilities of getting an infinite payoff, and unless the agent has a way of assigning zero epistemic probability to that religion, these infinitary considerations will swamp all the finite considerations. Thus, one wonders to oneself: "Should I self-flagellate?" There is an obvious answer: "No, because it hurts." But because there are religious views according to which such self-flagellation helps attain an infinite payoff, then unless one assigns zero probability to these views, the infinitary considerations swamp the finitary considerations coming from the fact that it hurts. One ends up having to compare the increased probability that one will get an infinite payoff if one self-flagellates on religious views that are pro-flagellation with the decreased probability of an infinite payoff on anti-flagellation religions, and the apparently relevant consideration that it hurts just drops out by the wayside (unless the infinitary considerations end up being perfectly balanced).

One might think one can dismiss the infinitary considerations because of problems with weighing infinities. But those can be solved fairly easily by adopting an appropriate version of non-standard arithmetic.

Maybe what this is, though, is not so much a reductio of standard decision theory, as a way of showing that practical rationality requires that one assign non-zero probability to at most one religious view (or maybe one moderately narrow family of closely-related religious views). Dogmatic atheists and dogmatic religionists would like this conclusion. And I am a dogmatic religionist, after all. :-)

Dark nebulae

Last night, I was observing a portion of the Pipe Nebula, which is a dark lane of dust obscuring the Milky Way. It was kind of cool: I could see stars to the left of it through the telescope, and then as I moved the telescope to the right, the field of view went almost completely dark, except for some stars on the fringes and some quite faint stars in the middle. But did I see the Pipe Nebula? It seems that what constituted "seeing" the Pipe Nebula was my not seeing the stars behind it. After all, intuitively seeing seems to be a causal process whereby the seen object causes light to reach the eyes. But the Pipe Nebula did not cause any light to reach the eyes. Of course, the same issue comes up when one "sees" a matte-black cube, a shadow, etc.

Maybe, then, we need to relax the intuitive concept of seeing as a process whereby the seen object causes light to reach the eyes. One might say that seeing is a process whereby the seen object causes light to reach or not reach the eyes (or, maybe better, causes a particular profile of wavelengths of light to reach the eyes, which profile might be empty). But if that were right, then we should say that a blindfolded person sees the blindfold (and that a person with eyes closed sees the inside of the eyelids). However, I do not think we say that—we say, rather, that a blindfolded person does not see anything.

Here is an alternative that accounts for shadows, ultra flat black cubes and dark nebulae: in seeing, the seen object causes a non-empty shaped pattern of light. There are two ways of causing a shaped pattern of light: one way is by causing the light (by reflection, emission or refraction) and the other way is by causing the shape. Here, "shape" must be understood in such a way that a field of view filled with uniform light counts as a shape (so that if one is right up against a uniform blue wall, one still sees the wall) while an empty field of view, as in the blindfold case, does not count as a shape.

A problem with this account is that if one's face is up against a red, or green, or blue wall, one counts as seeing the wall, but if the wall is painted with ultra flat black paint, then one isn't seeing the wall. I do not know how to give an account on which one counts as seeing the ultra flat black wall, but one doesn't count as seeing the blindfold.

Causation and presentism

Suppose:

1. Some events have causes that strictly precede them in time (i.e., the two events are never simultaneous).
2. If E causes F, then both E and F exist.

It follows that presentism is in trouble. For suppose that presentism is true, and that a present event F has a cause E that strictly precedes it in time. Since E strictly precedes F in time, it follows that if F is present, E is not present. And if E is not present then, according to presentism, E does not exist. But if E does not exist, then it does not cause F by (2). Nor can the presentist say that even though E doesn't cause F, E caused F. For at any time at which E might have been said to cause F, by (2) and presentism, both E and F would need to exist, while there is in fact no time at which they both exist.

The presentist might make the following move. Let E* be the state of affairs of its being the case that E occurred. Then, the presentist can deny that E causes F, but affirm that E* causes F, and say that that is close enough to do justice to our intuitions.

But it's not close enough as, surely, the cause of F was an event earlier than F, namely E, not an event like E* simultaneous with F. Granted, E might have acted through an intermediate cause, E₁, that is simultaneous with F, but E* is not an intermediate cause.

Moreover, if the cause of F is not E but E*, then what did E do? Let's suppose that E is present and F is going to happen. Then E is causing something. What is it causing? The presentist cannot say it's causing F. The presentist can only say it's causing F*, where F* is the state of affairs of its being the case that F will happen. So, the presentist will need to say that E* causes F and E causes F*.

But now consider this: What connection is there between these two complex states of affairs: (A) E* causes F and (B) E causes F*. They clearly are not independent. There must be some connection between them. This connection cannot be causal if presentism holds, because A is strictly earlier than B. This is puzzling. Is there maybe an explanatory relation between them? Is it, perhaps, the case that E* is causing F because E had caused F*, or maybe the other way around? Neither option seems right. But there should be some explanatory relation between them, or else both should be explained by some third thing. I can't think of what that third thing could be. So let's think whether maybe E* is causing F because E had caused F*, at the time of F. Observe that unless F is an intermediate cause between E and F*, which seems absurd, F had better be prior in the order of explanation to the state of affairs of E having caused F* for the reason that F is prior in the order of explanation to the state of affairs of F* having occurred. So it does not seem possible to make E* be causing F because E had caused F*, because F is prior to F*. Could we say that E was causing F* because E* is causing F? But now the past occurrence of a causal relation ends up happening because of a present occurrence of a causal relation. That does not seem right, either.

In any case, where on eternalist views we had one instance of causation, E causing F, the presentist has cut it up into two, an earlier and a later instance of causation. It is now (let's say) true that E* is causing F, but it was earlier true that E was causing F*. But this is weird: we have two instances of causation in place of one. And instead of the relation relating E with F as it should, what we have is one past causal relation from E to F* and a present one from E* to F.

Truth as a predicate on the prosentential approach

According to the prosentential theory of truth, sentences that make use of "is true" as a predicate are to be paraphrased into sentences where "is true" occurs only in the form "that is true" or "it is true", which acts prosententially—i.e., related to a sentence in the way a pronoun is to a noun. Grover, Camp and Belnap in their account of the prosentential theory claim that the theory makes good on the idea that truth is not a predicate.

However, one can use a prosententially acceptable sentence to define what seems to be a perfectly fine truth predicate of sentences (either tokens or types, as one prefers—with Hartry Field, I prefer tokens) which I shall call "truth*":

s is true* if and only if there is a proposition such that s expresses (or, says) that it is true and it is true.

Here "it is true" is to be understood prosententially.

Getting rid of "is true"

It is always tempting somehow to get rid of the predicate "is true" in order to escape the Liar Paradox on the cheap. I think there is no cheap escape (though I do think there is an escape). To that end, it's worth thinking through ranges of predicates other than "is true" which generate liar-type paradoxes. Some of these are expressly semantic, like "refers to x": We can redefine "is true" in terms of "refers" for instance as follows: "'s' is true iff 'the number 1 if s and the number 0 otherwise' refers to the number 1". Others are more everyday. For instance, consider the predicate "is reliable" as applied to a person. In the sense I am interested, "x is reliable" if and only if most of x's statements are true. But of course, "is reliable" is all we need for a liar paradox. We just imagine a possible world where most of George's statements are logically equivalent to "I am not reliable". Or, for a quite different case (not mine), take "is satisfied" as a predicate of desires, and imagine someone who desires not to have any satisfied desires: is that desire satisfied or not?

It is not plausible that one could not only get rid of "is true" but also of "refers to", "is reliable", "is satisfied" and the rest of the plethora of concepts each of which seems sufficient to generate a liar-type paradox.

Minimalism about truth

Consider the claim:

1. "Snow is white" is true because snow is white.

Say that a minimalist about truth is someone who thinks that statements like (1) fully explain all that calls out for explanation in the concept of truth.

Such a minimalist is wrong. It is clear that there is something fishy about (1) as a full explanation because the explanandum is about an object—the sentence "Snow is white"—which the explanans does not mention. In this regard, (1) is like the puzzling:

2. Fred smoked a cigarette because Maxine called up Patrick.

The explanandum is about Fred but the explanans has nothing about Fred. Claim (2) might be true—but if so, it is incomplete. It might be partially completed by adding that Patrick is a notorious gossip and Fred and Maxine had a deal that Fred would quit smoking while Maxine would quit gossiping.

Sometimes we do not notice that an explanation is incomplete because the additional facts are obvious: "Fred was jealous because Maxine kissed Patrick" needs nothing added if we know that Fred and Maxine are married and we know some facts of human psychology. But even so, the explanation is incomplete, enthymematic. And a sure sign of an anthymematic explanation is that the explanans does not mention the subject of the explanandum.

How to complete (1)? Maybe:

3. "Snow is white" is true because "Snow is white" says that snow is white, and snow is white.

Of course, normally we all know that "Snow is white" says that snow is white and so the first conjunct of the explanans is left off. Bu tit is needed, as is evident in cases where we do not understand the quoted phrase right away:

4. "Snieg jest bialy" is true because snow is white.

And once we relize that (1) is enthymematic for something like (3), we can see why (1) doesn't solve all the puzzles in the vicinity of "truth". For the obvious question after seeing (3) is: "Why does 'Snow is white' say that snow is white?" And here a correspondence theory may reappear as a side-effect of solving this problem of meaning (this observation is not original—I recall it in, I think, Ayer and in Davidson).

Tarski's (T) schema

Tarski's (T) schema says that:

1. X is true if, and only if, p

in every case in which X is a "name" for the sentence p. Elsewhere, Tarski makes it clear that every definition of p counts as a "name" for p. So, here's something fun. While, necessarily, every instance of the (T) schema is true, it is not the case that every instance of the (T) schema is necessarily true. For instance, if the first sentence that Janet uttered today is "Snow is white", then the following is an instance of the (T) schema:

2. The first sentence that Janet uttered today is true if, and only if, snow is white.

Indeed, (2) is true. But (2) is, plainly, not a necessary truth, since Janet's first sentence today could have been different.

Were the (T) schema Tarski's definition of truth, this could be the start of a criticism. For we do expect instances of definitional sentences to be necessary truth. E.g.,

3. Patrick's best friend is a bachelor if, and only if, Patrick's best friend is a never-married, marriageable man

is an instance of the definition of a bachelor, and it is a necessary truth. The issue here is that standard definitions are of the form:

4. F(X) if, and only if, G(X)

where X occurs in the definiendum and the definiens. Not so in the (T) schema. But, again, that seems to be alright because the (T) schema, while a material condition that any definition of truth must satisfy, is not taken by Tarski to be a definition of truth.

Omniscience

There are two hard problems of omniscience. One is metaphysical—how can a God who has aseity and is simple know contingent facts. The other is logical—how can one formulate omniscience in a way that avoids the paradoxes of truth. The paradoxes of truth are going to show up as soon as we have quantification over propositions and a predicate coextensive with truth. Every orthodox account of omniscience gives a predicate coextensive with truth: "is believed by God". The standard formulation of omniscience is that God knows all and only tue propositions. That gives us quantification over propositions, and so it seems we have everything needed for paradox.

One might say that this is a paradox everyone faces. Well, but not quite—only those who have a truth predicate face it.

Here is a solution. Don't quantify over propositions. Instead, say that just as logic allows one to infer "——" from "—— and ****", so too logic allows one to infer "——" from "x believes —— and omniscient(x)" and "x knows ——" from "——" and "omniscient(x)". This rule of inference no more gives rise to paradox than the rules of inference of first order logic.

Of course this does nothing to help with the metaphysical problem (for that, see my piece in the first Oxford Studies in Philosophy of Religion).

Understanding a sentence

If you don't like centered propositions, drop the "centered" from the following. I am using the phrase "knowledgeably understand" to boost understanding to a level that requires the kinds of justification that knowledge does. Perhaps understanding already has that built-in, in which case "knowledgeably" can be dropped.

Now, consider the following inconsistent triad, each proposition of which is defensible:

1. To knowledgeably understand a sentence it suffices to know the language and to apply appropriate symbol recognition, symbol manipulation and logical skills to that sentence.
2. Necessarily, someone who knowledgeably understands a sentence knows what (centered) proposition that sentence expresses or else knows that the sentence does not express a (centered) proposition.
3. There are sentences s such that one cannot know whether s expresses a proposition simply by knowing the language, and by applying appropriate symbol recognition, symbol manipulation and logical skills to that sentence.

I think (1) and (2) are quite intuitively plausible, but (3) needs an argument. Here is a standard argument (Kripke came up with cases like this). I erase my board and write on it "No sentence on Jon's board expresses a true (centered) proposition." Let s be this sentence. Then I cannot know whether s express a (centered) proposition unless I know what Jon has on his board. For Jon, being a philosopher, might easily have written on his board "Every sentence on Alex's board expresses a true (centered) proposition." But if that is what is on his board, then the sentence on my board cannot express a (centered) proposition. (If it expresses a true (centered) proposition p, then plainly p is true if and only if p is not true.) But I cannot know what Jon has on his board simply by knowing the language and applying symbolic and logical skills to the sentence on my board. Hence, (3) is true.

Given the above really good argument for (3), we need to reject (1) or (2). I am inclined to reject (1), as (2) seems very, very plausible. Or, perhaps better yet, we might reject the notion of sentences that the paradox is predicated on.

Actually, everybody should reject (1) in the case of natural languages, simply because of the problems of homonymy, and that's not very interesting. But the argument against (1) (assuming the notion of sentences that the paradox is based on) continues to work even if we distinguish homonyms with subscripts, and similarly deal with other "standard" contextual ambiguities.

Semantics

I am reading Tarski's "The Semantic Conception of Truth" and came across this paragraph which I just had to blog:

It is perhaps worth while saying that semantics as it is conceived in this paper (and in former papers of the author) is a sober and modest discipline which has no pretensions of being a universal patent-medicine for all the ills and diseases of mankind, whether imaginary or real. You will not find in semantics any remedy for decayed teeth or illusions of grandeur or class conflicts. Nor is semantics a device for establishing that everyone except the speaker and his friends is speaking nonsense.

(Sorry if there are typos—I am writing this with vim over ssh from my Treo.)

The truth of propositions

Suppose propositions exist, and truth is a property that some but not other propositions have. Could truth, then, be an intrinsic property of a true proposition? Observe that the proposition that George is round has truth if and only if George has roundness. Assuming (contrary to fact, but in order to simplify the example) that roundness is an intrinsic property, we now have a strange necessary coincidence between two different entities possessing intrinsic properties: necessarily, that George is round possesses truth if and only if George possesses roundness.

But the fact that necessarily x has an intrinsic property A if and only if a distinct entity y has an intrinsic property B surely calls out for, and had better have, an explanation. I am inclined to think that such correlations between the intrinsic properties of different individuals can only have a causal explanation. If so, then I think we have three options:

1. There is some third fact or entity z that both causes George to have roundness and the proposition that George is round to have truth.
2. George's having roundness causes the proposition that George is round to have truth.
3. That-George-is-round's having truth causes George to be round.

Somehow, none of these seem all that plausible to me, but if I were to choose between them and I were an atheist, I would opt for (2). If I thought that propositions were ideas in the mind of God, and I were choosing between these options, I might choose (3), and I might even further identify a proposition's having truth with that proposition's being known—that would yield Aquinas' claim that God's knowledge causes that which God knows.

Junk in the Platonic heaven

Typical Platonists admit all kinds of "useful" entities in the Platonic heaven such as sets, classes, properties and propositions. These are "useful" in that they relate to our lives as knowers and that theories positing them exhibit certain theoretical virtues. I wonder: Are there any useless entities in the Platonic heaven—entities that are not in any interesting way related to our minds and to the spatiotemporal cosmos? Obviously, barring something like divine revelation, we wouldn't have any reason to believe in any particular useless kind of Platonic entity. Still, one might think it would be really unlikely that the Platonic realm contain only entities of kinds that are useful. So, probably, there are useless Platonic entities, if Platonism is true.

A Kierkegaardian argument for miracles

Here is a valid, and perhaps even sound, argument. Kierkegaard would worry that 4 begs the question.

1. (Premise) If something is naturally impossible and it occurs, it occurs by miracle.
2. (Premise) If a proposition is incredible, it is naturally impossible to believe it.
3. (Premise) Christian doctrine is incredible.
4. (Premise) Someone believes Christian doctrine.
5. Therefore, there is at least one miracle.

Desires

On a standard view of desire, necessarily, one has a desire for A if and only if one has a tendency to pursue A. But even if this is true, it does not answer the question of what a desire is. One could identify the desire for A with the tendency to pursue A. But that would be mistaken, because the desire explains the tendency, while the tendency does not explain itself.

Perhaps, then, the desire is not the tendency, but the desire is defined as the immediate cause of the tendency, whatever that immediate cause might be. This suggestion is preferable to simply identifying the desire with the tendency. An interesting consequence of the standard view of desire conjoined with this identification is that necessarily every tendency to pursue A has a cause. This need not, however, be taken to commit us to a general Principle of Sufficient Reason (PSR). For it might well be that the notion of a behavioral tendency entails the existence of a cause, and indeed of a unitary one. If George on one occasion pursued A for one cause, on another he pursued A for another cause, and so on, that would not add up to a desire for A, and, if this is not to be a counterexample to the standard view, it would also not add up to a tendency. A tendency requires a unitary cause.

If this is right, then the standard view very neatly fits with a definition of a desire as the immediate cause of the tendency. But if we think about it, it's easy to come up with counterexamples. What if George has a tendency to pursue A because whenever the question comes up, Dr. Black zaps his brain in such a way that George pursues A. There is thus a pattern of pursuit of A, and this pattern has a unitary cause, namely Dr. Black. But Dr. Black is not identical with any of George's desires. Moreover, in a case like that, I think, we would not want to say that George has a desire for A.

Alright, so we need to modify the standard view, or at least to clarify the notion of a "tendency". Only internally-rooted tendencies count. But that's not good enough. For suppose that George's liver has a weird mutation such that it grew the neuro-zapper that Dr. Black was using, and the liver regularly zaps George's brain so that George ends up pursuing A. Now the tendency to pursue A is internally rooted in George. But it's not internally rooted in the right place. It's supposed to be internally rooted in George's mind. But that, too, wouldn't do. Suppose for simplicity (and contrary to fact—but I think the argument is very suggestive even without the false assumption) that George's mind is identical to his brain, and that his olfactory center grew the same neuro-zapper. Now the tendency is internally rooted in George's mind, indeed, but in the wrong part of the mind. Moreover, easy thought experiments show that not only must the tendency be rooted in the right place in George's mind to qualify as entailing the presence of a desire, but it must be rooted in the right way. In what place and in what way? Surely only one answer is possible: the tendency must rooted in one of George's desires, and the rooting must be of the right sort for desire-based motivation. The "right sort" condition will ensure that the tendency must be rooted in George's desire for A.

So, our standard account now says that one has a desire for A if and only if one has a tendency to pursue A that is caused in the right way by a desire for A. This isn't very helpful as an account of what it is to have a desire, is it? But it's not completely vacuous. The definition entails that a desire for A causes a tendency to pursue A.

Was I once a fetus?

Let x be the fetus in my past that grew into me. Here is a valid Aristotelian argument (though Aristotle himself would probably deny (4)).

1. (Premise) The identity of a bodily organ depends on the identity of the individual whose organ it is, so that if A is c's unshared heart (sharing occurs in the case of Siamese twins), and B is d's unshared heart, and c and d are distinct individuals, then A and B are distinct organs.
2. (Premise) x has exactly one heart, h_x, and it is unshared.
3. (Premise) I have exactly one heart, h_I, and it is unshared.
4. (Premise) h_x=h_I.
5. Therefore, I am x. (By 1-4)

The controversial premises are (1) and (4).