Counterfactuals

Let me, as often, think out loud.

Counterfactuals seem to be an extremely powerful philosophical tool. Except that they never seem to work. Think of the employment of counterfactuals in connection with epistemology (e.g., one only knows p if one would not have believed p had p not been true), the theory of truth (Russell: p is true iff to believe p would be to believe truly), causation (Lewis), free will (e.g., x does A freely only if x would not have done A had x not wanted to do A), intention (e.g., x does A in order to achieve F only if x would not have done A had she not believed that it would achieve F), etc. It seems largely, and perhaps entirely, a history of failure. Yet, at the same time, counterfactual claims continue to seem tantalizingly close to capturing something important about many phenomena. Counterfactual characterizations are roughly right, but then fall apart when the details are to be worked out, or odd cases are considered (sometimes, the initial counterexamples are odd indeed, but with more work one can see that these counterexamples are not quite as out of the way as one might have thought). Counterfactual accounts are roughly right, but they cannot be modified to be exactly right. These are surprising facts, and it would be nice if a theory of counterfactuals explained them.

A standard story is that in a lot of the cases where counterfactual relations aren't doing their job, it is because one also needs an "in the right way" constraint on the counterfactual. Now, taking the words "in the right way" literally suggests that a normative, proper-function based, constraint is needed.

Could there, perhaps, be something like a counterfactual but which has that constraint built-in? But the force of that constraint is different in different employments of counterfactuals.

Truth, logic and explanation

Consider the following two very plausible explanatory intuitions:

1. Roses are flowers or violets are yellow because roses are flowers.
2. "Roses are flowers or violets are yellow" is true because "Roses are flowers" is true or "Violets are yellow" is true.

Now, the intuition in (1), when generalized to the general principle that if p and not q, then p or q because p, yields:

3. "Roses are flowers" is true or "Violets are yellow" is true because "Roses are flowers" is true.

Explanation may or may not be transitive in general, but it seems correct in the case at hand to move from (2) and (3) to:

4. "Roses are flowers or violets are yellow" is true because "Roses are flowers" is true.

Observe that (1) and (4) are parallel. Now suppose we agree with the deflationist about truth that:

5. "Roses are flowers or violets are yellow" is true because roses are flowers or violets are yellow.

We now have two paths to explaining why "Roses are flowers or violets are yellow" is true. One explanation is (4) and the other is (5). Unless one of these two explanatory paths subsumes the other, it seems that we have a case of explanatory overdetermination. But neither path subsumes the other. First, the explanans in (4) does not explain the explanans in (5), since that "Roses are flowers" is true does not explain why it is that roses are flowers or violets are yellow, as the former is a fact about a sentence (we can also make the argument go with utterances, statements or propositions) while the latter is a fact about flowers. Second, the explanans in (5) does not explain the explanans in (4)—for that "Roses are flowers" is true may be explained by roses being flowers, but is surely not explained by roses being flowers or violets being yellow.

Thus, the deflationist who accepts (1) and (2) is pressed to accept that (4) and (5) are an overdetermining pair of explanations. But that is unappealing. Probably the deflationist will have to deny the Tarskian intuition in (2). I don't know how great the cost of that is.

So what should we say if we accept (1)-(4), and we are inflationists? We still have a bit of a puzzle, even if we deny (5). The problem is that the explanations in (1) and (4) are exactly parallel. But, we ask, what explains this parallelism? It seems too much to separately explain the truth of the disjunction by the the truth of the true disjunct, and to explain the disjunction by the true disjunct. There should be a way of unifying this. One way would be:

6. (a) Roses are flowers or violets are yellow because "Roses are flowers or violets are yellow" is true; (b) "Roses are flowers or violets are yellow" is true because "Roses are flowers" is true; and, finally, (c) "Roses are flowers" is true because roses are flowers.

(Or we can give a propositional variant. That would probably be better, but I'll stick to the linguistic here so I don't have to keep on saying "the proposition that...". And maybe to explain "Roses are flowers" being true we need a few more steps on the linguistic side—but maybe not, since it may be a logically simple claim about the natural kinds rose and flower rather than a quantified claim.) On this perhaps weird approach, the explanation in Tarski's Schema (T) sometimes goes in one direction and sometimes in the other. I don't fully like this weird approach, though, because step (b) is troubling. The obvious way to justify the explanation in step (b) seems to be: (bi) "Roses are flowers or violets are yellow" is true because "Roses are flowers" is true or "Violets are yellow" is true; and (bii) "Roses are flowers" is true or "Violets are yellow" is true because "Roses are flowers" is true. However, if (bii) has no further intermediate steps, then, by the same token, (1) shouldn't have any further intermediate steps, and (6) is wrongheaded. And if (bii) has further intermediate steps, then these steps will need to be expanded in the fashion of (6), which will result in circularity.

Maybe, though, we can get away with just making (6b) be immediate in the case where "Roses are flowers" is true. In that case, what makes certain complex apparently worldly facts true is stuff on the linguistic side, finally combined with something more basic on the worldly side. I suppose this is basically what Tarski was up to. A lesson of this approach would be that logically complex facts, like the fact that roses are flowers or violets are yellow, are very different from simpler ones.

Of course, if it can be shown that "explains" is used equivocally in (1)-(4), or that the instances of transitivity that I employed are unjustified, all of this goes out the window. But I do think that this may give some reason to be an inflationist about truth.

1 John, and love of non-Christian neighbor

It is clear from the Parable of the Good Samaritan that Christian love for neighbor must extend beyond the confines of the Church. The First Letter of John says many beautiful things about how our love for one another is necessarily intertwined with our love for God: we love one another in the relevant way if and only if we love God, and this love is the center of the Christian life. But a puzzling feature of the Letter is that the love for one another appears specifically to be a love only within the Christian community: it is love for another Christian.

One way of reading 1 John together with the Parable is hierarchical: yes, we have a duty to love all our neighbors, including non-Christians. But the love for fellow Christians is the apex of this love, and it is only in the love for fellow Christians that the love for God can fully spread its wings, which is why the author of the Letter focuses on it. Furthermore, one might add something about the specific purposes of the Letter tied to disturbances within the community it was addressed to.

That all may be a part of the truth. But I want to propose something that goes a little further. We love our non-Christian neighbor as someone with a potentiality for being a fellow Christian. And not just a mere potentiality, such as my potentiality, which I expect will never be actualized, for tap-dancing outside of St. Stephen's Basilica in Budapest (certainly, I have the capabilities for learning some rudimentary tap-dancing and traveling there—but I don't expect to actually do it), and it is no great loss that it will not be actualized. Rather, it is more like the fetus's potentiality for becoming an adult, in the sense that it is a potentiality that is grave loss to the individual when it is not actualized, a potentiality that is not merely a matter of possibility, but a matter of an impulsion to the end. But there is a difference between the non-Christian's potentiality for becoming a member of the body of Christ, and the fetus's potentiality for becoming an adult. The fetus's potentiality for becoming an adult is a natural power in the fetus that simply needs the right environment. The non-Christian needs grace, which God offers to all.

That we love the non-Christian as a potential Christian does not mean that all our focus is on making the non-Christian into a Christian. After all, the parent's love for the child should typically be focused on the child as a potential adult. At the same time, much of the expression of that love is not focused on making the child into an adult. We feed, clothe and play with the child. Obviously, if we fail to feed the child, she may well die and fail to develop into an adult. But that is typically not what we are thinking: we are fulfilling the child's imminent need. And playing helps form the child, too, but again that is often not what one is thinking—instead, one may well simply be enjoying the game. Nonetheless, the expression of the love as a whole is shaped by the fact that the love is a love of the child as a potential adult.

Nonetheless, that we love the non-Christian as a potential Christian does mean that evangelization is a central aspect of our love for neighbor. This evangelization may or may not be in words, of course, and need not be conscious. The evangelization is an expression of the desire for union with the neighbor: a union as fellow members of Christ's body.

If this is right, then 1 John is describing the normative case where the potentiality for being a fellow member of the body of Christ has been fulfilled, just as when ethicists discuss relationships with others, they often talk of the case of adults, which is in some way the normative case. But the love for the child is in continuity with and directed towards becoming the love for the adult, and the love for a non-Christian is in continuity with and directed towards becoming the love for a Christian.

Is the comparison of the non-Christian to a child offensive? Well, it does fail to capture one aspect of the situation: the Christian's own falling short of being what she is called to. Perhaps a better way, in many cases, is to think of the case of a somewhat older sibling, or maybe of fifteen-year old parents, who in many ways are still children themselves.

Sacramental theology

There are two approaches to Christianity (and perhaps to other religions). One is with a "metaphysicalizing impulse (MI)", and the other is a "pragmaticalizing impulse (PI)". Those with a PI are likely to take the central features of, say, baptism, matrimony and the Lord's Supper to be, broadly, pragmatic features: these liturgical actions are performatives in Austin's sense, which have normative and psychological effects. Those with an MI are likely to take the central features of these kinds of liturgical actions to be a metaphysical effect that provides at least partial truth-grounds for the normative effect and that supernaturally causes effects in the souls of those who genuinely participate.

It often seems like the difference between Christians who have the MI and those who have the PI has a basis in temperament more than anything else. To some people, metaphysicalizing comes naturally, and to others, pragmaticalizing comes naturally. The metaphysicalizers may accuse the pragmaticalizers of a shallowness and maybe sometimes a subjectivism. The pragmaticalizers may accuse the metaphysicalizers of a tendency to irrelevancy and maybe sometimes of using metaphysical speculation as a way to put off the hard work of living the Christian life.

Both metaphysicalizing and pragmaticalizing needs to be a part of Christian theology. That pragmaticalizing needs to be a part of Christian theology is clear from the fact that Christianity is not gnosticism. The Christian life is not a way of life centered on learning esoteric metaphysical claims, but is centered on living out the love for God in communion with others.

However, to neglect metaphysicalizing is to neglect a significant part of the difference between Old Testament and New Testament commandments. Some of the Old Testament commandments were normatively grounded merely in God's command. There is no intrinsic reason to avoid mixing different kinds of fabric in one's garments beyond the fact that God forbade it with his authority. Some of the commandments may have had a symbolic meaning, which was mysteriously fulfilled in the New Testament, and some may not have even had that. But the New Testament largely puts away the merely arbitrary and the merely symbolic divine commands (or, perhaps more precisely, transfers much of the authority over the merely symbolic to the Christian community, which then, as a diachronic and hierarchical community, gets to decide how exactly to celebrate that which God has put in place, with much more freedom—notice, for instance, how nobody thinks that in New Testament times God has very specific prescriptions for clerical dress, that being left to Church authority), focusing on that which is of intrinsic significance. If divinely prescribed central liturgical actions, such as those of baptism, matrimony and the Lord's Supper remain, these cannot simply be arbitrary and/or symbolic commands of the sort that were given in the Old Testament. The need for obedience here must be somehow grounded in reality. And the metaphysicalizer has an explanation here. Baptism changes the soul of the genuine participant, incorporating her into the Body of Christ in a mysterious way that goes beyond the symbolic and even beyond the performative (it is not just a human work—if it were a performative, it would be just a human work, and that is contrary to the focus on grace). Matrimony genuinely joins two people, not merely symbolically linking them together, not just being a performative, not even simply changing God's attitude to them ("making them married in the eyes of God"), but actually changing the people in a supernatural way that is quite mysterious, and that provides them with the grace to live out the pragmatic aspects. The Lord's Supper is commanded because in it, it is the Lord who offers himself quite literally to us for us to consume his flesh, thereby receiving the grace to live more fully as members of Christ's body.

Without metaphysicalizing, the distinction between the Old Testament and the New is obscured. The metaphysics provides a grounding for the normative effects. But without practicalizing, we have gnosticism.

Horwich's minimalism

I am reading Horwich's little book on truth. Horwich's minimalism is generated by one axiom:

1. Only propositions are true,

and one axiom schema:

2. <p> is true if and only if p.

The axioms, then, are (1) and all instances of (2). In the schema (2), any proposition can be inserted, except for ones that generate liar paradoxes.

Two objections come to mind (the first may be answered later on in the book—I haven't finished the book). First, what if some other worlds contain propositions that our world does not contain? We should be able to say that in such a world it, say, still the case that every proposition which is true is true, and so on. But minimalism as it stands does not seem to let us say that. One could make the axioms vary between worlds, but then it would be unclear that we are talking about the same thing, truth, in all of them.

The second is it's going to be pretty tricky to restrict the range of propositions p it's permissible to substitute in (2) in order to avoid liar paradoxes. The big problem will be with contingent liar paradoxes, like the proposition p that Plantinga's favorite proposition is not true, which proposition is unproblematic, unless it contingently happens to be Plantinga's favorite. It seems that if one is going to handle liar paradoxes by restricting the range of instance of instances of (2), one will have a different axiom schema in different worlds.

Of course, contingent liars will be a problem for everybody, and it may be that the minimalist may be able to adopt a different solution. I rather like approaches on which paradoxical "sentences" (contrary to the mainstream, I don't think they actually are sentences) don't express propositions. Let's see if that works for the minimalist. I don't know what actually is Plantinga's favorite proposition. Maybe it's the proposition that if Christianity is true, then Christian belief is justified. Now, let p be the proposition that Plantinga's favorite proposition is not true. Then, p is not actually Plantinga's favorite proposition. Moreover, p cannot be Plantinga's favorite proposition. For if p were Plantinga's favorite proposition, it would be true if and only if not true. But that is a very strange result. After all, couldn't p be inscribed somewhere, and couldn't Plantinga somehow form an odd liking for "the proposition expressed by the words inscribed there", even without reading these words?

One approach one could take here is this: Deny that p exists in those worlds in which it is Plantinga's favorite. But that is not available to the minimalist, because the minimalist appears to be committed to propositions being necessary beings. So not every solution is available to the minimalist. But I am not sure this is the best solution anyway. It might be better simply to deny the possibility of p becoming Plantinga's favorite proposition. This would have the consequence that in any world such that on page 17 of some book, on line three, it is written "Plantinga's favorite proposition is false", then that "sentence" fails to express a proposition in any world in which Plantinga's favorite proposition is "the proposition written on page 17, on line three, of that book" (note: a favorite proposition can be favorite under a description; it need not be grasped to be favorite). And this solution is available to the minimalist.

I rather like the following view, by the way: Minimalism is basically true as a theory of the truth of propositions; but an inflationary view of the meaning, and hence truth, of sentences is also correct.

Truthmakers

It is fairly standard to say that the truthmaker of a proposition p is what makes p be true. But suppose we accept a non-deflationary theory of truth on which the claim that p is true is distinct from the claim that p, and is the attribution of the property of truth to p. Now let p be the proposition that there are horses. Then, any horse (or maybe the sum of them all) is a truthmaker for p, or so it is pretty standard to think. But while a horse makes there be horses, a horse is not enough to make it be true that there are horses, since the latter claim involves something other than a horse, namely the proposition p. So, we need to distinguish between making there be horses and making it true that there are horses. A horse suffices for the former task. But for the latter task, we need a horse, p, and whatever relations and properties are involved in the attribution of truth to p (e.g., an instance of a correspondence relation). (I am grateful to Dan Johnson for helping me get clear on what this latter task involves.)

We now have a linguistic question. Is the "truthmaker" of p just a horse, or a horse, p and whatever else is needed? Since "truthmaker" is entirely a stipulative term of art, nothing deeply significant rides on this question, but the question does have two aspects: the sociological question of just how the word "truthmaker" has been used by philosophers, and the question of which way of using the word gets at a more fundamental concept. Say that a "truthmaker(1)" is the concept that goes with the answer "a horse" and a "truthmaker(2)" is the concept that goes with the answer that also includes p. Then there is a natural way of defining truthmakers(2) in terms of truthmakers(1). The truthmaker(2) of p is identical to the truthmaker(1) of the proposition that p is true. One might try to define a truthmaker(1) in terms of taking a truthmaker(2) and subtracting the proposition and the relation, but that definition will be messy and difficult to give. So, it seems that the truthmaker(1) is the more fundamental of the two concepts. Moreover, sociologically, I think "truthmaker(1)" is the right reading of how "truthmaker" has been used, because as a matter of fact most users of truthmakers don't include the proposition and the correspondence relation in the truthmaker.

But now we see that unless we have a deflationary theory of truth, the term "truthmaker", understood as truthmaker(1), is a bit of a misnomer. For the truthmaker of p isn't what makes p be true. It is only a part of what makes p be true: makes p be true is not just the truthmaker(1) but also p and how its related to the truthmaker(1).

It may, of course, turn out that deflationary theories of truth are correct. But unless deflationary theories are established to be true, as much of our theorizing as possible should be compatible with non-deflationary theories as well, and so we should be sensitive to the difference between the condition that p and the condition that p is true.

Two other areas where the distinction could matter are these: (1) Is it a part of our concept of knowledge that if x knows p, then p is true, or should we rather say that if x knows p, then p? (2) Should we require it to be a part of omniscience that for all p, God knows p if p is true, or that for all p, God knows p iff p? With a bivalent logic and an acceptance of Schema (T) as a necessary truth, the answers are going to be necessarily extensionally equivalent. But conceptually there may be a difference, and how we answer (1) and (2) may affect some of our intuitions.

Such sensitivity will also be important when we consider non-bivalent logic, even if we only consider them to dismiss them. For instance, suppose we deny that contingent propositions about the future are true or false, but accept excluded middle. Then if we understand omniscience as implying that God knows p if p is true, God can be omniscient without knowing contingent propositions about the future. But if we understand omniscience as implying that God knows p if p, then omniscience requires God to know some contingent propositions about the future, even if none such are true.

Introspection of judging

Consider the concept of a judging. A judging is a believing operating occurrently and consciously (this is stipulative). Sometimes, a judging comes at the beginning of believing: after weighing the evidence, I judge that p, and my judging that p is the beginning of my believing that p, a believing that soon slides from occurrence into dispositionality. Sometimes, perhaps, I have a belief dispositionally which I never acquired by means of a judging, but which belief comes to the mental foreground, and becomes a judging.

Let us suppose that for every believing there is a belief, namely a proposition that is believed. Then, since a judging is a kind of believing, every judging is associated with a proposition that is adjudged, a proposition that one might call the judgment. (Actually, "belief" and "judgment" are ambiguous in English between the proposition and the mental act; so I am here stipulating that I will use an "-ing" form for the mental act—e.g., "believing" or "making a judgment"—and "belief" and "judgment" for the propositional object of the mental act.) I shall also assume that a proposition, perhaps unlike a declarative sentence, is always either true or false.

Here is an anti-Cartesian thesis that I am going to offer an argument for, and then discuss whether one can get out of the argument:

1. It need not be possible to introspect whether a mental act is a judgment, and whether a mental act is a judgment is not an internal property of the mental act.

The argument is fairly simple. It is possible for me to judge that

2. Fred right now is not making a judgment that is true.

In judging (2), I might even be judging correctly—for instance, if Fred is asleep, or if Fred is judging that I do not exist. By exactly the same token, it is possible for Fred to judge that

3. Alex right now is making a judgment that is true.

Now imagine three possible worlds w₁, w₂ and w₃. These worlds are exact duplicates up to but not including t₀. In particular, prior to t₀, the distinctions between the three worlds are is not introspectible either to me or to Fred. Assume also that neither of us is within sensory range of the other at t₀. Now suppose that in w₁ at t₀, I make the judgment (2), and I am right, because Fred has just fallen asleep at t₀. In w₂ at t₀, I have just fallen asleep, and Fred makes the judgment (3), which judgment is thus wrong. Now, in w₃ at t₀, I have exactly the internal properties that I do in w₁, while Fred has exactly the internal properties that he does in w₂. But now observe that there is a very good argument that it is not the case that both I and Fred make a judgment at t₀ in w₃. For if I make a judgment at t₀ in w₃, it is surely the judgment (2). And if Fred makes a judgment at t₀ in w₃, it is surely the judgment (3). Let p₁ and p₂ be the respective judgments—the propositions adjudged. Then, plainly, p₁ is true if and only if p₂ is false, and p₂ is true if and only if p₁ is true. But that is a contradiction.

But introspectively, surely, w₃ at t₀ is just like w₁ for me, and just like w₂ for Fred. In w₁, I do make a judgment, and in w₂, Fred makes a judgment. Therefore, if I fail to make a judgment at t₀ in w₃, then whether I make a judgment is not introspectible, nor is it a matter of my internal properties, as I have the same internal properties at t₀ in w₁ and w₃, and hence (1) is true. Likewise, if Fred fails to make a judgment at t₀ in w₃, (1) is true. Since at least one of us fails to make a judgment at t₀ in w₃, it follows that (1) is true.

Can a Cartesian get out of the argument? I think the following are the main controversial premises (all of them purporting to be a necessary truth): (a) all judgments are propositional, (b) all propositions are true or false, (c) introspection depends on one's internal states, (d) one's internal states do not depend on what is simultaneously happening far away, and (e) if I or Fred make a judgment in w₃ at t₀, the judgment is (2) or (3), respectively.

If we're not Cartesians, perhaps we will happily embrace (1). But I think (1) has an unfortunate result, namely that it opens up the possibility of a sceptical hypothesis far more radical than any Descartes considers: the hypothesis that perhaps I am not actually making any judgments, and that this is true all the way down (I do not actually judge myself to be thinking, nor do I actually judge myself to be judging to be thinking, etc.)

The easiest way out for the Cartesian might be to deny (a). But then the Cartesian still has the unfortunate result that one cannot introspect whether there is a proposition that one is judging. That will, probably, be rather uncomfortable for the Cartesian, and the resulting sceptical hypothesis will still be nasty.

I myself am attracted to really crazy solutions, and in particular I think that each of (c), (d) and (e) is such that one can non-absurdly deny it.

As for (c), it might be trivially true. If it's trivially true, then (1) is less interesting. What is interesting is not whether we can always know by "introspection" whether we are judging, but whether we can always tell directly whether we are judging. The view under consideration would be one on which one has a non-natural way of recognizing what is going on far away, but perhaps one is unable to express it. This is weird, but not absurd.

The radical externalist will deny (d). The theist who believes in divine simplicity will have reason to deny (d) in the case of God. And one might have a weird non-naturalist view on which (d) is denied in our case. Again, not absurd.

As for (e), I think its denial is perhaps the most interesting option for the Cartesian. Spinoza thought all our judgments were true. A consequence of his view was that sometimes we can be unwittingly behaving as if we were judging that p, while in fact we are not judging that q. We behave as if we believed the stick in the water is broken. But in fact, what we are judging, according to Spinoza, is that our bodies are broken-stickly affected. It is only in the case, Spinoza insists, where we have conclusive and infallible evidence of the stick's being broken that we are judging that the stick is broken. This is weird indeed. But it may well indeed be where certain Cartesian thoughts taken to their natural conclusion lead. I do not want to go all the way with Spinoza to say that all our judgments are true, though I think his view can be defended more effectively than one might at first suppose. Rather, I want to focus on Spinoza's insight that the content of one's judgments may be belied by the words with which one expresses them, even in the case of someone who has mastered the language.

The debate on truth

As my previous posts indicate, I've been thinking a lot about truth. Let me make a big picture comment. I find it striking just how much the 20th century debate is driven by naturalism, even physicalism. A notable episode in the history, for instance, is Putnam's departure from metaphysical realism on the grounds that if metaphysical realism is accepted, it is going to be a scientific realism, and hence will lead to a physicalism incompatible with the language-world connections that metaphysical realism needs, as well as with ethics, so that we should reject metaphysical realism. It is widely accepted that if there is going to be a genuine language-world or mind-world truth connection of the sort that non-minimal correspondence theories claim, it will be causal and hence natural.

This makes certain portions of the debate not very interesting to me. It's obvious to me that physicalistic causal theories of reference have no hope of working, because we will all over the place need normative concepts (standard conditions, normal observers, typical cases, etc.), and attempts to spell these out in non-normative ways (evolutionary or statistical) only provide opportunities for the ever fun parlor game (a game for playing which can get tenure, which fact I am grateful for) of "Pin the Counterexample on the Theory".

At the same time, I think one can stand back from the truth debate as a whole, and say that there is something we can learn from the debate: it is hard to be a realist of a non-minimal sort (i.e., one with a positive theory of truth that goes beyond Schema (T)) while yet being a physicalist. There is an intellectual strain.

Nonetheless, I do not think the debate is worthless for those of us who are not naturalists. For some of the arguments in the debate probably work just fine even if one does not assume naturalism. Non-naturalism isn't itself a theory of truth! The task of finding a theory of truth is a really hard one for the non-naturalist, too. However, the non-naturalist labors under the advantage that some of the difficulties in the literature in coming up with a theory of truth are artifacts of the assumed naturalism.

It is worth noting that the traditional theist has a tool available for the theory of truth, a tool that should help progress to be made, namely a commitment to the existence of an extensionally correct and logically non-trivial characterization of truth:

1. A sentence is true if and only if God believes what it says.

I do not propose (1) as a definition of truth. Nor is it a reduction of "true" to a non-semantic concept, since it presupposes the semantically loaded relation of x's believing what sentence s says. Nonetheless, it is just as much a "definition" of truth as Tarski's recursive one is: it gives an extensionally correct and non-circular characterization of which sentences are true. (One might worry about circularity if God is defined as omniscient. But then let's not define God as omniscient. Just define him as the perfect being, or as pure actuality, or as the necessarily existing first cause.)

Truth is a property

We play a game. There are ten outwardly identical boxes, containing pieces of paper with ink marks on them that are unambiguous inscriptions of non-indexical sentences in the predominant local language. Five of these sentences are true, and five are false. You get to pick out a box. If it's one of the ones containing a true sentence, you get $100, and if it's one of the ones containing a false sentence, you pay $100. Then, there is a fact of the matter whether a given box is such that were you to pick it, it would be correct to declare you the winner. But it is hard to avoid the conclusion that in some sense—perhaps not the ontologically beefiest if one is a sparse property theorist—five of the boxes have the property of being winning boxes and five of them have the property of being losing boxes. Moreover, these properties are not ontologically rock bottom. They plainly depend on geometrical properties of the ink marks within the boxes, and, further, on the truth of the sentence determined by these geometrical properties. It seems that if truth is not a property, then neither is being a winning box a property. But being a winning box is a property, and so is truth.

Anything that is a basis for objective classification is a property, and truth, plainly, is a basis for objective classification of boxes into ones that under the rules are winners and ones that under the rules are not winners.

Moreover, this example shows that truth is explanatory. That a given sentence is true can explain why you owe me $100. In fact, this case shows that just about any fact is explanatory, since one can center a game on just about any fact. This won't impress non-realists about normative states of affairs.

Evolution and deflationism about truth

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.