Life is short

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

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

Caves and holes

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

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

Ponzi schemes

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

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

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

Pascal's wager and decision theory

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

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

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

Dark nebulae

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

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

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

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

Causation and presentism

Suppose:

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

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

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

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

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

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

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

Truth as a predicate on the prosentential approach

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

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

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

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

Getting rid of "is true"

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

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

Minimalism about truth

Consider the claim:

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

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

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

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

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

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

How to complete (1)? Maybe:

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

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

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

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

Tarski's (T) schema

Tarski's (T) schema says that:

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

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

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

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

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

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

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

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

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

Omniscience

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

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

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

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

Understanding a sentence

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

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

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

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

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

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

Semantics

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

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

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

The truth of propositions

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

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

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

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

Junk in the Platonic heaven

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