Ethics and therapy of the soul

Plausibly, ethics ought to be in part a practical discipline, one teaching us just how to become virtuous and avoid vice. In fact, this desideratum seems particularly fitting in the case of virtue ethics. I wonder how far ethics, and in particular virtue ethics, fulfills this.

In part, it does. I have learned some useful things from the Nicomachean Ethics about friendship. But in general, I rarely learn much that is useful for combating vice and pursuing virtue from secular philosophers, either ancient or modern. On the other hand, I learn a lot from Christian writers, both ancient and modern. These point out subtle dangers in the moral and spiritual life which I would not otherwise have noticed, and give useful advice on how to avoid these dangers and progress in virtue.

In part this is because many of the Christian writers are people who can draw on a rich experience of helping others, such as penitents, parishioners or spiritual directees, grow morally. This is a rich fund of data about the moral life which the secular philosopher has typically been completely bereft of. It seems clear that the secular moral philosopher who wishes to take seriously the therapeutic aspect of philosophy must study this fund of data.

But I also wonder if there isn't another reason for why secular ethics is only helpful to a point, a point that does not do much for one. For, ultimately, among fallen humans, moral progress is the work of the Holy Spirit, and in the moral life we contend not merely against what is human but also against the subtle intellects of demons.

Observing log: December 28, 2008

I had a delightful two hour session last night just outside Waco. M31, 32, 33, 42, 43, 74, 77, 81, 82, 103, 110. NGC253, 281 (maybe, just barely), 457, 1023, 2236, 7331, 7662. Double Cluster. Rosette Nebula (maybe, just barely). Basically, I got everything on my observing list for the night. But I cheated and almost always used the paper setting circles on my Dobsonian telescope, together with AstroInfo 3.10(prerelease) for n-star alignment on my PDA (eventually, the setting circles gave 0.25 degree precision for most objects, or better).

Arithmetic

When we teach arithmetic to children, we make use of counterfactuals: "If you had two oranges, and got two more, you would have four. So, two and two makes four." Then, later on, we say "Two plus two is four." There are three steps here. First, the counterfactual. Then, an implicitly universal claim: two and two (always) makes four. Finally, a categorical mathematical claim: two plus two is four. I wonder if it might not be a mistake to focus on the final claim in philosophy of mathematics. Perhaps it is a mere abstraction from the first and second, having no additional content?

A dilemma for naturalists: Second horn

For the definitions, see yesterday's post.

Horn 2: Truth is nomically coextensive with a Natural property.

We will now generate a problem for the naturalist from the following very plausible claims:

1. If naturalism holds, any syntactic property of utterances is a Natural property.
2. If naturalism holds, then Utterance is, of nomic necessity, a Natural kind.
3. Nomically necessarily, if naturalism holds, and s is any sentence in an interpreted typed first-order language L such that (a) the types coincide with Natural kinds, (b) quantification is restricted to within a type and (c) all predication is of Natural properties, then s expresses a proposition which is either true or false.

Now, let L be a rich enough subset of technical English that satisfies the condition in (3). Let T be the Natural property that is of nomic necessity coextensive with Truth. Let s be any sentence-type of the form:

For all utterances u, if P(u), then u does not have T,

where P is an explicit statement of a finitely-expressible Natural property of an utterance sufficient to nomically entail that all and only utterances of type s satisfy P. (I'll construct P in a moment. Technically, P(u) in the above should be in right-angle brackets.)

Now, if naturalism holds, then for any finite sentence type in L, there is a nomically possible world in which naturalism also holds and where that sentence type is uttered exactly once. Let w be a world where s is uttered exactly once. If u is the utterance of s in w, then at w, u satisfies P and only utterances of s satisfy P. But then u is true if and only if u is false, since T is coextensive with truth at w. And this is absurd.

To construct P, we presumably can use Goedel numbers as in the proof of the diagonal lemma in Goedel's theorem. Or perhaps more simply, we can use what I call "modified Goedel numbers". A "numeric expression" is a literal number in a sentence, e.g., "44.58" or "-1909". The modified Goedel number of a sentence with no numeric expressions is -1. If a sentence s constains a numeric expression, we let s* be the sentence with its first numeric expression replaced by 0, and let n(s) be the numeric value of that first numeric expression of s. If the Goedel number of s* is equal to n(s), then the modified Goedel number of s is n(s). Otherwise, the modified Geodel number of s is -1. Then, it's really easy to construct P. We let N be a numeric expression of the Goedel number of "For all utterances u, if 0 equals the modified Goedel number of u, then u does not have T", and then let P(u) be "N equals the modified Goedel number of u" (where here N is expanded out—it should be in right-angle brackets, I guess). Since P(u) expresses a syntactic property of u, it follows that it expresses a Natural property of u.

The argument can be modified by replacing (1) with the weaker claim that enough basic syntactic properties for computing the modified Goedel number of a sentence are of nomic necessity coextensive with Natural properties.

Hence, absurdity also follows from the second horn of the dilemma.

Therefore, naturalism is false.

A dilemma for naturalists: First horn

This argument is a dilemma, of which I will only give the first horn today. First we need two definitions. Say that a property is "Natural" provided that it either occurs in a correct scientific account of the world or else can be constructed, in a finite number of steps, from ingredients that occur in correct scientific accounts of the world. Say that two properties A and B are "nomically coextensive" provided that in any world that has the same laws as our world, the two properties have the same extension (i.e., are had by the same particulars). Finally, "Truth" shall be the property that an utterance (a token of a sentence) has in virtue of being true.

Suppose naturalism is true. The dilemma is this: Either Truth is nomically coextensive with a Natural property or it is not.

Horn 1: Truth is not nomically coextensive with any Natural property.

There are now two kinds of problems for the naturalist. The first is the question of how we got to have the concept of Truth. A naive account of concept formation is that we observe particulars, and then from these particulars we abstract the simplest, i.e., most natural (in Lewis's sense), properties that these particulars have in common. Thus, we observe a bunch of massive objects, and the simplest property they all have in common is Mass, and so we form the concept of mass. This naive account may need to be modified in various ways. For instance, perhaps we do not need to make all the observations ourselves—our cultural or even genetic forebears might have made some of them. We might not always opt for the very simplest property that the particulars have in common, as there may be explanatory constraints on the properties beside simplicity. Thus, we might from a bunch of particulars extract not just the simplest property that they have in common, but the simplest property that they have in common which explains some common phenomenon (such as the phenomenon of being observed by us in a particular way). Furthermore, given a bunch of concepts abstracted from particulars, we can form new concepts through various combinations. Further modifications are needed to take care of determinables (like mass of x grams).

But however we modify it, I think the following will hold: If naturalism holds, we will only ever arrive at concepts of Natural properties. It is only Natural properties that enter into genuine explanations or that are causally efficacious if naturalism holds, after all. And the simplest property that a bunch of instances has in common will never be a non-Natural property, since, given naturalism, a non-Natural property is either not at all a natural property (in Lewis's sense) or is formed as an infinitely describable combination of natural properties. But if we can only ever arrive at concepts of Natural properties, and Truth is not one of those (since it's not nomically coextensive to one of those) then we do not have the concept of Truth.

The second problem is that if Truth is not nomically coextensive with a Natural property, none of our cognitive faculties could have been evolutionarily selected for truth. (Here I am sliding a bit between Truth as a property of utterances and truth as a property of belief-tokens. But just about all I say about utterances holds for belief-tokens, too.) For only Natural properties stand in causal relations if naturalism holds, and only properties that stand in causal relations occur in evolutionary explanations. But it seems to be at least partly definitory of our doxastic faculties that they are for the sake of truth. A part of what distinguishes a belief from a desire, for instance, is that a belief is something that ought only occur when it is true. If Truth is not Natural, and if naturalism holds, then our doxastic faculties do not have this normativity, and we do not have beliefs at all (including the belief in naturalism).

Moreover, if Truth is not nomically coextensive with a Natural property, not only will it fail to be the case that our doxastic faculties are selected for generating correct beliefs, but neither will there be another evolutionary explanation, say using exaptation, of any truth-tendency in our beliefs. For all scientific explanations are of the possession of Natural properties or at best (and I am sceptical of this) of the possession of properties nomically coextensive with Natural ones. But then scepticism threatens, as in Plantinga's argument.

One might hold, however, that while Truth simpliciter is not nomically coextensive with a Natural property, Truth in some limited realm, such as the truth of simple claims about mastodons and potatoes is nomically coextensive with a Natural property (the argument in the second horn of the dilemma will not contradict this). Fine. But the belief in naturalism will not fall within this limited realm. Hence the belief in naturalism still undercuts itself.

Tomorrow, we'll look at the second horn.

Death and resurrection

I think that among the conditions that an account of resurrection needs to satisfy is this one: the account has to make it possible to explain why it is that it is very bad bad to die even if one is going to be resurrected. This condition is important. Unless it is met, it is going to be unclear why it is intrinsically very bad and unloving to kill innocent people.

Some accounts of resurrection satisfy this. For instance, Peter van Inwagen once played with the following materialist story: at death, a crucial chunk of your brain is removed, and taken elsewhere, and replaced by a copy in the corpse. On this account, death is very bad, because it involves one's existing in severely truncated form. It is clearly very bad to lose all one's limbs and sensory organs, and a fortiori it is very bad to lose all of one's body except for that chunk of the brain. (This doesn't mean that the account is otherwise satisfactory. This account fails to distinguish between death and an accident where everything but that chunk of one's brain is destroyed.) Likewise, on a dualist account on which the soul survives, death reduces one to an even more severely disabled form—one loses all of one's body.

On the other hand, an account (whether materialist or not) on which at the time of death you simply skip ahead—time travel—to the time of the resurrection, so that you simply enjoy gappy existence seems to fail this criterion, since then death does not seem a bad—it's just time-travel.

Whether accounts on which you cease to exist, but then later you are reconstituted (either directly by the power of God or by some new causal power that was implanted in you at the time of your death and that works across a temporal gap) pass this criterion depends on whether they can be distinguished from the time-travel account.[note 1]

The impossibility of a naturalistic semantics

The stuff below may be old hat. But it's fun.

A naturalistic semantics would give an account of the truth of a naturalistically acceptable sentence (i.e., sequence of symbols) in scientific terms (I am not asking for the naturalistic semantics to give an account of the truth of non-naturalistic sentences, though that might be letting the naturalist off too easy). It would, thus, give a naturalistically acceptable predicate (perhaps a very logically complex one) T such that a naturalistically acceptable sentence s satisfies T if and only if s expresses a truth. Thus, for instance, T will be such that "A dog is running" satisfies T if and only if a dog is running.

A complete naturalistic semantics is impossible, and its impossibility can be shown in a way parallel to the proof of Goedel's first incompleteness theorem. (I am now thinking of ways of generalizing the incompleteness theorem to something very, very general. This is just one application.) Any syntactically permissible combination of naturalistically acceptable terms, logical constants, and quantification over naturalistically acceptable entities (and that should include sentences, since we can model these mathematically as sequences of symbols) should be a naturalistically acceptable sentence. Let P be any naturalistically acceptable predicate such that the sentence

1. Every sentence s satisfying P fails to satisfy T

is in fact the one and only sentence that satisfies P. (For instance, P might simply specify the time and place at which (1) is written.) Then (1) is a naturalistically acceptable sentence, and so (1) is true iff (1) satisfies T. It follows from the fact that (1) is the one and only sentence that satisfies P that (1) is true iff (1) is false, which is absurd.

I think a case can be made from this that there is no naturalistically acceptable property equivalent to truth. This is a good argument against naturalism.

(A challenge is to show that this does not lead to a paradox for the non-naturalist. I think there is a principled way in which one can count as nonsense sentences that directly or indirectly talk of their own truth. But (1) doesn't do that—it talks of the sentence s's satisfying T, where T is some natural predicate, not truth.)

Liar and truth-teller paradoxes

Here is a fun similarity between the liar paradox:

1. Claim (1) is false

and the truth-teller paradox:

2. Claim (2) is true.

Intuitively, (1) and (2) should be respectively equivalent to the following infinite claims:

3. false(false(false(...)))
4. true(true(true(...))),

where true(p) and false(p) are the claims that p is true and that p is false, respectively. But (4) is equivalent to (3), as we see from the fact that true(p) is equivalent to false(false(p)) so that (4) is equivalent to:

5. false(false(false(false(false(false(...))))))

which of course is just (3).

For a long time I've thought the two sentences were closely related, but it didn't occur to me that they're related this closely.

Sorry for subjecting everybody to this set of ruminations on the liar paradox. Blame Mike Almeida. His post on prosblogion on Grim set me on this line of thought. :-)

Liar regress

This has turned into a week on the liar paradox. Here is an interesting variant on the liar paradox that includes no self-reference, either direct or indirect. There is a possible world which contains infinitely many sentence tokens s₁,s₂,.... (Perhaps they exist simultaneously, or perhaps they exist successively. If successively, they may exist successively in either direction—s₁ before s₂ before s₃ ... or s₁ after s₂ after s₃ ....) Now suppose that s_n says:

s_n+1 is false.

Now, in one sense there is no paradox here. We could just say that s₁,s₃,s₅,... are true and s₂,s₄,s₆,... are false. There is no contradiction. But that is ad hoc. There is no more reason for this truth-value assignment than for the opposite truth-value assignment. Truth is about reality. But the reality of the possible world containing these tokens is equally compatible with one truth-value assignment and with the other.

If I want to make the problem more pressing, I can suppose a doubly infinite sequence of sentence tokens: ...,s₋₃,s₋₂,s₋₁,s₀,s₁,s₂,s₃,.... Suppose that the tokens do not differ in any significant way (if the Principle of the Identity of Indiscernibles holds, they must differ in some way), because each one of them says:

The next token in the sequence is false.

Then there can be no reason for distinguishing, say, the even-numbered ones for being true and the odd-numbered ones for being false, rather than the other way around.

I can also do this as a version of the truth-teller paradox. Just let s_n say:

s_n+1 is true.

Then, if we're going to have a truth-value assignment, the same truth-value will be assigned to each sentence. But there is no more and no less reason to assign true to all of them than to assign false.

So not only must we be careful about self-reference, but also about regresses.

If affirming truth of a sentence is a way of taking up that sentence into one's own speech, as per one version of deflationism, then it is easy to see why we can't have self-reference, circular reference or infinite regress in respect of truth, since these processes fail to produce a finite well-formed sentence—they produce an infinite nonsensical sentence like "It is not the case that it is not the case that it is not the case that....". (Quantification would presumably be done in terms of possibly infinite conjunctions or disjunctions. But unfortunately, deflationism has trouble with quantification and modality. Thus, the claim that possibly George's favorite proposition is false, which claim is surely true, is troubling if we evaluate it by inserting George's favorite proposition in it—for that proposition might, as a matter of fact, be a necessary truth.) This book may be very much relevant, and may in fact already contain a full development of my inchoate ideas, and I've ordered it from interlibrary loan.

It's interesting, by the way, to note that some infinite sentences are nonsense, but others aren't. Thus,

1. 2 is even and 4 is even and 6 is even and ...

makes perfect sense. But

2. it is false that it is false that it is false that ...

is nonsense. It would be nice to have a criterion for when an infinite first-order sentence is nonsense. I think that the answer is that it is nonsense when one gets a vicious regress for explaining what makes it true.

Sorry, I'm rambling. This post is really just a bunch of notes for me to think about later.

Nonsense and externalism (Language, Part VI)

is I will assume at first a fairly standard view of language, not my own weird view.

The following two claims are very plausible:

1. Whether a particular sequence of words from a language L expresses a proposition does not depend on anything other than facts about L.
2. A proposition is either true or false.

But in fact, (1) and (2) are not both true. For, consider the following line of words at the top of a page:

3. The next line of words expresses a true proposition.

Assuming a proposition is either true or false, it follows that whether (3) expresses a proposition depends on what the next line of words is. If the next line of words is "The sky is blue" or "Pigs can fly", then (3) expresses a proposition. But if the next line of words is

4. The previous line of words does not express a true proposition,

then (3) (or more precisely, the proposition expressed by (3)) can neither be true nor false. For if it is false, then the next line expresses a truth, and hence (3) is true. And if (3) is true, then (4) is true, and (3) is false. Since a proposition is either true or false, if (3) is followed by (4), (3) does not express a proposition. Thus, whether (3) expresses a proposition depends on what the next line of words is.

Observe that the two lines of words can be written independently by two different people. Thus, whether a sequence of words uttered by me expresses a proposition can depend on what someone else says—even on what someone else says later, assuming (2).

We thus need to reject either (1) or (2) or both. In fact, I think we should reject (1). Rejecting (2) forces a non-classical logic. Call a sequence of words that does not express a proposition "nonsense". Then what we have learned is that whether a sequence of words is nonsense can depend on non-linguistic facts about the external world. Thus, just as we learned from Kripke that judging whether a proposition is possible is not in general a matter for an armchair investigator, so, too, judging whether a sequence of words is nonsense is not in general a matter for an armchair investigator.

Or at least that's what happens if one has a standard view of language. I myself have a non-standard one. On my view engaging in sentential anaphora (as in (3)) makes the anaphorically referred-to sentence be a part of one's own sentence—it is a way of taking up another's words and making them one's own. This is a version of deflationism. (By the way, I love the joke about deflationary semantics of "true". You want to be famous? You write a paper that says: "Everything Brandom says in his next paper is true." Then when Brandom publishes his paper, you say: "He's right, but I said it first.")

This all works a bit better on an eternalist theory of time.

Lying beliefs

Liar paradoxes are easy and fun to generate. Here is one that is fun: My latest belief, let us suppose, is that George's latest belief is false. And George's latest belief is that my latest belief is true. Who is right?

[Edited: Fixed a typo.]

Liar paradox with only quantification

The following remark is inspired by Williamson's "Everything" piece. Here is a liar paradox that uses no direct reference (as in "This sentence is false"), and indeed where the only funny business going on in it is a quantification over all sentences:

No actually tokened written sentence is true if it both ends with a decimal number which is the MD5 checksum of all of that sentence minus its last sequence of non-space symbols and if the MD5 checksum of all of that sentence minus its last sequence of non-space symbols is 187835884982830523138282294681725949791.

The paradox relies on the extremely likely claim (probability about 1−2⁻¹²⁸, I suppose) that nobody ever tokens a different written sentence satisfying the condition after the "if". Take my word for it that the sentence above does satisfy the condition.

Note that "that sentence" is not directly referential—it is, rather, a bound variable, bound by the quantification over sentences.

What should we do? Well, I think we can should either reject quantification over sentences, or reject something like compositionality. Neither is an appealing prospect, though I've got other reasons to be suspicious of compositionality and its relatives.

If one says that one should reject quantification over sentences, but allow quantification over sentence tokens, then I'll offer the following variant:

No actually written sentence token is true if it both ends with a decimal number which is the MD5 checksum of all of that sentence token minus its last sequence of non-space symbols and if the MD5 checksum of all of that sentence token minus its last sequence of non-space symbols is 127533944667835603647534200477710876898.

This yields interesting arguments. If one allows compositionality, then one should reject quantification over all sentences or all sentence tokens. I think this forces one to be an irrealist about sentences and sentence tokens. Or one can just disallow compositionality, and thus deny that the items in block quotes are bona fide sentences, expressive of propositions.

An argument against shaving

The argument is a reductio.

1. Shaving is sometimes permissible.
2. There is a relation I such that IxP holds if and only if P is a property which x has.
3. Define the property N by NP=~IPP.
4. Either N has N, N does not have N.
5. If N has N then ~INN by definition of N, and so N does not have N, which is absurd.
6. If N does not have N then by definition of N we do not have ~INN, and so by double negation, we do have INN, and so N has N, which is absurd.
7. Thus absurdity ensues on both horns of the dilemma in (4).

The reader will, of course, notice that (1) is not used anywhere in the argument. Instead, the argument gives (1), and then launches into a standard variant of Russell's paradox. It's obvious, thus, that we learn nothing from the argument about the permissibility of shaving.

But one can dress up the argument if one so desires, so that (1) gets used further on down. For instance, instead of working with I, one can work with I_s where I_sxP holds if and only if P is a property which x has and shaving is sometimes permissible. If N_sP=~I_sPP, then absurdity ensues from assuming that N_sN_s only assuming that shaving is sometimes permissible. (If shaving is not permissible, then N_sN_s holds because I_sN_sN_s unproblematically fails as the second conjunct in its definition fails.) Thus, we can take the paradox and dress it up into an argument against the permissibility of shaving. But of course we still learn little about shaving from it.

I claim that Patrick Grim's arguments against omniscience are another such dressing up of this paradox, and hence we learn little about omniscience from them. But I am not going to argue for this here, since I am still working on the paper where I show this.

Deep Thoughts XV

No truth is false.

A really weird A-ish theory of time

Start with the following fairly normal A-theory. There is an A-timeline, and it is logically primary. It is marked: "... -5yr -4yr -3yr -2yr -1yr now 1yr 2yr 3yr 4yr 5yr ..." with inbetween markings. Markings on the A-timeline are called "A-times". They are the only real, ontologically basic times. 193 years ago, it was the case that the Battle of Waterloo is (was?) near the "now" marking. Now the Battle of Waterloo is near the "-193yr" marking. It moved--it moved from now to -193yr. The phrase "the present" is ambiguous. Sometimes it means "now"--call that "present1". In that sense, 193y ears ago, the Battle of Waterloo was at the present1, but no longer is. Sometimes "the present" is the changing descriptor: "the A-time of the occurrence of dthose events which are present1" (where "dthose" is Kaplan's rigidifying operator). This is "present2". In that sense, when the Battle of Waterloo took place, it was 193 years before the present2. The present2 keeps on moving through the A-timeline.

If we need B-times like 2008, we have to identify them with sets of simultaneous events or something like that, and then we need acounterpart theory for identifying B-times across worlds. (I actually do myself think we need a counterpart theory for identifying B-times across worlds, because I am a relationalist about times.) Thus, while the real, genuine, rock-bottom time of the Battle of Waterloo keeps on changing (it keeps on getting more negative), the B-time of the Battle of Waterloo is fixed. But it's not an ontologically interesting time. It's the A-times that have ontological significance. This is a genuine A-theory. It requires, as primitives, a number-line of times, with (a) a distinguished direction (from minus to plus), (b) a distinguished origin (zero), and (c) a distinguished equidistance ternary relation--abEcd iff a is the same distance and direction fromb as c is from d and satisfying appropriate axioms. Call this a "moving event" theory, because events move relative to the timeline.

Now, for the really weird A-ish theory of time. One takes the moving event theory, but one impoverishes it by throwing out the distinguished origin, while keeping the distinguished direction and the distinguished equidistance relation. Basically, the idea is that we erase the contentful "... -5yr ... now ... 5yr ..." labels on the A-timeline, and replace them with something completely non-contentful, like "... t81 ... t124 ...t441 ...", albeit still with a direction and an equidistance operation. We then add the following semantic claim: We've (as far as the theory is concerned, arbitrarily) settled on calling t124 "the present1". But t124's difference from t81 and t441is merely numerical (just as on a substantivalist B-theory, the year 2008 only differs numerically from 2007). Still, we call t124 "the present1". Let's say t7 is 193 years before t124. Then, at t7, i.e., 193years ago, it was the case that the Battle of Waterloo is occurring at t124. Currently, at t124, it is the case that the Battle of Waterloo is occurring at t7. Thus, we have a moving event theory, but no distinguished present.

This is a really crazy theory. It is a "dynamic" theory of time in the sense in which the A-theory is "dynamic": events acquire new objective temporal properties as time progresses. (I actually think this is a mistaken understanding of what "dynamism" is, but that's a different story.) But unlike the A-theory, the past, present and future are all ontologically on par, and the distinction between them is ontologically insignificant.

It may seem like this theory has all the disadvantages of the A- and B-theories combined. But not quite. It has the advantage that it escapes this argument against the A-theory. But then so does the B-theory, and it's simpler to opt for the B-theory.