Wednesday, December 31, 2008

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.

Monday, December 29, 2008

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).


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?

Sunday, December 28, 2008

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.

Saturday, December 27, 2008

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.

Tuesday, December 23, 2008

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]

Sunday, December 21, 2008

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.)

Saturday, December 20, 2008

Liar and truth-teller paradoxes

Here is a fun similarity between the liar paradox:

  1. Claim (1) is false
and the truth-teller paradox:
  1. Claim (2) is true.
Intuitively, (1) and (2) should be respectively equivalent to the following infinite claims:
  1. false(false(false(...)))
  2. 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:
  1. 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. :-)

Friday, December 19, 2008

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 sn says:

sn+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 sn say:

sn+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
  1. 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.

Thursday, December 18, 2008

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:
  1. 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
  1. 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.

Wednesday, December 17, 2008

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.]

Tuesday, December 16, 2008

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.

Monday, December 15, 2008

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 Is where IsxP holds if and only if P is a property which x has and shaving is sometimes permissible. If NsP=~IsPP, then absurdity ensues from assuming that NsNs only assuming that shaving is sometimes permissible. (If shaving is not permissible, then NsNs holds because IsNsNs 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.

Friday, December 12, 2008

Thursday, December 11, 2008

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.

Wednesday, December 10, 2008

Is knowledge a natural concept?

Consider the following argument:

  1. The best accounts of "x knows p" are conjunctive, i.e., of the form R1(x,p) & R2(x,p) & ... (with at least two conjuncts).
  2. Therefore, probably, knowledge is a conjunctive concept. (See this post and this one)
  3. No conjunctive concept is natural.
  4. Therefore, knowledge is not a natural concept.
Alternately, one could claim that knowledge is a natural concept, and hence the best accounts of "x knows p" are false.

Tuesday, December 9, 2008

A quick argument against Open Future views

Open Future views hold that if p is a proposition making a contingent claim about the future, then p is not true (on some versions, p lacks truth value, and on other versions, p is false).

Now suppose you find out that at t0, on an ordinary autumn morning in New York City, Bill Gates tossed down a million twenty-dollar bills from an airplane, each with a sticker attached saying: "Please take this. It's a gift from Bill Gates." You are then in a position to know the following fact:

  1. At t0+48hrs, at least one of the twenties is not be where it fell.

But if Open Future views are true, then you don't know this, unless you know something more about t0. For if t0 is somewhere in the last 48hrs, then (1) is a future contingent. Being a future contingent, you cannot know it. For the only propositions that can be known are ones that are true. But since you do know (1), Open Future views are false.

To put it differently: Oddly, if Open Future views hold, then whether you know (1) depends on whether t0 was in the last 48hrs, or further back, regardless of further evidence. Thus, what inferences can be made from a fact depends on how far back that fact is. This is not very plausible.

Monday, December 8, 2008

Evil and the cosmological argument

Here is a valid non-deductive argument:

  1. There are some evils whose best explanation involves an evil supernatural agent. (Premise)
  2. Therefore, there is an evil supernatural agent, call him S. (By (1), ampliatively)
  3. If there is a necessarily existing first cause of everything else, it is not an evil agent. (Premise)
  4. There is a necessarily existing first cause of everything else. (Premise)
  5. S is not the necessarily existing first cause of everything else. (By (2) and (3))
  6. There is a necessarily existing first cause of everything who is a cause of S. (By (4) and (5))
  7. The cause of a supernatural being is supernatural. (Premise)
  8. There is a necessarily existing supernatural first cause of everything. (By (6) and (7))
The really controversial premises are (1), which by itself is sufficient to refute naturalism, (3), which I've argued for in this post, and (4), which requires a cosmological argument, which I've defended at length in print.

I bet there are other interesting theistic arguments starting with (2). One might, for instance, be able to argue that an evil agent cannot be simple and unchangeable, and an agent who is not simple and unchangeable must have a cause, and go on from there.

Saturday, December 6, 2008

An affixal theory of some indexicals (Language, Part V)

This post continues from earlier reflections on indexicals, but in a slightly different way. I want to offer a very strange theory of indexicals like "I", "now" and "this". They are not words at all. They are affixes, like the "-ing" in "walking" and the "in-" in "indoor". An affix is added to a root, and thereby yields a word. The affix indicates how the sentence makes use of the concept indicated by the root. In highly inflected languages, affixes may play a significant role in indicating whether a given noun is, say, the subject, direct object, indirect object, etc. of the sentence.

We might more accurately think of affixes as functions from partial words to words, remembering that adding an affix may force changes in the "root" part. Moreover, in my sense, an affix might not actually be contiguous with a word. Thus, in Polish the personal endings of past-tense verbs are sometimes allowed to float free of the verb and attach to something else. Thus, one can say: "My w domu bylismy" (="We at home were"), where "bylismy" is "byli" (=past tense of "to be" with a plural "-i" suffix) plus "-smy", the first personal plural ending for past-tense verbs, but one can also move the "-smy" to be after the "My" (="We"): "Mysmy w domu byli." One way—maybe not the way most Slavic grammarians will do it—to read this is as a sentence whose words are "My" (="We"), "-smy ... byli" (="were"), "w" (="at") and "domu" (="home"). The "-smy ... byli" is a scattered word there, written non-contiguously.

"I", "now" and "this" are such non-contiguous affixes. But where is the partial word to which the affix is attached? In ordinary-speech cases of "I" and "now", the answer is easy. With "I", the root is the speaker, and with "now", the root is the time of speech. In other words, when I say "I am now at home", the first word in the sentence is a scattered word consisting of two parts: me (the six-foot-tall guy having a body and a soul) and "I". The third word is a scattered word consisting of two parts: the actual time of speech (whatever the ontology there is—I do not think we need to insist on words or parts of words being something we take ontologically seriously, so we probably don't need to worry whether there are times) and "now". "This" is harder. My inclination is to take it as an affix attached to an activity of pointing at something, perhaps including just the pointing gesture (mental or physical, perhaps contextual), but perhaps including that which is pointed at. I don't have a very good analysis of that.

Fictional speech is puzzling for this view. When the narrator uses "I", if that is the affix, where is the root? I don't know what to say. But fictional speech is anyway problematic. Perhaps I can say that a "sentence" said by a fictional narrator is not really a sentence but a fictitious sentence, just as a "murder" committed by a fictional narrator is not really a murder but a fictitious murder.

And what about cases of "I" and "now" that do not really refer? For instance, you tell me: "The other day, George told me: 'I am not at home.'" But George is your imaginary friend. Whom does the "I" refer to? Well, there is no "I" in your sentence. There is only an "'I'". What is between quotation marks is not a sentence, and not even a candidate for a sentence, because it is incomplete, in the way "George Bush was -ing down the street" is.

This is a really revisionary view of language. Does it have any advantages? I think it does. For one, it makes indexicals not stand out as some disparate category. They are just affixes to a root that is often Lagadonian. Moreover, I think this is the sort of view at which one may end up if one has a general enough view of the possibilities for language—dropping any insistence on a linear structure, for instance, allowing Lagadonian languages, etc.

[Edited to fix typo and remove an embarrassing slip.]

Friday, December 5, 2008

Eliminativism about minds

Here is a hypothesis: A mature neuro-science will, as the eliminativists claim, have no room for concepts like "belief", "desire", etc. Suppose this hypothesis proves true. What should we then do? Obviously, it would be absurd to deny that we have beliefs or desires. Instead, we should deny that belief, desire, etc. occur in the neural system, which is what the neuro-science studies, and hold that they occur elsewhere. Since there is no other plausible candidate for the mind in the physical world besides the neural system, we should conclude that belief, desire, etc. occur outside the physical world, i.e., that some form of dualism is true. Moreover, I suspect that a neuro-science that would have no room for beliefs and desires would also have no room for the idea that there are states of the brain on which beliefs and desires supervene. Thus, it would lead us to a non-supervenient dualism.

But this is just an exercise in hypotheticality, since we are in no position to make such specific predictions about future science.

Can timeless things change?

It seems that the answer has to be negative—isn't the idea utterly absurd? But suppose that an A-theory is true and Fred is a timeless being. Let W be the property of being (timelessly) in a world where a war is (presently) occurring. It seems that on A-theories this is a genuine property, and it was true in 1944 that Fred then had W and it is no longer true in 2008 that Fred has W. So it seems that Fred has changed in respect of W. The B-theorist is apt to deny the existence of such a property as W, and instead talk of the family of properties Wt of being (timelessly) in a world where a war is occurring at t. It was true Fred in 1944 had W1944 and it is true in 2008 that he does not have W2008, but that is not a change, since likewise it was true in 1944 that Fred had not-W2008 and it is true in 2008 that Fred has W1944.

So, if the A-theory is true (or at least if one of those A-theories is true that allow tensed properties like W), it follows that timeless beings change. Of course, the change is extrinsic. But even extrinsic change is puzzling in the case of a timeless being. Look at it from Fred's point of view. Does he or does not have W? It seems both, but that is absurd. In the case of a being in time, we would say that the question is ambiguous—does he have W at what time? But we cannot disambiguate this from Fred's point of view.

Here is something an A-theorist might say. She might say—in fact, I think that on independent grounds she should say it—that at every time, a different world is actual. (Right now, a world without a present world war is actual. In 1944, a world with a present world war was actual.) Then there is no contradiction in Fred's both having and not having W, since since in one world (the 1944 one) he has W and in the other (the 2008 one) he does not.

If we take this route, then the "objective change" that A-theorists are enamored of will be a movement (an orderly one) from one world to another. But Fred undergoes that movement just as much as you and I—in 2005 he was in the 2005 world, and in 2008 he is in the 2008 world—though there is a difference whose significance I am unable to evaluate at present (Fred exists timelessly in both worlds, while you and I exist presently in both worlds). It seems, then, that Fred undergoes objective change, while being outside of time. That seems absurd. Moreover, if we take this route then the following conceptual truth becomes really hard to account for: Nothing outside of time can undergo intrinsic change. But why can't Fred have one set of intrinsic properties in the 1944 world and another in the 2008 world? And if he did, then he would be changing in respect of intrinsic properties.

If the above is right, then it seems that what the A-theorist needs to do is to deny the possibility of timeless beings. This has some interesting consequences. If time began with the big bang, and if we are realists about mathematical entities, then the number 7 is about fifteen billion years old, give or take a couple of billion, and if time were to come to an end, then the number 7 would cease to exist. And once we've allowed abstracta to be in time, why should it be any more absurd to allow them in space? I do not know if these kinds of considerations form knock-down arguments against the view (and hence against the A-theory, if the A-theorist needs to go there), but they are worth thinking about.

Thursday, December 4, 2008

How many zebras lived in the 19th century?

Here is a puzzle for a presentist. There seems to be a determinate answer to the question "How many zebras lived (at least in part) in the 19th century?" or at least it is quite possible there is a determinate answer.[note 1] But can the presentist make any sense of the question?

This puzzle is somewhat different from the general puzzle about truths about the past. I am willing to grant for the sake of argument that the presentist can make sense of questions like: "Did Napoleon win at Waterloo?" For the presentist can take the proposition p that Napoleon wins at Waterloo, and say that p was false at the relevant time, and hence the answer is negative.

But the question how many zebras lived in the 19th century is much tougher. Given any time t in the 19th century, the presentist can make sense of the question how many zebras there were alive at t.[note 2] That question is the question of what number z(t) is such that it was true at t that there are z(t) zebras. But the answer to the question of how many zebras lived in the 19th century does not supervene on the values of z(t) as t ranges over the 19th century.

If the presentist has haecceities in her ontology, she can probably make sense of the question. For then the question is: "How many haecceities h are there such that h is a haecceity of a zebra, and h was instantiated in the 19th century?" So the haecceitist presentist seems to be out of trouble.

Can a non-haecceitist presentist do the job? Yes, if she is a closed-future presentist. (A closed-future presentist accepts bivalence for claims about the future.) But it is surprisingly tricky (at least if we want to take into account the possibility that a zebra might have a temporally gappy existence). Here is the simplest way I have. Let T be the set of times in the 19th century. Let S be a non-empty subset of T. Let z(S) be defined as follows. Choose any t in S. Let z(S) be the unique number n such that it was true at t that there exist exactly n zebras z such that PS(z). Here, PS(z) is the claim that for every time t' in S, z exists, existed or will exist at t', and for no time t' in TS is it the case that z exists, existed or will exist at t'. (AB is the set of all members of A that are not members of B.) (This a definition apparently compatible with presentism, but since PS(z) partly concerns the then-future, only a closed-future presentist will have no qualms about it.) Then the number of zebras that lived in the 19th century is equal to the sum of z(S) as S ranges over all non-empty subsets of T.

Maybe there is a simpler way of counting 19th century zebras on presentism. But I can't think of one. More obvious solutions fail (thus one might keep track of when zebras come into existence, and count the comings into existence, but this doesn't work very well on presentist grounds for zebras that come into existence on an interval of times open at the bottom end).

There may be a clever way to do this within the confines of open-future presentism. But it's going to be tricky and messy. If it can't be done, then we have an argument why an open-future presentist should be a haecceitist.

I wonder if how complicated the answer to the question is does not give an argument against presentism. For, intuitively, the claim that there were exactly n1 zebras at noon on January 18, 1855 should be made true similarly to the way the claim that there were n2 zebras in the 19th cenutry is made true. But the non-haecceitist presentist will have to use very different counting methods for the two cases.

Wednesday, December 3, 2008

Two problems for conspecificity as primitive

Here is something growing out of last night's neo-Aristotelian metaphysics class with Rob Koons. Suppose we take the relation of conspecificity as a primitive, in order to be a nominalist about species. (The context here is Aristotelian, so "species" may include "Northern leopard frog", but it may also include "electron".) Then we will have a hard time making sense of claims like:

  1. Possibly, none of the actual members of x's species exist (in the timeless sense), but there is some member of x's species.
Suppose for instance x is an electron. Then, surely, there is a possible world where there are electrons, but none of the actual world's electrons exist. But to make sense of (1) on an account that takes conspecificity to be primitive would require a conspecificity relation between an electron in the actual world and an electron in the possible world. But how can there be a relation one of whose relata does not exist? (Intentional relations are like that, but I don't think we want conspecificity to be like that.) The realist about species doesn't have this particular problem. She just explains (1) by saying that if s is the species of x, then possibly none of the actual members of s exist but s nonetheless has a member. Also, if one takes conspecificity as primitive but allows the existence of non-actual individuals, the problem disappears, since then we can unproblematically relate a non-actual individual with an actual one.

The problem here is that of interworld conspecificity. What makes an individual a1 in a world w1 conspecific to an individual a2 in w2? If there is an individual a2 in w1 conspecific to a1 who also exists in w2 and is conspecific to a2, by transitivity of (Aristotelian) conspecificity this is not a problem. We can generalize this solution by saying that a1 in w1 is conspecific to a2 in w2 provided that there are chains of worlds W1,...,Wn and entities A1,...,An such that

  • W1=w1, Wn=w2, A1=a1, and An=a2
  • bi is in both Wi and in Wi+1 for i=1,...,n−1
  • bi and bi+1 are conspecifics in Wi+1 for i=1,...,n−1.
For this approach to give a good account of interworld conspecificity it has to be the case that conspecificity is transitive and that species membership is essential. (But the approach can also work if species membership is not essential, as long as we have individual forms, and the membership of an individual form in a species is essential. For then we can give the story not in terms of chains of particulars, but chains of individual forms.)

The above account does, however, entail the following metaphysical principle:

  1. Whenever worlds w1 and w2 contain individuals a1 and a2 who are members of species s (understood nominalistically), then there is a finite chain of possible worlds, starting at w1 and ending at w2, such that every pair of successive members of the chain has a common member of s.
Is (2) true? Well, it seems hard to come up with counterexamples to it, at least. If we could imagine a species whose possible members could be divided into two classes, A and B, such that no member of A could exist in a world that contains a member of B, then we would have a violation of (2). But I am not sure we have much reason to think such species exist.

But now consider a different problem for the account. Two photons can collide and produce an electron-positron pair. Suppose we are in a world where there are lots of photons, but only one collision has occurred, producing electron e (and a positron that I don't care about). We now want to be able to say this:

  1. A pair of photons p1 and p2 jointly have the power of producing an electron.
Presumably this should reduce to some claim about how they have the power of producing a conspecific to e. But that is an extrinsic characterization of the power of the photons. Yet it is an intrinsic feature of the joint power of p1 and p2 that it is a power to produce an electron (and a positron). Moreover, supposing that no collisions occurred, and hence there was no e in sight, we would still want to be able to say this:
  1. A pair of photons p1 and p2 jointly have the power of producing a conspecific to something that photons p3 and p4 jointly have the power of producing.
Tricky, tricky. Here is a suggestion. We slice powers, considered as particulars ("x's power to do A") finely enough that we can talk of a particular power that p1 and p2 jointly have (or maybe one has the power to operate on the other in some Aristotelian way), the power of producing an electron (this power can only be exercised together with a power to produce a positron). Now, we can talk of the primitive conspecificity not just of particles, but of productive powers, and we can characterize the conspecificity of two entities disjunctively:
  1. e1 and e2 are conspecific (non-primitively) if and only if either e1 and e2 are primitively conspecific or e1 results from the exercise of a power primitively conspecific to a power the exercise of which results in e2 or e1 results from the exercise of a power which results from the exercise of a power primitively conspecific to a power the exercise of which results in a power the exercise of which results in e2 or ....
Assuming that powers are characterized by what they produce, any disjunct further down in the disjunction entails all the disjuncts further up in the disjunction. Now we can make sense of (3) and (4) in an intrinsic way, in terms of the conspecificity of the powers of producing electrons. Moreover, we can make the chain-of-worlds move as needed for non-primitive conspecificity. This will yield a very complicated analogue of (2), but that analogue will, if anything, be even more plausible than (2).

This is all too messy, but maybe mess is unavoidable.


Is being dependent an intrinsic property of an entity?

Suppose we say that it is intrinsic. Then we have the following interesting consequence. Assuming there are dependent entities, it is possible to have an intrinsic property, D, whose possession entails the obtaining of a genuine relation (a dependence relation) to another entity, but where D is, nonetheless, not relational. This would force us to deny strong recombination principles in accounts of modality. And that would be a good thing from my point of view. For one, it would force a humility in the move from apparent conceivability to possibility. (The modal problem of evil is one place where this matters.)

Could we say that being dependent is not an intrinsic property? That, I think, would be odd. If being dependent is not an intrinsic property, or at least is not entailed by the intrinsic properties of the entity (all I need for the arguments of the previous paragraph is that being dependent is entailed by the intrinsic properties of a thing), then being dependent is not a matter of some kind of inner need or lack in the entity. If George could survive without water, and without any substitute (natural or supernatural) for water, and without without any intrinsic difference in him, then he is not really dependent on water for his existence. My intuition is that the notion of a dependence that does not supervene on the intrinsic properties of a thing and that (therefore) is merely accidental is a sham dependence. I don't yet have a very good argument here, beyond just restatements of the intuition.

If I am right, then Hume has no conceptual resources to affirm that any entity is genuinely causally dependent. For on his view, "causal dependence" would have to be an extrinsic property of an entity, and hence, if I am right, would at best be just a sham dependence.

Tuesday, December 2, 2008

A sound argument against necessary tensism

Necessary tensism is the thesis that necessarily tensism is true.

  1. Tensism holds if and only if everything that exists in some way, either existed, or exists presently, or will exist. (Definition)
I think a lot of presentists are tensists. The "exists in some way" is a tricky thing. Maybe it should be glossed as: "can be quantified over"?

Here is an argument that tensism is not a necessary truth. In all of the premises, "the present" and tensed expressions must be taken to narrow temporal scope. I take definitions to be necessary truths. I will use "exists*" as an abbreviation for "existed, exists presently or will exist".

  1. Two times are temporally related if and only if they are simultaneous or one is earlier than the other. (Definition)
  2. Necessarily, if x existed, then it existed at a time earlier than the present. (Premise)
  3. Necessarily, if x will exist, then it will exist at a time later than the present. (Premise)
  4. Necessarily, if x exists presently, then it exists at a time simultaneous with the present. (Premise)
  5. Necessarily, if x exists*, then x exists in some way. (Premise)
  6. It is possible for there to exist in some way an entity at a time not temporally related to the present. (Premise)
  7. Necessarily, if tensism holds and x exists in some way, then x exists in some way at a time temporally related to the present. (By (1)-(6))
  8. Possibly, tensism is false. (By (7) and (8))
No tensist will be convinced, I suppose, since they will deny (7) (they may quibble about other premises, but I don't think these are a big deal). But I think (7) is very plausible. Surely it is possible for there to be parallel time lines with no temporal relations between them. Likewise, surely it is possible that there be no fact of the matter to the effect that a short-lived entity on Alpha Centauri has existed pastly, and no fact of the matter that it exists presently, and no fact of the matter that it will exist futurely. (One just thinks a little about relativity theory, and this becomes plausible.)

Moreover, not only is it possible that tensism is false, but we are not in a position to know tensism to be true. For we are in no position to know that there are no parallel timelines, and if there are, then tensism is false.

Monday, December 1, 2008

Spiritual sickness and spiritual death

There is a temptation for Catholics—also present for non-Catholic Christians but with different terminology—to settle for avoiding mortal sin. After all, if one has living faith and does not reject Christ's salvific grace through mortal sin, one will be saved. So why should one worry about venial sin?

Leaving aside the question of purgatory—for that is not the heart of the issue, but something more in the way of an effect of it—here is one thing that is wrong with this. In a state of mortal sin, one is bereft of living faith, of charity and of Christian hope. One is spiritually dead. If one is not a state of mortal sin, then one is spiritually alive. But surely we are not merely satisfied with being alive.

It would be silly to say: "I shall not go to the doctor. Yes, I have a great big ulcer, but after all, I am alive, and that is all that matters." While there may be contexts where it is appropriate to shout with joy "I am alive!" as if that was all that mattered—for instance, right after one's life (spiritual or physical) has just been saved. But as regards the body, we do not just want life. We want a life of health. One can be alive, but very ill, close to death. There is still reason to have the joy of life—there is a qualitative difference between that life and death—but that is not what we aspire to. (Here, of course, one recalls what Socrates says about how happiness is thought to require health of body and in fact requires health of soul.)

But there is a disanalogy between the physical illness of those who are physically alive and the spiritual illness of those who are spiritually alive. For while this particular physical illness may not win out, our mortal body is after all heading for the grave—perhaps unless the eschaton intervenes.[note 1] But while spiritually ill though in a state of grace, there is reason to hope—not just hope to overcome that particular illness, but to overcome them all, by the grace of Christ living in us. Thus we do have more reason to rejoice over being spiritually alive than over physically alive—but this rejoicing cannot lead to idleness, since after all, how much do we want to prolong our ill health?