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May 31, 2005

Some Animadversions on Hume's Law

(Note added 1/6/05: you know, that word doesn't mean anything like what I thought it meant...)

I'm back from FEW. Actually, I was back yesterday, but I returned with an idea for a paper which I might be able to write relatively quickly - as in, maybe a couple of weeks, rather than a couple of years - so I've been writing away and putting off this blog entry until a time when I'm feeling less productive.

But I really want to reply to the three people who commented on the last post. This reply might not be all that satisfactory for now, but it's probably more satisfactory than being ignored while your interlocutor writes a different paper...

So, hi to Brendan, who wrote:

Suppose ought implies can. So if I ought to do it, I can. Presumably what I can do is descriptive: it follows from my personal abilities, human nature, social influences etc.

Now if ought implies can, then if I cannot do it, I ought not to. Modus Tollens.
But now if what I can do is descriptive then what I ought to do is determined by what I can do. In which case(here is the question), are we not making out normative claims based on descriptive claims and Hume is wrong?

Well, the contra-positive of "if I ought to do it, then I can do it" is "if I can't do it, then it's not the case that I ought to do it" (and not "I ought not to do it", which means something else.) But with that minor adjustment you have a great point, against which the following fact will no doubt seem horrendously inadequate: there's no alethic necessity operator in the langauge of the strong deontic logic for which we proved our two Hume's Law theorems.

Peter Vranas had a similar question about the paper at FEW, though what he said was that this is the implication we ought to worry about:


So, given our approach, one obstacle to answering this question properly is that we haven't been working in a rich enough framework; Greg and I need to take a look at bi-modal logics and see if we can still get our approach to work.

But I can make some points about how, intuitively, it ought to go. I used to think we had a great answer to the Ought-Implies-Can question, which was a variant of a structurally similar objection to our version of Russell's law (the claim that you can't derive a universal sentence from particular one.) Suppose someone argues that since Fa is entailed by ∀xFx, the contrapositive, i.e.


is a counterexample to Russell's law.

This is not a counterexample to our formulation of Russell's law, because the conclusion - though it contains a universal quantifier - is not genuinely universal on our definition, but rather a particular sentence. Intuitively, it's just ∃x¬Fx in disguise.

One obstacle to carring this over to Hume's Law - apart from our lack of a good model theory for a bi-modal logic - has been my messing around with the definition of normativity at the end of the paper. Unfortunately ¬OA really is normative on our dijunctive definition, even though it is perserved under normative extension, because it is fragile under normative translation.

I think there is lots more to be said here, but - for time reasons - I have to leave it there for now. (In particular I should probably have included a brief summary of the "Barriers" paper in the post above, for readers who don't have a clue what I'm talking about. ) Last time we talked to Gerhard Schurz about this he pointed out that the symmetric inter-model relations (like history-sharing and normative translation) support symmetric barrier theses (such as Hume's second law) whereas the anti-symmetric relations support directional barrier theses (e.g. you can derive a particular from a universal, but not vice versa.)

So for the next post I promise a concise summary of the ideas in the paper (which is linked to from the previous post) and proper replies to Ralph and Dilip, and I'll talk about another serious problem that Peter raised in his comments at FEW.

Posted by logican at 9:39 AM | TrackBack

May 23, 2005


Like Jonah and Kenny, I'm off to FEW tomorrow. On Thursday I'll be presenting a paper that I wrote with Greg Restall, "Barriers to Inference," which is about how to formulate and prove inference barrier theses such as these:

Russell's Law: you can't get a universal claim from particular claims
Hume's Law: you can't get a normative claim from a descriptive claim (no 'ought' from an 'is')
Kant's Law: you can't get necessity-style claims from contingent claims
Hume's 2nd Law: you can't get claims about the future from claims about the past and present.

The slides for the talk are available as a pdf here. Since I don't really believe in reading out slides as a presentation method, there isn't a lot of explanation on the slides themselves. If you're interested in a more explicit exposition, you might like to take a look at my paper "In Defence of Hume's Law" and Greg's and my "Barriers" paper, both available here (and both well under 20 pages!)

FEW promises to be unusually technologically advanced for a philosophy conference (ok, CS-readers, stop smirking) and, according to the schedule:

There will be wireless access in the room. You are encouraged to bring laptops with wireless capability.

So perhaps I'll be able to post some news from the conference. (If I'd been reporting on the AAP last year, I could have told you about Karen Bennett rescuing Kit Fine from sharks...)

Posted by logican at 2:32 AM | TrackBack

May 22, 2005

Via Richard Zach

John MacFarlane on logical constants.

Posted by logican at 3:23 AM | TrackBack

May 21, 2005

Horsebreeders are nuts (slight return)

Thanks to a link from Brian, the most popular post on this blog in recent times has been Acer and Bandit, a heart-rending tale of horse-breeding, time travel and non-semantic paradox. Though no-one has come out and said it, it is possible that some readers thought my story (however philosophically illuminating) a little far-fetched.

But perhaps I didn't fetch all that far after all. Check this article out.

Posted by logican at 12:43 AM | TrackBack

May 20, 2005

Comment Spam

This weblog was started on the 5th March 2005, and today it received its first ever piece of comment spam. For the blissfully ignorant, just as email spam is unwelcome email, in practice often designed to get you to buy pharmaceuticals, loans, software or perhaps take part in intriguing African business adventures, so spam comments are unwelcome comments on weblogs, in practice often including links to other sites promoting porn, gambling, pharmaceuticals or credit.

Today I had just a single piece of comment spam, though other bloggers report getting hundreds per hour. Perhaps the spammers were testing the blog for susceptibility to more serious attacks. Thanks to warnings from from fellow bloggers (especially Greg Restall and Matt Carter) this blog is not especially susceptible. Among other measures, I have been running MT Blacklist for several months now, and moderate all comments from unregistered users.

Yet it is also reasonable to believe that until now this blog has benefited from "security through obscurity" - languageandlogic.net was relatively new and so the spammers simply didn't know that it existed. Sometimes I have heard people say that security though obscurity is not really security at all. I suppose they are thinking that instead of taking exciting and (possibly expensive) measures to foil security-enemies, security through obscurity is merely a matter of lying low and hoping for the best. But it seems to me that obscurity can be very effective. In fact, isn't that how passwords work? (Not every security measure works through obscurity though, e.g. guards, walls, alarms, (maybe the kind of dna identification one sees in Gattica?)) And the mere fact that no-one knows what security systems one has in place (at, say, a bank, or an ancient tomb of interest to the likes of Lara Croft or Indiana Jones) can be very effective at keeping something secure. Of course, if you are in charge of security at a bank, you probably don't want that to be your only security measure...

Posted by logican at 10:53 PM | TrackBack

May 18, 2005

Via PhiNews

From Logical Lyrics:

For the amusement of all those who gave us help, we dedicate our book to all model theorists who have never dedicated a book to themselves. (C.C. Chang and H. Jerome Keisler)

Posted by logican at 1:40 AM | TrackBack

May 17, 2005

Dear Morty,

At the end of this post about Tarski, I was wishing that I knew what drove him to reject the analytic/synthetic distinction. Fortunately, in the comments, Juhani remembered a letter from Tarski to Morton White, in which Tarski lays out his reasons. I have managed to track it down, so here, for anyone with J-stor access, is a link to the letter.

At the beginning of the letter, Tarski remarks that he does not have much to say beyond what he has already said "in my article on logical consequence and in the recent one on truth (notice, in particular, my remarks in S14.)" Morton White tells us that these two articles are "On the Concept of Logical Consequence" and "The Semantic Conception of Truth and the Foundations of Semantics" (jstor) respectively. I was surprised by this, since I know these two articles reasonably well, and I had no suspicion, until I spoke to Bernard Linsky last week, that Tarski rejected the analytic/synthetic distinction.

Section of 14 of "The Semantic Conception of Truth" is the beginning of the "polemical" part of the paper, and it contains five major paragraphs. In the first Tarski declines to claim that his semantic conception of truth is the only right one, saying that he has no wish to contribute to debates over whether it is the right conception of truth, since the question makes no sense. In the second paragraph two he writes:

Disputes of this type are by no means restricted to the notion of truth. They occur in all domains where - instead of an exact, scientific terminology - common language with all its vagueness and ambiguity is used; and they are always meaningless, and therefore in vain.

In paragraph three he recommends a course of action:

we should reconcile ourselves with the fact that we are confronted, not with one concept, but with several concepts which are denoted by one word; we should try to make these concepts as clear as possible, (by means of definition, or of an axiomatic procedure, or in some other way); to avoid further confusions we should agree to use different terms for different concepts; and then we may proceed to a quiet and systematic study of all the concepts involved, which will exhibit their main properties and mutual relations.

In paragraph four he notes that in the case of truth, some people recommend the pragmatic conception, or the coherence conception.

Then in the final paragraph of section 14 he says that none of those conceptions has been stated sufficiently clearly, but that that may change, and then, when we have several clearly stated but different conceptions of truth, we should invent new terms to express them:

Personally, I should not feel hurt if a future world congress of the "theoreticians of truth" should decide - by a majority of votes - to reserve the word "true" for one of the non-classical conceptions, and should suggest another word - say, "frue," for the conception considered here. But I cannot imagine that anyone could present cogent arguments to the effect that the semantic conception is "wrong" and should be entirely abandoned.

What is there in here that is in tension with the analytic-synthetic distinction? Nothing very much, on a casual reading and there is plenty that is unQuinean (definitions giving the meanings of words, "axioms" that look very like meaning postulates, the study of concepts and the view that nothing could show his view of the meaning of "true" to be wrong.) I'll come back to this in another post and see if I can reconstruct anything like a plausible argument against the analytic/synthetic distinction.

Posted by logican at 4:11 PM | TrackBack

May 16, 2005

More on Comments

When I first started this weblog, I expressed my reservations about the comments system. (And Greg Restall responded to my remarks.) In particular, I wrote:

One can allow the hoi polloi to trample all over one's carefully crafted weblog, misunderstanding one's posts, adding their comments about their dogs and getting into private and badly edited conversations.

Well, I take it all back. One hears a little about bloggers having to be thick-skinned enough to enough to handle abusive comments, but the comments left on this weblog have all been polite, and are usually on topic (or at least off-topic on grounds other than self-promotion) and friendly. Regular commentors are often graduate students or professors in philosophy or computer science and I think my commentors have also done a reasonable job of judging appropriate tone and register for a weblog comment, which is often quite difficult.

So, the quality of the comments has surprised me and my suspicions were unfounded.

There is something remarkable about the comments to date though. I am suspicious of the hype about the majority of bloggers being male, but it does seem as if the majority of commentors on this site are male. Here are some stats:

Total number of comments on this blog to date: 119
Number of comments left by me: 25
Number of comments left by readers of undiscoverable gender: 1
Comments left by readers who are not me, and whose gender I can reasonably judge: 93
Of those 93, number I judge to be female: 2
Of those 93, number I judge to be male: 91

(Some examples of such judging: commentor leaves the name "Anna" - judged to be female. Commentor leaves the name "pedantic bore" - no judgement of gender. Commentor leaves the name "David" - judged to be male. It is possible that such judgements are wrong in some cases.)

I don't see this as something that needs to change - it's not as if commenting on my weblog is a condition to which a gender should aspire - but it is remarkable, all the same.

Posted by logican at 1:46 PM | TrackBack

The Real Thing

More than one person thought of him as "kingly"; others used the cliché "Napoleonic" to describe his attitude as well as his size. At lectures he always made an entrance and when walking through a crowded room he never hesitated or shifted from side to side to weave his way around people. Chest out, with quick little steps he walked straight through the middle, expecting the waters to part.[...] He had a protruding forehead with pulsing veins, giving the impression of having so much brain there wasn't enough room in his head for the whole of it; bright blue eyes, a bulbous nose, a full mouth, seldom quiet; always talking, always smoking, often drinking; he would screw up his face and virtually shudder with disapproval when he shook his head to say he disagreed or that something was not to his taste. He liked to laugh, especially at his own jokes and the gossipy stories he told and retold.[...] Using the power of his words, he was a forceful and tireless campaigner for everything he thought was due him, both professionally and personally. He did not like to hear the word "no" in any situation. (1-2) Alfred Tarksi: Life and Logic Anita Burdman Feferman and Solomon Feferman

I don't think I can explain this very well, and no doubt it is unreasonable for me to feel this way, but I can't help being a little bit disappointed that Tarski was so extrovert. (I suppose this is just more evidence that we have ridiculous expectations of our heros.) Confident and charismatic I can cope with, - I think one might have wondered about this after reading sections of "The Semantic Conception of Truth" - smoking, drinking, ugly, even opinionated - no problem, but what's with all the laughing at his own jokes and the talking?

My image of Tarski is taking quite a beating at the moment. Bernard Linsky told me just the other day that Tarski came to agree with Quine on the subject of the analytic/synthetic distinction. I wish I knew which argument convinced him.

Posted by logican at 12:39 PM | TrackBack

May 12, 2005

Performatives and Embedded Sentences

Suppose someone sincerely and reflectively utters the following sentence:

I declare that the Earth is flat.

Have they said something false? Is that very utterance false?

Had they sincerely and reflectively uttered:

The Earth is flat.

then, of course, the answer to both questions would be 'yes,' but that's not what they utter, they utter:

I declare that the Earth is flat.

Lewis, touching on this briefly in "General Semantics," says that the sentence is true, though "one might be tempted to say he [the utterer] has spoken falsely, because the sentence embedded in his performative - the content of his declaration, the belief he avows, is false."

The sentence seems to be one of Austin's performatives. Just like with these:

I promise to pay you five pounds.
I hereby declare you man and wife.
I name this ship "Pride of Bridlington."

uttering "I declare that the Earth is flat" is a way of doing something, in this case, a way of declaring that the Earth is flat. Similarly, uttering the sentences above are (if conditions are right) ways of promising to pay someone 5 pounds, declaring someone man and wife, and naming a ship. (In Austin's memorable phrase, they allow us to "do things with words.")

What's interesting about the flat earth sentence, is that what uttering that sentence allows us to do is say something false, and even odder, we do it by uttering a sentence which says something true.

So I think it is natural to answer the two questions above as follows:

The sentence token is true (since the speaker really does declare that.) The speaker thus says something true by uttering it, but, as it is a performative, he also, by uttering that very sentence, does something: he says something false (by which I mean that he also asserts a second, false, proposition, not that he asserts a proposition that is both true and false!) The sentence-token, however, does not say the false thing (the false proposition is not its content.) Only the speaker achieves that.

(Similarly, when I say "I name this ship "Pride of Bridlington," " my sentence token is not the baptiser - only I am the baptiser.)

Posted by logican at 4:53 PM | TrackBack

Woolley Logic

Jim Hacker: Are you telling me the Foreign Office is keeping something from me?
Bernard Woolley: Yes.
Jim: Well, what?
Bernard: Well I don't know, they're keeping it from me too.
Jim: How do you know?
Bernard: I don't know.
Jim: You just said that the Foreign Office is keeping something from me. How do you know if you don't know?
Bernard: I don't know specifically what, Prime Minister, but I do know that the Foreign Office keep everything from everybody. It's normal practise.
- A Victory for Democracy, Yes, Prime Minister

On Monday Richard Zach posted a quote from Buffy as an example of someone asserting a disjunction without being prepared to commit to either of the disjuncts. In the same spirit, the above is a quote from Yes, Prime Minister in which Bernard Wooley believes himself justified in accepting an existential claim, though he didn't infer it from any instances of that claim.

Unfortunately, it is hard to get these kinds of examples to tell us anything interesting about logic (that intuitionist logic is unnecessarily restrictive, for example) once we have distinguished inference and implication, since the example is clearly one about what it is reasonable to believe or infer, given the evidence, and we are looking for a conclusion about implication relations between sentences. Similarly, it is reasonable for me to believe that sun will rise tomorrow, but that does not show that sentences expressing the data on which I base that belief deductively imply the sentence "the sun will rise tomorrow."

I don't see why that should stand in the way of a quote from Yes, Prime Minister though. There are some more below the fold, and some of them have a tenuous link to language, though nothing I won't even attempt the kind of sophisticated analysis that you'll see here. If you want to see a few clips, the BBC has some posted here.

The lines quoted above are immediately followed by:

Jim: Who does know?
Bernard: May I just clarify the question? You are asking who would know what it is that I don't know and you don't know, but the Foreign Office know that they know, that they are keeping from you so that you don't know but they do know, and all we know is that there is something we don't know but we want to know but we don't know what because we don't know. Is that it?
Jim: May I clarify the question? Who knows Foreign Office secrets apart from the Foreign Office?
Bernard: Oh that's easy, only the Kremlin.
- A Victory for Democracy

OK, made it down here? For the uninitiated, the main characters are Jim Hacker, a self-centered cabinet minister (later Prime Minister) Sir Humphrey Appelby, the brilliant and devious head of the civil service for Hacker's department and Bernard Woolley, who is Hacker's Private Secretary (a kind of civil servant.) Bernard is often torn between loyalty to Hacker, and loyalty to the civil service.

British democracy recognises that you need a system to protect the important things of life, and keep them out of the hands of the barbarians. Things like the Opera, Radio Three, the countryside, the law, the universities ... both of them.
- Sir Humphrey, Power to the People

Sir Humphrey: If local authorities don't send us the statistics that we ask for, then government figures will be a nonsense.
Jim: Why?
Sir Humphrey: They'll be incomplete.
Jim: But government figures are a nonsense anyway.
Bernard: I think Sir Humphrey wants to ensure they're a complete nonsense.
- The Skeleton in the Cupboard

Sir Humphrey: It is so difficult for me you see, as I am wearing two hats.
Jim: Yes, isn't that rather awkward for you.
Sir Humphrey: Not if one is in two minds.
Bernard: Or has two faces.
- A Real Partnership

A clarification is not to make oneself clear, it is to put oneself in the clear.
- Sir Humphrey, The Tangled Web

Sir Humphrey: East Yemen, isn't that a democracy?
Sir Richard: Its' full name is the Peoples' Democratic Republic of East Yemen.
Sir Humphrey: Ah I see, so it's a communist dictatorship.
- A Victory for Democracy

Jim: I am going to do something about the number of women in the Civil Service.
Sir Humphrey: Surely there aren't all that many.
- Equal Opportunities

Geoffrey: Personally I find it hard enough to believe that one of us was one of them, but if two of us were one of them ... two of them, all of us could be ... um could be ... um ...
Jim: All of them.
- One of Us?

Bernard: You remember that letter you wrote Round Objects on?
Jim: Oh yes.
Bernard: It's come back from Sir Humphrey's office, he's commented on it.
Jim: What does he say?
Bernard: Who is Round and to what does he object?
- Equal Opportunities

Well, I suppose we could put some sort of government health warning on the rifle butts, this gun can seriously damage your health.
- Sir Humphrey, The Whisky Priest

It [conscription] will give our young people a comprehensive education, to make up for their Comprehensive Education.
- Jim, The Grand Design

Bishops tend to have long lives, apparently the Lord isn't all that keen for them to join him.
- Sir Humphrey, The Bishops Gambit

Peter: Soames has been waiting for a bishopric for years.
Sir Humphrey: Long time no See
- The Bishops Gambit

It is necessary to get behind somebody before you stab them in the back.
- Sir Humphrey, A Conflict of Interest

Sir Humphrey: Unfortunately, although the answer was indeed clear, simple and straightforward there is some difficulty in justifiably assigning to it the fourth of the epithets you applied to the statement, inasmuch as the precise correlation between the information you communicated, and the facts insofar as they can be determined and demonstrated is such as to cause epistemological problems, of sufficient magnitude as to lay upon the logical and semantic resources of the English language a heavier burden than they can reasonably be expected to bare.
Jim: Epistemological, what are you talking about?
Sir Humphrey: You told a lie.
Jim: A lie?
Sir Humphrey: A lie.
Jim: What do you mean, a lie.
Sir Humphrey: I mean you ... lied. Ah yes, I know this is a difficult concept to get across to a politician um ... you ah ... ah sorry ... ah yes, you did not tell the truth.
- The Tangled Web

Master: It's such an awful country, they cut peoples' hands off. And women get stoned when they commit adultery.
Sir Humphrey: Unlike Britain where women commit adultery when they get stoned.
- The Bishops Gambit

Jim: Now this happens and they charge in like a herd of vultures.
Bernard: Not herd, Prime Minister.
Jim: Charge in, like a herd of vultures.
Bernard: No, I mean vultures don't herd, they flock. And they don't charge they ... um ...
Jim: Yes, what do they do Bernard.
Bernard: They ... er ... (does imitation of vulture)
Jim: Sit down Bernard.
- Official Secrets

Many thanks to Shawn Stanley and this very helpful site for the quotations.

Posted by logican at 12:12 AM | TrackBack

May 10, 2005

Acer and Bandit

Nat "Metathought" Simeon thinks almost any philosopher worth his salt has thought up a paradox or two. Luckily, I was doing some paradox-mongering in February, otherwise I don't know what I'd have told the Dean.

I'll include some of the lead-up here, but if you want you can just skip ahead to the paradoxes.

Paradox and Semantics
Since the Liar is a paradox concerning a semantic property - truth - it has been natural for us to call it a semantic paradox. Close relations of the traditional Liar, such as truth-tellers, multi-sentence (or proposition) Liars and strengthened Liars also concern truth and others still, such as Grelling's, rely on other semantic properties and relations, such as the satisfaction of predicates. This might encourage us to think that there is something peculiar to semantics which explains the paradoxes and pathologies.

But are there related paradoxes which do not concern semantic expressions? And does it matter if there are?

The notion of relatedness in play here is vague, yet our intuitions about the relatedness of paradoxes matter to the extent that we value a uniform treatment of closely related paradoxes. In "Semantical Paradox" (Journal of Philosophy 76), Burge wrote of one solution to the traditional Liar which had nothing to say about strengthened Liars:

[S]uch an approach, though technically feasible, promises little philosophical illumination. The semantical paradoxes are remarkable in their similarity. The strengthened Liar does not appear to have sources fundamentally different from those of the ordinary Liar. What is wrong with the proposed account is that it gives no insight into the general phenomenon of semantical pathology and offers instead a hodgepodge of makeshift and merely technical remedies."(92)

Are there any non-semantic paradoxes which are closely related to the semantic ones? I will argue that there are. Will this mean that the Liar is an instance of some more general, non-semantic pathology which requires a more general, non-semantic (or, at least, not merely semantic) solution? I will argue that though the problem is not restricted to semantics in the sense that it is not a problem restricted to semantic predicates such as 'true' 'satisfies' etc, it is a semantic phenomenon in that it arises because of a problem with the meaning of the pathological expressions, whether those expressions are themselves semantic ones or not. (In fact I probably won't get that far in this post.)

Non-Semantic Paradox

We are looking for a paradox related to one of the semantic paradoxes, yet not involving a semantic relation or property. The most obvious candidate is Russell's, which seems similar to the Liar, yet is generated by the membership relation of naive set theory. It does not look as if that membership relation is a semantic relation, rather, it looks as if it belongs to the non-semantic realm of set theory. Yet perhaps there is room for doubt on this point; some philosophers think that second-order logic is set theory in sheep's clothing. Is there room for someone to claim that set theory is, in some sense, semantics in disguise?

Perhaps, but the plausibility of such a claim need not concern us, since I will now present two paradoxes which clearly turn on non-semantic properties - that of being an American Paint, and that of being an even winner. I believe that that these paradoxes should receive the same diagnoses as the truth-teller and the Liar.

The Paradoxes
An American Paint is a kind of horse. A horse is an American Paint if and only if i) its sire and dam are both American Paints and ii) it exhibits a distinctive patchy kind of colouring, including a certain amount of white hair over unpigmented skin. The patchy colouring will not play a large part in what follows, and hence forth I will express condition ii) simply as `the colouring constraints.' (For now I'll ignore complications about how there could ever have been a first American Paint. I suppose, if pushed, we could add some kind of `base clause' to this definition. Adapted from the definition on the website of the American Paint Horse Association.)

Let's represent this information about the meaning of "American Paint" in the following definition:

[A] For all horses x, (x is an American Paint if, and only if, x's Dam and Sire are themselves American Paints and x meets the colouring constraints.)

Now consider Acer and his pedigree. Acer is a horse who meets the colouring constraints. Condor, Acer's Dam, is an American paint, but things are less clear on the sire's side. Bandit is Acer's sire and meets the colouring constraints. Bandit's dam is Dundee, an American Paint herself. But Bandit's sire---Acer's grandsire---is Acer himself, thanks to the machinations of a pair of ambitious horsebreeders who sent Acer back in time and mated him with his granddam. The resulting family tree looks like this:


Given the situation I have described, the sentence

[1] Acer is an American Paint

is pathological in a very similar way to the truth-teller. The question of whether Acer is an American Paint cannot be decided until we know whether his sire is an American Paint, and that depends crucially on whether Acer is an American Paint. We may consistently assume either that Acer is an American Paint, or that he is not, yet this would not change the fact that our assumption would be groundless.

In a similar way, we can construct sentences containing only non-semantic concepts which mirror the Liar itself. Suppose that a group of serious yet suggestible punters began to study patterns in horse bloodlines, with the aim of eventually making (even) more accurate predictions about the outcomes of races. Unsurprisingly, they show a special interest in the thoroughbred breed - the descendants of the so-called foundation stallions, a small group of horses brought to England from the Mediterranean at the start of the 17th century. (For the purposes of this example, I will assume that any horse with one thoroughbred parent is a thoroughbred.) In their obsession, our gamblers develop complicated theories about inheritance and traits which are inherited on one side or another, and which may or may not skip generations. They also develop a terminology for discussing such traits. They define an even winner as follows:

[Bi] The foundation stallions are all even winners.
[Bii] Any other thoroughbred is an even winner iff its sire is not an even winner.

Now consider Ain't Misbehavin''s pedigree. All of his ancestors going back three generations are thoroughbreds (though none of them are foundation stallions). Once Ain't Misbehavin''s finest years on the turf were over, his trainers sent him back in time, where he was mated with Head Over Heels and subsequently sired his own grandfather. The resulting family tree looks like this:


Now we can construct the following paradox:

Suppose that Ain't Misbehavin' is an even winner. Then, by the definition of "even winner" his sire, Bit of Bother, is not an even winner. That means, again, by the definition, that Bit of Bother's sire, Drop Dead, was an even winner, which in turn means that his sire was not. But Ain't Misbehavin' is Drop Dead's sire, and, by hypothesis, he is an even winner. Contradiction.

We have shown by reductio that Ain't Misbehavin' is not an even winner. That means (by the definition) that Ain't Misbehavin''s sire was an even winner, and that his grandsire was not an even winner, and hence that his great-grandsire was an even winner. But Ain't Misbehavin' is his own great-grandsire, so it follows that Ain't Misbehavin' is an even winner, contradicting the result of the previous paragraph.

Posted by logican at 1:37 AM | TrackBack

May 9, 2005

Montague Intrigue

I decided that I wanted to know more about Montague grammar, in part because I have always been curious about Montague and his work, and in part because I have a hunch that it might help me with the chapter I am writing. Not really knowing where to start, I searched Amazon and the university library, which taught me that the only book of his that really looked promising (Formal Philosophy - his selected papers) wasn't owned by the University of Alberta library system and was out of print, though I could have a photocopy from Amazon for US$109 (the latter fact is amazing in two distinct ways.)

Not to be thwarted, I went to check out the few library search results that promised even a glimmer of a suggestion of hope, and discovered Montague Grammar, a collection of articles edited by Barbara Partee. Partee also has a two-page summary of his life and work here. Here's what she writes in the preface to the collection:

[T]hose linguists, philosophers, and other students of language who have heard of Montague grammar but have not become aquainted with it may well find some of the papers in this book a gentler introduction to the subject than Montague's work or the few explications of it in print. For the reader with little or no aquantance with Montague Grammar, I would suggest the following order of reading the articles: (1) Lewis (2) Partee ...

Bingo. So er (sheepishly) that's where I've been for the last week.

Meanwhile, it seems Amazon don't even have Partee's volume listed - intrigue upon intrigue. If I were (even) more self-absorbed I would assume that this was all part of a conspiracy to leave me completely obsessed with Richard Montague. But how come so many interesting books on the border of logic and the philosophy of language are so hard to find, or so expensive? Some examples: Kaplan's Demonstratives: first you need to know that you're looking for "Themes from Kaplan", not something called "Demonstratives," and second, you have to cough up US$78 (The book does have the best Amazon cover photo ever though.) I remember looking for this book when I realised that I should probably replace my 2nd battered photocopy of it, and passing over the innocuously titled Themes, not realising that it was exaclty what I was looking for (there are a lot of search results for "Kaplan".) Another example: Priest's In Contradiction, list price: US$244, Amazon.com price: US$244 (I guess that makes sense really, as if 5 bucks off would swing it for you...) Approaches to Natural Language US$74 but they aren't promising anything...

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May 4, 2005

Mumblings and Grumblings

Chris Ragg, at Mumblings and Grumblings, has been doing some blogging on the descriptivism/causal theory of reference debate, though of course the first sentence in this post makes absolutely no sense...

Through Chris' blog I stumbled upon the promisingly titled Bishop Berkeley, Bacon and Bird (that's Charlie Bird (givin' the word) I am thinking, so I hope that my friend Mr Mole is listening.) Recent topics include the epistemology of the rules of logic, a descriptivist response to Williamson on mental states and some thoughts on an essay on Coltrane (man supreme.)

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May 3, 2005

Austin and the Exploding Canaries

Dear Reader,

I need your help tracking down an example...

I've just been chatting to Professor Linsky (henceforth, Bernie) about the various reasons that people reject the analytic-synthetic distinction. I said that one of them is connected with intensional vagueness. Some people think that the rules which govern our expressions need not, and often do not, extend to cover all possible cases. To take an example from Carnap, it might be indeterminate whether the expression "Mensch" (the German word meaning person) can be correctly applied to a creature which is half hawk, half man - the rules for using the expression, which work perfectly well in everyday life, just don't extend to decide that case. Or to take Donnellan's example, it might be indeterminate whether "mammal" can apply to a creature which breathes normally out of the water, but through gills under the water, so that if we discovered that some whales had (tiny, hidden, rarely used) gills, the rules for our language do not yet legislate on whether we should still think that all whales are mammals. It would be up to us, as speakers of the language, to decide on the best way to use the expressions "whale" and "mammal" in those circumstances. As a result, here and now, the content of the sentence "all whales are mammals" is not straight-forwardly necessary.

The related argument against analyticity goes like this: if a (non-indexical) sentence is analytic, then it expresses a necessary truth. But where the intensions of expressions are not defined for all possible cases, there may be no fact of the matter about whether the sentence is necessary. Yet if it were analytic, there would be. So the sentence is not analytic. (Usually it is then suggested that such partially defined intensions are widespread in natural language, and the conclusion is drawn that there are hardly any analytic sentences.)

Here's what I need from you: Bernie thinks that J. L. Austin once argued (like Carnap and Donnellan) that expressions need not be defined for all possible cases, and gave an example involving exploding canaries (or goldfinches?) which was later picked up and used by someone else. (Possibly Morton White?) I'd like to track down the Austin example in particular. Does anyone recognise it? If so I would be grateful if you could point me in the right direction, either in the comments (which may be anonymous, or, if you would prefer a more private method of communication, by emailing me at grussell - AT - artsci - DOT - wustl - DOT - edu (you get the actual address by uniform substitution of "@" for each occurrence of " - AT - " and "." for each occurrence of " - DOT - .") Thank you very much!

Update: 3/5/05 David Chalmers has alerted me to the fact that the passage in question (which concerns goldfinches) can be found in Austin's "Other Minds," reprinted in his Philosophical Papers which is available online if your library subscribes to Oxford Scholarship.

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