Thursday, September 28, 2006
Vagueness in the Nineties
Something I'd like to know a lot more about is the initial reaction to Williamson's defense of epistemicism. It's hard not to get the feeling that the idea that bivalence could be seriously defended for vague discourse was regarded as pretty laughable even in the years leading up to the publication of Vagueness, and this despite well-known attempts to get the view on the table by James Cargile and Roy Sorensen as early as 1969 and 1988 respectively. (Not to mention Williamson's flirtation with the view in his first book).
Here's a quote that highlights the kind of attitude that seems to have been around at the time, taken from the introduction to Wright's Realism, Meaning & Truth, first published in 1987:
'To suggest that Bivalence is, or should be, the hallmark of realism everywhere is accordingly to be committed to claiming either that there is no such thing as realism about vague discourse, or that the vagueness of a statement, whatever it is held to consist in, is a feature consistent with its possession of a determinate truth-value. Neither suggestion is remotely plausible.' (p4)
I don't think Wright would find the view much more plausible now - but he'd certainly recognise that more work would have to be done to dismiss it.
We find Sainsbury writing in 1990's 'Concepts Without Boundaries':
'Sets have sharp boundaries, or, if you prefer, are sharp objects: for any set, and any object, either the object quite definitely belongs to the set or else it quite definitely does not. Suppose there were a set of things of which "red" is true: it would be the set of red things. However, "red" is vague: there are objects of which it is neither the case that "red" is (definitely) true nor the case that "red" is (definitely) not true. Such an object would neither definitely belong to the set of red things nor definitely fail to belong to this set. But this is impossible, by the very nature of sets. Hence there is no set of red things.
This seems to me as certain as anything in philosophy...'
(p252 in the Keefe and Smith reader. My italics)
The first edition of his book Paradoxes, published in 1987, also defined the phenomenon of vagueness in a way that left no room for epistemicism. By 1995's second edition, things have shifted:
'I found my earlier discussion of vagueness very unsatisfactory, in the main because it defined vagueness in such a way as to exclude the epistemic theory. I do not accept this theory, but Timothy Williamson has shown me that I am not able to refute a skilful and determined opponent.' (ix)
What's happened in the 5 years between the first quote and the second? First of all, Williamson has published his Joint session paper 'Vagueness and Ignorance' in 1992, arguing that the most common objections to epistemicism aren't in fact nearly as powerful as people have thought, and that's been followed by Vagueness in 1994.
How did people feel when they first realised they were going to have to take this view seriously? It really seems like it must have come as a complete shock to a lot of philosophers working on vagueness at the time.
Sunday, September 24, 2006
Kripke's Puzzle again
Here's the worry. It's not really an objection to the ambiguity thesis that some entailments go missing - the proposal was expressly designed to block certain entailments. In David's case, he reconstructs Kripke's argument in 'A Puzzle About Belief' so that one needs to move from 'Peter believes that Paderewski has musical talent and Peter believes that Paderewski does not have musical talent' to 'Peter has contradictory beliefs'. The entailment looks pretty good, but David suggests it requires something like the following principle (388): (H) 'If a name in ordinary language has a single referent then it may correctly be represented logically by a single constant'. And David urges two things; firstly that Kripke's puzzles can be treated as a reductio of this principle, and secondly this principle is, like Shakespeareanism, a distinctive committment of the theorist who holds that the semantic contribution of a proper name is exhausted by its bearer, i.e. the Millian. The non-Millian can allow that different occurrences of coreferential names do not share meaning, since their meaning isn't exhausted by that common referent. This means the non-Millian, but not the Millian, can reject principle (H) and thus block the entailment. I'll spare the details, but I was trying to block some related entailments.
I still think the entailment I discussed last time, from 'Paderewski is a musician and Paderewski is a politician' to 'there is some single person who is both a musician and a politician' is a deeply unwelcome casualty. Even if there is more to the meaning of the proper names than their referents, it looks like the mere fact that the two occurrences of the proper name are coreferential looks like it should guarentee the truth of the conclusion. It won't guarentee that someone who has been initiated into the 'Paderewski'-using practice will be able to recognise that entailment; but my point last time was just that this is a different issue.
Notice the contrast to the kind of entailment David wished to block. In effect, he blocks the entailment from 'Peter believes that Paderewski has musical talent and Peter believes that Paderewski does not have musical talent' to 'Peter has contradictory beliefs' by denying that 'Paderewski does not have musical talent' is genuinely the negation of 'Paderewski has musical talent'. This time, the mere fact that the two occurrences of the proper name are coreferential doesn't look like it should guarentee the truth of the conclusion; for that, we need more, namely that the semantic contribution of each occurrence is the same. But that's just what's in dispute between the Millian and David's non-Millian.
So, just to attempt to get clearer, here's what I'm taking to be the germane contrast. The acceptability of the entailment discussed by David turns on the issue which is the real point of contention between the Millian and the ambiguity guy; whether the semantic contribution of a proper name is uniform on different occurrences. In contrast, the acceptability of the entailment I discussed in discussing closure last time looks like it should be settled by something that is common-ground between these guys; that these distinct occurrences are coreferential. That's why I think the entailment I discussed is a genuine casualty of war, and not just a part of the ambiguity proposal which it would be question-begging to call into question.
Thursday, September 21, 2006
Closure and Kripke's Puzzle
As Hawthorne presents the Lottery Paradox, it relies crucially on an epistemic closure principle. The paradox is as follows.
Ordinary proposition: I won't have enough money to go on safari this year
Lottery proposition: (Though I will purchase tickets) I won't win a major lottery this year.
Now the following appear inconsistent:
1. I know the ordinary proposition
2. I know that the ordinary proposition entails the lottery proposition
3. I don't know the lottery proposition
4. Epistemic closure (roughly: knowledge is closed under known logical entailment)
But all of these seem compelling.
Closure has been famously challenged by Dretske, Nozick and others, so it seems worth exploring the thought that it is the weakest link. To close off that avenue, Hawthorne catalogs the miseries of life without closure, and he does so pretty compellingly. But he concedes that more care needs to be taken in formulating the principle than one usually finds. It's in this context that Hawthorne writes (32):
'Some popular views treat singular terms within the scope of propositional attitude verbs as transparent. These views, if correct, make the standard closure principle utterly unacceptable.'
Then in an attached footnote, he cites Soames, and expands on the point:
'On his view, if I know that Hesperus is F, I ipso facto know that Phosphorus is F. Suppose that I know that Hesperus is loved by me and Phosphorus is loved by you, but I do not realize that 'Hesperus is Phosphorus' expresses a truth. I know that [Necessarily]((Hesperus is loved by me and Hesperus is loved by you) -> some single thing is loved by both of us). And I know that Hesperus is loved by me and Hesperus is loved by you (since I know that Hesperus is loved by me and Phosphorus is loved by you, which, on the transparency view, is just the same thing as knowing that Hesperus is loved by me and Hesperus is loved by you). But in this situation, I by no means know--nor am even in a position to easily come to know--that some single thing is loved by both of us. On this view, then, it is not at all true in general that if one knows p and knows p -> q, then one is in a position to come to know q.'
The counterexample seems pretty compelling, and I think Hawthorne is probably right that even a Millian like Soames who embraces Shakespeareanism, and so endorses all kinds of inferences involving the substitution of coreferential names into supposedly intensional contexts, won't want to accept the conclusion we get from closure here.
But notice the problem isn't obviously restricted to Millian views. In 'A Puzzle About Belief', Kripke tried to show that the puzzles surrounding intensional contexts can be generated without Shakespeareanism, and on the face of it Hawthorne's puzzle is no exception:
Suppose I know that Paderewski is a musician and that Paderewski is a politician, but I have failed to realise that I have been intiated twice into a single name-using practice. Necessarily, ((if Paderewski is a musician and Paderewski is a politician) -> there is some single person who is both a musician and a politician). But I don't know, and given my current state of knowledge am not in a position to know, that there is some single person who is both a musician and a politician.
Now, notice I've been tricky here; to really rerun Hawthorne argument, it needs to be the case that I know that necessarily ((if Paderewski is a musician and Paderewski is a politician) -> there is some single person who is both a musician and a politician). And that's extremely hard to stomach, even if we make the assumption with Kripke that in this scenario I'm not logically incapable.
Does this cast suspicion on the analogous attribution of knowledge of the entailment in Hawthorne's argument? Well, yes, but not in a way that matters for his purposes; it is a distinctive committment of Shakespeareanism, so Hawthorne's point still goes through.
What this does suggest, however, is that epistemic closure offers us a constraint on any acceptable solution to Kripke's puzzle. It needs to be the case that entailments like ((if Paderewski is a musician and Paderewski is a politician) -> there is some single person who is both a musician and a politician) are not things I know even if know the antecedent and have been initiated in the relevant name-using practice, since otherwise closure is in trouble.
Positing an ambiguity in the proper name 'Paderewski' (as UT's own David Sosa did in 'The Import of the Puzzle about Belief', and as I did, rather less well, in a talk here in January) accomplishes this, but in a slightly odd manner. It's not the case that someone ignorant of the fact that both occurances of 'Paderewski' are coreferential is in a position to know that necessarily, ((if Paderewski is a musician and Paderewski is a politician) -> there is some single person who is both a musician and a politician). So far so good. But that's because there isn't really an entailment here on this view; it's really of the form:
Necessarily, ((Fa & Gb) -> there exists something that is both F and G).
Now, adding that a=b to the antecedent of this conditional fixes things, and this might seem a good model for the Paderewski case; if I were to learn that both occurances of 'Paderewski' in 'Paderewski is a musician and Paderewski is a politician' referred to the same object, and I knew that conjunction itself, then I would be in a position to know that some single person is both a musician and a politician. But what we've done is closed the gap between the entailments of 'Paderewski is a musician and Paderewski is a politician', and the entailments a subject lacking knowledge that all the occurances of the proper name are coreferential would be in a position to recognise. This is unacceptable; intuitively, 'Paderewski is a musician and Paderewski is a politician' does entail 'some single person is both a musician and a politician', even if we are not always in a position to recognise the entailment.
It's worth noting that Mark Sainsbury's solution to the Paderewski problem, which I've been mentally resisting for some time now but which has become increasingly attractive, does strikingly well here. Mark follows McDowell in letting a Davidsonian truth-theoretic theory of meaning become our theory of sense; for example, the difference in sense between 'Hersperus' and 'Phosphorus' is drawn by letting them have distinct homophonic axioms. We can't do that with 'Paderewski' without positing some sort of unwelcome ambiguity, so the two occurances of 'Paderewski' in 'Paderewski is a musician and Paderewski is a politician' have the same sense for Mark. But Mark holds that I am in no position in this case to know that both occurances share their sense; contrary to what Dummett says in Truth and Other Enigmas, sameness and distinctness of sense are not transparent, even to a subject who understands both expressions. Now, we have conventions which are designed to suggest sameness of sense (Mark focuses on two: anaphoric dependence and repeat use of a single name within the same conversation), and for the most part sensitivity to these conventions will suffice. (For example, sensitivity to these conventions will usually allow one to warrantedly infer from Fa & Ga that there is something which is both F and G). But crucially, and this is the lesson we should draw from the Paderewski case, sensitivity to these conventions does not offer one infallible knowledge of whether two expressions one understands share their sense. On this view, and in contrast to the ambiguity proposal, it is true that, necessarily, ((if Paderewski is a musician and Paderewski is a politician) -> there is some single person who is both a musician and a politician). But I'm in no position to know the entailment because I'm in no position to know that these occurances of the proper name share their sense. This blocks the Paderewski version of Hawthorne's argument, so epistemic closure is vindicated in a very neat way.
Hawthorne, J. 2004. Knowledge and Lotteries. OUP.
McGlynn, A. 'Is Minimal Fregeanism too minimal?', text of talk.
Sainsbury, M. 2004. 'Sameness and Difference of Sense', Philosophical Books 45: 210-7.
Sosa, D. 1996. 'The Import of the Puzzle about Belief', Philosophical Review 105: 373-402.
Tuesday, September 12, 2006
I won't make a habit of posting then hiding, but I really didn't want people to start reading a post of that length if there's nothing solid to it.
Sunday, September 10, 2006
Bunny and Formalism
Saturday, September 09, 2006
Another Fine Mess
"We've noticed that customers who have purchased The Limits of Abstraction by Kit Fine have also ordered Miracles in Enlightenment England by Jane Shaw."
The plot thickens....
Sunday, September 03, 2006
The Reason's Proper Study is itself.....
The book's all about the propects, both technical and philosophical, of somehow maintaining that our knowledge of various mathematical theories can be accounted for using our knowledge of some appropriate (higher-order) logic plus abstraction principles; second-order principles of the form:
For all A and all B, (%(A) = %(B) if and only if A//B),
where % is a 'term forming operator applicable to expressions of the type of [A, B] and [//] is an equivalence relation on entities denoted by expressions of that type'. (The quote's from the intro to Hale and Wright's The Reason's Proper Study). Examples are Hume's Principle:
for all A and all B, the number of As = the number of Bs iff the As are 1-1 with the Bs,
and Basic Law V:
for all A and all B, the extension of A = the extension of B iff A is coextensive with B.
(The latter's not a particularly popular abstraction principle, since despite sounding obviously true, it's basically a principle of naive comprehension for sets.)
Interestingly, the keywords for the review include 'Health-related quality of life', 'Mental health', and 'Physical health'. Good to see Roy and Philip showing once again that the common mis-perception that philosophy of mathematics is cut-off from real-world, real-life concerns is bogus.