the boundaries of language

I'm currently rereading Hawthorne's Knowledge and Lotteries, and I spotted something in a footnote that I remember finding interesting first time round. (I apologise in advance for my numerous and horrendous use/mention confusions throughout - I'm not even going to attempt to fix things).

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.

References

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.

Labels: Epistemology, John Hawthorne, Mark Sainsbury, Philosophy of Language