Monday, October 30, 2006

Boghossian on Epistemic Analyticity

I'm posting the nearly-final draft of my paper on Boghossian on Epistemic Analyticity. Comments welcome. The paper upholds the objection that knowledge of meaning through implicit definition cannot be a source of a priori knowledge, since in order to use implicit definitions, one must already know the propositions knowledge of which we are trying to account for. This claim itself is not new, but I aim to do four new things: firstly, drawing on some recent work by my former colleague Philip Ebert, I put a new structure on the objection, showing how it works on either of two possible readings of one of Boghossian's premises. Secondly, I argue that Boghossian's recent attempts to answer this sort of objection are unsuccessful. Thirdly, I offer some new side-objections to Boghossian. Finally, I resist Ebert's reasons for thinking what's wrong with Boghossian's argument is that it fails to transmit warrant (and also explain how the objection I defend is different).

Update: The link now points to a new draft, changes to which have been based in part on the discussion in the comments on this post.

11 comments:

Daniel Elstein said...

Hi Carrie,

Interesting paper! I tend to take Boghossian's side in this debate, so I found what you say really helpful in understanding what people find unacceptable about his argument. I'll sketch a response that perhaps wouldn't be acceptable to Boghossian himself, so apologies if this is less than 100% helpful...

I suppose the crucial point is Bonjour's: that in order to take S as implicitly defining a term within it I must already know that S is true on its intended interpretation. I'm happy to grant that. But you continue his point in a way I find dubious (p7): "We must first know that the proposition S expresses on a certain interpretation is a true proposition, in order to see that this interpretation is the intended interpretation. The question then is: how do we explain this apparently prior knowledge of the truth of the proposition which S expresses on the intended interpretation?"

This seems to me not to follow. Suppose I am simply told that S is true on its intended interpretation i.e. somebody says to me, "S is true on its intended interpretation." That does not involve my first knowing of the proposition which S expresses that it is true, and thus it does not involve my knowing that 4 is true.

If I understand the moves in the paper, this kind of response goes with a de dicto reading of 2. And you say that this is insufficient to avoid the objection, because I cannot disquote without knowing the meaning of 'and' (p12): "If our understanding of 'and' rests on our knowledge of 4 (as it does if 'and' is implicitly defined and the BonJour point is correct), then the disquotational step cannot be made except by someone who already knows 4." I find this confusing: it seems to me that it is only on a de re reading of 2 that Bonjour's point shows that our understanding of 'and' rests on our knowledge of 4.

Perhaps the problem is that your gloss of Bonjour (p7) - "But this process of interpretation would seem to require that we already know that S is true on the intended interpretation of the terms" - itself admits of both de dicto and de re interpretations. I can just about hear a de re reading of this, so that it says that we must already know, on the intended interpretation of the terms, that S is true. That might do the work required, but I don't find the claim plausible read in that way. Was this the intended reading? And if so, why should we believe that, rather than what is expressed by the de dicto reading?

I might have more to say, but right now I'm stuck trying to figure out exactly what Bonjour's point is and how it's meant to show that understanding of 'and' rests on knowledge of 4.

Carrie Jenkins said...

Hi Daniel,

Thanks for the comments!

The BonJour point is supposed to work on the disquotational step however you read premise 2.

Suppose S is a sentence that is supposed to implicitly define '&'. And suppose someone tells you that S is true on its intended interpretation *and that's all you know about what '&' means*. Then in order to know what '&' means you have to work out which interpretation makes S true. Suppose you notice that it's interpretation I. That requires you to know that the thing S expresses on interpretation I is a truth. Knowing that it is a truth is what enables you to see that this is the intended interpretation.

Does that help at all?

Daniel Elstein said...

Thanks, that helps. I'm worried that the point simply assumes that there is some understanding of the meaning of '&' to be had that goes beyond the knowledge that the sentences which implicitly define it are true on their intended interpretations. In other words, there has to be some way of describing the intended interpretation I other than giving the inference rules for '&'. I'm inclined to doubt that this is so. (And might it beg the question against Boghossian to assume that we do have some other grasp of the meaning of '&'?).

If our only grasp of the meaning of '&' is knowledge of the truth of the implicitly defining sentences, then we are entitled to the disquotational step. For Ebert's demand was that we understand the sentence we are disquoting, and if 1 and 2 constitute this understanding they thus entitle us to disquote. Only by assuming that our understanding is not so constituted could you find a problem with the disquotational step.

This may be connected to your comments regarding Mentalese (though they seem to focus on a different point). You could reply that we do have an alternative way of grasping the intended interpretation of '&': it is the same as that of 'and'. If the metalanguage and object language are genuinely distinct, then this route will always be open. But I suppose that this was always obvious; the question is how you learn the meaning of the constant for conjunction in the first language you learn that possesses such a constant (I don't think that Boghossian was being misleading by giving his examples in English - it's hard to give examples in Mentalese). Perhaps you intend that we can grasp the meaning of 'and' pre-linguistically. If so, then you are committed to denying that there is a language of thought, and to holding that our non-linguistic thoughts are nevertheless capable of possessing logical structure (so that we can entertain non-linguistic conjunctive thoughts). This seems sufficiently mysterious to make it reasonable to believe in Mentalese implicit definition as an alternative.

Carrie Jenkins said...

Interesting ...

But there must be more to our understanding of 'and' than seeing that 'P and Q' implies 'P' (plus the other rules).

For one thing, we distinguish the meaning of 'and'-involving claims from that of other logically equivalent claims, which by the lights of your proposed view it would seem we can't do. If all that goes into our understanding of 'and' is our accepting that 'P and Q' implies 'P' (plus some other implication facts like this), nothing settles whether we understand 'and' as taking us to the conjunction of 'P' with 'Q', *or* to the conjunction of 'P' with 'Q' and with itself. But clearly this matter *is* settled.

Daniel Elstein said...

Well, once I have a connective for conjunction defined by the relevant inference rules, I can see that P & Q is equivalent to P & (Q & P), in that the rules for '&' license their inter-derivability. So at that point I can settle the matter. Presumably you will object that I might *originally* have meant P & (Q & P) when I said 'P & Q', in which case the distinction I end up making is really between P & (Q & P) and an even more complex formula.

But we can rule that possibility out as follows: the inference rules allow me to grasp an equivalence class of connectives; I can see that any connective within that equivalence class can be iterated in a way structurally identical to the above iteration (because the rules license it); I can thereby grasp the idea of a connective within that equivalence class which is not to be understood as involving the iteration of any more basic connective; and I am told that this is the intended interpretation of the implicitly defined term; so my understanding of '&' determines that & is the intended interpretation.

That doesn't seem like too much of stretch, because when you ask how I know that I mean P & Q rather than P & (Q & P) when I say 'P & Q', my only answer is that I intended '&' as a basic connective, and I would explain that in the above way (perhaps there's a simpler way of explaining it, but I don't see it right now).

Carrie Jenkins said...

What about logical equivalents which are not attained through iteration? E.g., P&Q is (classically) logically equivalent to ~P/~Q.

Daniel Elstein said...

Once I have grasped rules for the various connectives, I can see that various sets of them (considered purely in terms of their rules) are expressively complete, e.g. {~,v}, {|} etc. The intended interpretation of '&' is as a basic connective (not involving the combination or iteration of more basic connectives) in a system involving only '&' and '~', and mutatis mutandis for the other connectives. So in particular the interpretation of 'P & Q' as ~P / ~Q is excluded, since this would not allow for a system taking only '&' and '~' as basic.

Carrie Jenkins said...

So you presuppose a grasp of '~' in the definition of '&' and the other connectives? How will '~' itself get defined?

(Also, there are worries about whether the required notion of 'basicness' is sufficiently robust, or whether it is comparable to the sense in which 'blue' and 'green' are the basic notions for you and me but 'grue' and 'bleen' are basic for gruesome folks.)

Daniel Elstein said...

My idea is that the connectives can be partially defined individually, though this only gets down to the level of an equivalence class of possible interpretations that satisfy the rules and which do not involve iterations of the connective being defined. For '/' and '|' we can give full definitions individually. The definitions of the other connectives have to be made precise all at once, or at least in pairs.

I suppose you can worry about how robust basicness is. But we're looking at this problem in different ways. For you, we're considering problems with one particular way of explaining our grasp of the meanings of the logical connectives. But since I don't see any alternative way, your arguments seem like sceptical arguments, to the effect that we don't attach fully determinate meanings to the connectives at all. So if I thought that the story I've outlined involving basicness didn't work, I might retreat to a Lewisian story about eligibility to lock down the meanings (though I can't see how that would work right now). Another possible line is that we can back up basicness by appeal to Boolean logic gates in electronics as physical manifestations of the connectives; and there the world supplies determinacy. But how can I tell that the AND gate is a manifestation of '&'? Surely because I thick of '&' as basic...

Vanessa said...

Hi Carrie,

I just tried to download your Boghossian-paper, buth it is obviously a broken link. Could you tell me the actual link?

Carrie Jenkins said...

Sorry about that - it's fixed now. I was putting up a new version, and only got as far as taking down the old one!