Jim,

I've gone through Millican and Wolfram more closely, and I think I have a better grasp of what's going on.

My original concern was that Millican (following Wolfram) talks about analyticity as a property of sentences, and not statements.  I couldn't see how this made sense.  Strawson regards the meaning of a sentence as how that sentence is (or could be) used, where statements are how sentences are used in particular cases.  Truth and falsity are properties of statements, not sentences.  Since analyticity is truth by virtue of meaning, I thought only statements could be analytic.  For we cannot say a sentence is true by virtue of its meaning, if sentences cannot be true or false to begin with.  Thus, the entire discussion seemed to me to be based on a misunderstanding of the sentence/statement distinction.

But now I think I was looking at this the wrong way.  For, if analyticity were a property of statements, then it would depend upon the particular occasion of a sentence's use.  Yet, we do not say a sentence is analytically true by virtue of the context in which it is uttered, unless we mean the rules of discourse which determine the sentence's meaning as such.  Indeed, it is by reference to the rules of discourse that we identify analyticity.  An analytic sentence is such by virtue of the meaning of its terms, and not by their use in any particular case.  If we take a Strawsonian approach to sentence meaning, we can then say that an analytic sentence is one with a meaning such that it can only express true statements.  This meaning entails the truth of whatever statement it can be used to express. 

This is how Wolfram regards analyticity, and I think it makes sense, with one qualification.  As I pointed out much earlier in this discussion, the sentence "nine is greater than seven" (let's call this sentence T) can be used to express a synthetic judgment:  namely, that one much prefers the number nine over seven.  Such a statement need not be true.  So it is not true that T can only be used to express truths.  I doubt that any natural language sentences can only be used to express true statements.

It is not that a sentence is analytically true if it can only be used to express true statements.  Rather, as I initially thought, sentences cannot be analytically true.  Only propositions can be analytically true, and propositions are neither sentences nor statements by Wolfram's account.  Two sentences express the same proposition if they have the same meaning--that is, if they have the same rules, habits, and conventions for their use.  That is, two sentences express the same proposition if they could be used in all the same ways.

The same sentence can express multiple propositions, not all of which are true by virtue of the language.  The fact that T can also mean "nine is better than seven" indicates that the same sentence has both analytic and synthetic meanings.

So my initial concern has been alleviated, I think.  There's also the issue of distinguishing between analytic and synthetic meanings.  For, how do I know the utterance of a sentence is an application of its analytic meaning, and not some other meaning?  To understand this, we need to understand what it means for the meaning of a sentence to entail that it can only be used to express true statements.  Clearly, analytic propositions cannot be used to express statements which depend on extra-linguistic factors for their truth.  Further, they cannot be used to express statements which refer to linguistic factors which are not implicated by the proposition itself.  (For there are many statements about linguistic rules which can be false.)  Analytic propositions must indicate the very linguistic rules that give them meaning, and nothing else.  To say that the use of a sentence is an application of its analytic meaning is therefore only to say that what is asserted is the rules of the language, and nothing else.  For a proposition which can only be used to express true statements is a proposition which can only be used to make its own rules explicit.

There is one other issue:  I still don't see how "The number of planets is greater than seven" (let's call this sentence S) refers to the number nine.  S expresses the same proposition as "the planets number more than seven," where the subject is "the planets," not a number.  We could express the same proposition by saying "the planets are greater than seven."  The noun phrase "the number of planets" misleads us into thinking that the number is the referent, when it is really the planets.  This is why the two statements in Quine's 'Necessity Argument' do not express the same proposition.  Thus, regardless of the strengths or weaknesses of Wolfram and Millican's responses to Quine, I do not think his Necessity Argument poses much of a threat here.  I still think I was right to point out that S does not mean T.  For the two sentences do not have the same rules and habits of use, and so do not express the same proposition.  Sentence S has no clearly analytic meaning, while T does.

I agree that Wolfram and Millican's arguments might be worth considering, even if they are not required to overcome Quine.  Though my interest here was more to do with how to interpret Strawson, and how to preserve both the sentence/statement and analytic/synthetic distinctions.  I feel content with the way this all looks, at least for the time being.  So thanks again for the help.  I needed that push to get me to look closer at what Wolfram was doing.


Regards,

Jason
Nov. 20, 2009