Kit Fine, Compositionality Proper and Coordination Relations

I apologize for the slight delay in the promised forthcoming posts.  I had intended to read Kit Fine's paper sooner and send him some questions/comments, but I now have suspicions that he may be sitting on NYU's admissions committee.  Since I have applied to NYU (although sadly, it appears I was not a first round draft pick), I'd rather not do anything that might be perceived as a pathetic attempt at insincere, opportunistic ladder-climbing.

At the UCSB conference, Kit Fine presented a revised version of Frege's argument in which he substituted variables for proper names.  You can see a quick sketch of Frege's original argument here.  Fine's version appeals to what seems to be an obvious fact: the cognitive significance, i.e., meaning, of "x" is no different from the cognitive significance of "y".  For the record, Fine was careful to avoid talk of "cognitive significance" when he presented, but since I just intend one to read that as "meaning", I'll use the term occasionaly for the sake of literary variation.  Now you're asked to consider the meaning of the identities "x = x" and "x = y".  Just like "Hesperus = Hesperus" differs in meaning from "Hesperus = Phosphorus", "x = x" differs in meaning from "x = y".  The same values need not be substituted for the variables in "x = y".   But if reference is the only kind of meaning, and if the meaning of a sentence is wholly a function of the meaning of its parts, how does one account for this?

Fine's answer is to deny the principle of compositionality being appealed to.  In my last post, here, I offered premise two as a gesture in the direction of compositionality: the meaning of a sentence is wholly a function of the meaning of its parts.  Now that's not exactly compositionality, of course, but I intended lines (5) and (6) of the argument to be going a long way towards giving more of the idea behind compositionality.  A full and precise statement of the principle of compositionality being appealed to in Frege's argument would involve a complicated syntactic algebra, and the rules of such an algebra will operate on the components of the sentence in a well-defined order that depends upon the structure of the sentence as the function f(x, =, y) suggests.  Obviously, the value of f(x, =, y) will not be the same as the value of f(=, x, y).  But enough of that.  Fine wishes to reject this simpler principle of compositionality (i.e., the principle Frege relies upon) for what he called "Compositionality Proper".

It's easy to see what Compositionality Proper is, but it's not so easy to see whether or not it's true.  Or, at least, whether or not it's true in way that allows it to underwrite semantic facts.  In effect, Fine wants the new compositionality function to operate not on the crude ordered sequence containing only "x", "=", "y", but rather on a more fine-grained sequence you can think of as containing subdivisions of "x", "=", and "y".  Subdivisions of variables, names, properties, etc... are created by introducing "coordination relations" as basic semantic facts.  Say that "x" can be subdivided into "x*" (x star) and "x'" (x prime). Compositionality Proper (CP) operates not over the crude variable "x", but over "x*" and "x'".  Using CP will return different values for the following functions 1) f(x* = x*) and 2) f(x* = x').  Say that (1) is coordinated while (2) is not.

Now you know have a nifty analog of Frege's argument argument which uses variables, you know which step in the argument Fine rejects, you know what Compositionality Proper is, and you've got a straightforward account of what these coordination relations are.  I consider this post a success.  (Fine's argument is reproduced solely from memory, but I think this is exactly right.)  If you want to picture these coordination relations as Fine does, think of a little strings linking the coordinated variables.  Soames humorously dubbed this "string theory".

Comments

[Madhav Gopal]

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