Thursday, July 17, 2008

Is Anything Wrong With My Ontology of Languages?

The notion of language I've been using here makes unusually fine-grained distinctions. By what criteria do I individuate languages? This is still not very clear to me, and contains some theoretical presuppositions which I’d like to make more explicit. Maybe the presuppositions are inconsistent or involve factual error. A little help figuring out whether this is the case would be appreciated. Anyway - the presuppositions.

A language has a set of wffs (or perhaps a function that assigns degrees of well-formedness to strings), so that if s is well-formed (to degree n) in L1, and not in L2, then L1 is not the same language as L2.

A language can also have a logic. We might conceive of a logic as a class of "transformation rules" in Carnap's sense. If a sequence of strings proves s in L1, but not in L2, then L1 is not the same language as L2.

A language has a semantics. In some sense, perhaps involving no platonistic ontological commitments, a language assigns meanings to sentences, words, and phrases. If x has some semantic property relative to L1, but not relative to L2, then L1 is not the same language as L2.

The meaning of a word, whatever it is (or however it is to be eliminated in favor of some less committal idiom), is sometimes derived in part from the word’s role in some larger theory. “Electron” derives its meaning, in part, from its occurrence in a central chunk of physical theory. “Phlogiston” derives its meaning, in part, from its occurrence in a central chunk of phlogiston theory. Now, “electron” occurs both in

(E) Every electron has a charge of -1

and in

(E`) Every electron has a charge of -10.

“Phlogiston” occurs both in

(P) When a flammable substance is burned, phlogiston escapes it

and in

(P`) It is not the case that when a flammable substance is burned, phlogiston escapes it.

We might suppose that “electron” derives its meaning, in part, from its occurrence in (E) but not in (E`), and that “phlogiston” derives its meaning, in part, from its occurrence in (P) but not in (P`). So there must be some special property of (any combination of) “electron”, (E), and the languages containing them in virtue of which this is the case; likewise for (P) and “phlogiston”. It can’t just be that (E) is true and (E`) is not, because the same distinction can’t be made between (P) and (P`). I don’t think it can just be that (E) is actually in physical theory, and (P) in phlogiston theory. This is because I think theories are best thought of as classes of sentences. “Electron” occurs in both physical theory and physical` theory, which is the set of sentences gotten by replacing (E) with (E`) in physical theory; likewise for “phlogiston”. If physical theory is well-formed or expressible in a language, then physical` theory is almost certainly well-formed or expressible in that language; likewise for phlogiston theory and phlogiston` theory. There is certainly something special about physical theory and phlogiston theory, and it has to do with the meanings of “electron” and “phlogiston”, but it isn’t yet clear what this special something is.

My guess about how to make it clear is basically to individuate languages more finely. Assume that languages have unique assignments of truth-values to certain of their sentences. These include the sentences from which words derive their meanings. Words can derive their meanings only from sentences which are assigned a truth-value by a language. If L1 assigns a different truth-value to s than L2, and t derives its meaning in part from s, then t has a different meaning in L1 than in L2. The hypothesis is that “electron” actually has the meaning it does in the language of physical theory in part because that language assigns the value “true” to (E) but not to (E`), and “electron” is actually used in the language of physical theory, not the language of physical` theory.* We avoid the problems related to “phlogiston” in the following way. (P`) is not incoherent or analytically false in our language. Rather it is elliptical for a complicated statement about the sub-optimality of the language of phlogiston theory. This is the language which gave and continues to give “phlogiston” its meaning. Fully unpacked, (P`) might be glossed “The language of phlogiston theory is sub-optimal because there is no worthwhile concept to which (P) lends meaning.” “Phlogiston” means what it does, and is to be unpacked this way, because it was introduced in the language of phlogiston theory, and not, for instance, the language of phlogiston` theory.

I guess the idea overall is that theories in which theoretical terms derive their meaning, in part, from their occurrence in other sentences of the theory are, as Ayer might have said, disguised linguistic proposals. Or maybe the idea is that languages are disguised theoretical proposals.

I understand that the apparatus here involves a number of assumptions, but I’m ready to take them on unless they’re controverted by fact or internal inconsistency. Well - are they?

* - I say “language”, but I allow that physical theory – the class of strings assigned certain meanings – could be conducted simultaneously in many different languages. The actual meaning and use of “electron” and other special theoretical terms might not determine a single language for physical theory, in our sense of “language”.
Update: At least one thing is wrong with this ontology. I think the epistemology of analyticity for which I have primarily made use of it is no good. Also, I don't like the ellipticality stuff. If semantic representations are mental representations, then this is way implausible.

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