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Quine and the Meaning of Meaning

January 21, 2012

I just finished reading “From a Logical Point of View” by W V O Quine, an analytical philosopher. Having been published in 1953, I was surprised by the extend to which it’s perspective on language resonates with Chomsky’s. For example, they agree that (1) language makes infinite variety of a finite medium (2) we can see language as an either/or system, utterances are either in the language or not; there are no “fuzzy” cases, “the middle” is excluded”; (3) we can understand the structure of language while ignoring language change. (By the way, I disagree with points (2) and (3).) Chomsky certainly did much for linguistics by showing the problems with the Skinnerian paradigm and adapting the mathematics of recursion to the study of syntax. But perhaps there was less of a philosophical jump then I realized.

I am most interested in Quine’s exploration of meaning as interchangeability orsubstitutivity. For example, “bachelor” means “unmarried man” in so far as one phrase can be swapped out for the other in a sentence like:

George Clooney is a bachelor.

But we quickly run into problems, because such a swap isn’t always possible. The following sentence is acceptable:

The word bachelor has eight letters.

But not:

The word unmarried man has eight letters.

So we have to distinguish between words as words and words as referring to concepts. “Bachelor” can be substituted for “unmarried man” only when their being used to refer to their concepts.

Here’s another problem: Bob and Tom could agree that “Morning Star” refers to a particular concept and “Evening Star” refers to a particular concept, while Bob believes that both concepts refer to the same physical object, and Tom doesn’t. So do “Morning Star” and “Evening Star” mean the same thing? Quine thinks we have to choose and says no, meaning must be restricted to substitutivity due to conceptual equivalence.

Quine goes through more problems (and articulates them better than I can), and deals with them by either reducing what is meant by meaning or piling on more vocabulary to the metalanguage through which we hope to understand language. The latter approach is ad hoc and the former, where the concept of meaning is reduced, will eventually get you to the disquotational theory of meaning, where the meaning of “snow is white” is that snow is white.

Other writers have pointed out wider problems with substitutivity, such as that any two phrases you like will always have subtle differences in meaning. For example, no one would object to:

The Pope is an unmarried man.

But some would not accept:

The Pope is a bachelor.

I believe all these problems are rooted in substitutivity being too blunt a tool. Some refinement is needed. When can what be substituted with what? Here, a little formality goes a long way. Before I give my definition of meaning, some notation will be needed:

Let V be the vocabulary/lexicon/set of all words in our speaker’s language.

Let S be the set of sentences that would be accepted as true by our particular speaker at a particular time.

Let S_w be the subset of S consisting of those sentences that contain the word w.

Let P(S_w) be the powerset of S_w. That is, the set of all subsets of S_w.

For sentence s and words w and u, let s[w->u] be the sentence s with the word u swapped in for the word w. For example, if s is “the house is blue” then s[“blue”->”green”] is the sentence “the house is green.”

Okay, now let’s define the meaning of a word w with a function f_w from V to P(S_w), such that f_w(u) is the subset of S_w such that for every sentence s in in that subset, s[w->u] is also in S. That is, s[w->u] is accepted as true. Note the duality: If s is in f_w(u) then s[w->u] is in f_u(w). Now distinctions like word/concept/physical reference are embodied by our definition of meaning instead of underpinning it.

Where is the word that will unwind the word? O language! I am quite agitated with desire to understand you. I can’t sleep; I forget to eat. Language: Undress. I want to see you in your beginning.

Here are some lines from Dickinson that I posted yesterday, but today for ‘Grace’ I read ‘the historical emergence of language’ and for ‘every Dawn’ I read ‘the individual’s acquisition of their language’:

“Old the Grace, but new the Subjects —
Old, indeed, the East,
Yet upon His Purple Programme
Every Dawn, is first.”

Oh, language. I am quite exhausted by my desire to understand you.

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