The Varieties of Extensionalism

For those who ascribe to such a "unity of science thesis", the correlate to this claim in the philosophy of language is that any sentence in a non-extenuional language is translatable (without loss of meaning) into a sentence in some extensional language. While such a reductionist thesis may appear guite radical (indeed, let us refer to it as "radical" extensionalism), a lot depends upon what is to count as an extensional language. Following the insights of Carnap's Meaning and Necessity, one means of defining an extensTonal language (or, in Carnap's words, an extensional system) is to say that a language is extensional just in case all of its sentences are extensional. With regards to the definition of an extensional sentence, Carnap claims that a sentence is extensional just in case the replacement of any designative component of that sentence by some other appropriately related (e.g., coreferential) designative component leaves the truthvalue of the sentence unchanged. Accepting this as an account of what an extensional language is, it follows that the rationale of one's ascribing to any sort or reductionist thesis (for the philosophy of language) turns on the rationale for claiming that there is some relation such that the substitution of appropriately related designative components does not alter the truth value of the sentence in which the substitution takes place. For Carnap this is complicated by the recognition of (at least) four types of designators: (declarative) sentences, predicators, functors, and singular terms. Carnap's complexities aside, the assumption of this paper is that the function of singular terms in extensional sentences is paradigmatic of the function of other types of designators. Hence, if one can understand both (i) what the adoption of radical extensionalism in the case of singular terms amounts to