This is the second of my posts related to an online discussion of Putnam’s book “Reason, Truth and History”. Hence the “RTH2” in the title of this post. For the first such post, check here.
Starting at page 32 of his book, Putnam presents an argument that has come to be known as the “Cats and Cherries” argument, or sometimes as the model theoretic argument. The model theory background from mathematical logic is the Löwenheim–Skolem theorem. The theorem itself says that, under suitable assumptions, a theory might have infinitely many interpretations. If we take natural language to be a theory (as the term “theory” is used in mathematical logic), then this raises the possibility that there might be different ways that natural language words could refer to real world entities.
Putnam considers the possibility of a radical reinterpretation of the English language, such that whenever we say “the cat is on the mat” we really mean “the cherry is on the tree.”
How important is the argument?
Most people, self included, will probably see this as a silly argument. Of course, nobody is seriously suggesting that you might wake up tomorrow morning and discover that the meanings of words have somehow flipped. The argument is not intended to question our ordinary conversational use of language. Rather, it is a skeptical argument about theories of language, theories of how sentences refer to things in the real world. In that sense, it is somewhat analogous to Quine’s thesis on the indeterminacy of translation and the inscrutability of reference.
The argument is most clearly relevant to theories of language which see a language as a logical structure which somehow manages to reference things in the world. Much of the philosophy of language seems to fit that description. However, Wittgenstein’s view of “the language game” as a social practice within a culture would seem to completely escape the “Cats and Cherries” argument. It is my understanding, perhaps mistaken, that the Putnam argument is part of what led George Lakoff to dissent from Chomsky’s theory of language.
For myself, I have never thought of natural language as a logic system, nor have I ever seen any point to Chomsky’s analysis of language. So, for me, the “Cats and Cherries” argument is but a minor curiosity of no real importance.
In our discussions of the correspondence theory of truth, some of the participants did consider Putnam’s argument to be a cause for concern. I have outlined the argument here, since it is mentioned in those discussions of truth.