RTH2 – Cats and cherries

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.”