Abstract:

The nature of the variable was, for Russell's generation, a metaphysical or semantic puzzle. We know that Quine was aware of this (the first dissertation written under his supervision was about it!). Other features of "Mathematical Logic" were designed to teach as much by example as by precept. I suggest that the axiomatization of quantifier logic in the book may have been chosen in order to demonstrate that the puzzles need not arise in formal logic.