Two excellent quotes from John MacFarlane’s thesis:
“In his introduction to Model-Theoretic Logics, Jon Barwise suggests that those who draw a line between ‘logical concepts’ (i.e. the constants of first-order logic) and other mathematical concepts are ‘…[confusing] the subject matter of logic with one of its tools. FOL is just an artificial language constructed to help investigate logic, much as the telescope is a tool constructed to help study heavenly bodies. From the perspective of the mathematician in the street, the FO thesis is like the claim that astronomy is the study of the telescope.’
And in a footnote:
“Chihara points out that in Etchemendy and Barwise’s computer program Tarski’s World, the sentence ‘for all x and y, if x is to the left of y then y is to the right of x’ is given as an example of a ‘logically valid’ sentence.”
Tarski’s World and Barwise and Etchemendy’s text were what we used in my first logic class as an undergrad. I wish I still had them so I could see the idiosyncratic things I didn’t notice the first time through.

I came across these after writing the earlier post on Parsons, which made them jump out at me. I feel like there should be a discussion of Barwise’s introduction somewhere. It is delightful.

Advertisements