Wednesday, May 28, 2008

A couple of quotes from MacFarlane

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.

5 comments:

Ole Thomassen Hjortland said...

Hi Shawn,
Another interesting post-Quinean view on the relationship between logic and math can be found in Shapiro's book on second-order logic (Foundations without Foundationalism). I suspect he might be heavily influenced by Barwise.

Richard Zach said...

Funny, two telescope quotes within a week. The other is by Williamson.

Shawn said...

Ole,
I will have to check that book out. This is the third or fourth recommendation to read it that I've gotten.

Richard,
There is also that Naming and Necessity quote by Kripke about possible worlds and telescopes. Maybe really smart philosophers have a thing for telescopes cause they all got them as children or something.

Ole Thomassen Hjortland said...

Wait a minute. Isn't there a telescope and moon example from Frege? Correct me if I'm wrong.

Shawn said...

Yeah. I think it is in "On Sense and Reference". He talks about not confusing the image of the moon in lens of the telescope with the moon in space as a way of explaining sense and reference. I think it is by way of trying to explain how one can maintain some sort of objectivity even though sense seems subjective.