Is there anyone who has read Quine's Mathematical Logic and understands his proofs?

[phantom]

And would like to help me understand them?

I'm over halfway through the book, and I follow what he's doing, and I can read and understand most of his metatheorems, but I've just been skipping the proofs because I can't follow the ultra-condensed notation he uses. I'm not concerned with being able to derive theorems myself, but it would be nice to know that I can look at a proof and understand what's going on if I want to.

Just wonderin'...

 

[SLushhYYY]

I havnt read his book, but I just got done with taking a math logic class based on set theory etc...
Post one of his most obscure proof statements if you can, I'm curious of his contributions to it all.

 

[BigApplePi]

I havnt read his book, but I just got done with taking a math logic class based on set theory etc...
Post one of his most obscure proof statements if you can, I'm curious of his contributions to it all.

Sounds interesting. Or if you can't post the notation, do an easier one.

 

[phantom]

Here is a summary of the work if you're just interested in what he talks about: http://vserver1.cscs.lsa.umich.edu/~crshalizi/reviews/mathematical-logic/

Unfortunately it would be near impossible to type up any of his proofs. I might try to scan a page just so you can see what it looks like...

I took logic in the philosophy dept, and what we did basically followed the first part of Quine (statements & quantifiers), except some of the notation we used was different. I don't know about set theory, but I imagine his work has been very influential. I get the impression that people have adopted a lot of his principles but not all of his excessively concise notation.

 

[SLushhYYY]

Very similar to what I've learned about.

Ill do an easy proof that you can probably follow.

(c-)=subset
(x)=cross product
(E)=element of

Let A,B,C,D be sets where A c- C and B c- D. Then A x B c- C x D is true.

Proof: Assume A c- C and B c- D. We must show A x B c- C x D. Let (x,y) be an element of A x B. We must show (x,y) E C x D. Since (x,y) E A x B, then x E A and y E B. Since A belongs to C and A contains x and B belongs to D and B contains y, since we know A c- C and B c- D. Therefore x E C and y E D. Thus (x,y) E C x D. We have shown that if (x,y) E A x B then (x,y) E C x D, consequently, A x B c- C x D.