Is Peano Arithmetic Essential for Understanding the Logic-Math Connection?

[robertjford80]

It seems that learning PA is necessary if you want to understand the relationship between logic and math.

Should I track down this book at the library, a chore which will take up an hour of my precious time

The principles of arithmetic, presented by a new method" in Jean van Heijenoort, 1967. A Source Book in Mathematical Logic, 1879–1931. Harvard Univ. Press: 83–97.

Or will this pdf I found on the internet serve the same purpose?

http://ocw.mit.edu/courses/linguist...pring-2004/lecture-notes/peano_arithmetic.pdf

 

[jgens]

It seems that learning PA is necessary if you want to understand the relationship between logic and math.

Logic is not my particular area of expertise, but I imagine the level of understanding needed depends on where exactly your interests lie. There are large parts of mathematical logic that depend little on a deep knowledge of PA.

Or will this pdf I found on the internet serve the same purpose?

Unless you have some prior grounding in logic some parts of that pdf will probably be rough going. It mentions connections to model theory and second-order logic at the end, and while it does not appear to require anything especially deep from either, some understanding will undoubtably be missed without it.

 

[robertjford80]

I already took a look at it. I keep putting the cart before the horse. I have three books on intro to proof theory and three books on intro to set theory. I'm going to read those first before I give mathematical logic a second shot because my first shot at mathematical logic resulted in failure.