logic question-

I was arguing with my roomate about this. I think that logic and math are inextricably tied, and she thinks the opposite- that math is unnecessary in logic.


my thinking- why bother using words when you can just write 2+2=4.


keep in mind I never took logic in school, so be easy on me :P


There is a connection. Logic can be seen as a branch of Philosophy but also as a branch of Mathematics and Computer Science. There were some famous guys that wanted to totally "axiomitize" (is that a word?) Mathematics, so that you could deduce all mathematic true statements from some basic Logic Laws. Leibniz for example thought they were both part of a Universal language/Logic. I also think That Frege and B Russel tried to "axiomitize" mathematics on a foundation of Logic, but first of all they connected arithmetics with set-teory. However, with the arrival of Goedels Incompletness-theory, that whole project kind of died out.

This is just my 2 cents, I just read a great book of the History of Logic and I may have gotten some things wrong. Perhaps Dogbert knows more.

 

Logic is of course strongly connected to philosophy. But insofar as one can easily makes the rules of logical reasoning abstract, one can use math to examine what logic can do and what logic can´t do. Mathematics had a huge impact on logic, and there was some impact in the other direction too.

Fudo isn´t completely correct on the historical side. What has failed was the attempt to use only axioms of logic to prove all of mathematics. But by employing set theory, whose axioms can be formulated (sp?) using only logic, practically all of math can be axiomatized. What Gödel and co have shown is that set theory is either inconsistent (nobody really believes that) or that some things can neither be proved nor be proved wrong. There are some known example of this.

aha, ok

what part did I get wrong btw?

The problem is not to give a axomatic foundation of math, but a complete one.

Aha, that is true and an important distinction. Thanks

 

btw, did I tell you that I just finished a basic Logic-course (Propositional logic, notation, calculating truthvalue-tables etc)  here at Rio University. It was much more fun then I expected and I look forward very much to the continuation in a couple of weeks.

 

cool, thanks guys.

I LOVED logic when I took the class. I wanted to go there everyday it was so much fun.

The irony is that I could have just read the book and aced the exams, but why would I? It was Ed Gettier teaching. The man's a legend, and he was retiring that year. He is a total logic whiz.

Logic class rules!

~TT

"btw, did I tell you that I just finished a basic Logic-course (Propositional logic, notation, calculating truthvalue-tables etc) here at Rio University. It was much more fun then I expected and I look forward very much to the continuation in a couple of weeks."

You told once that you took such a course. Welcome to circle of cogniscienti!

Logic for everyone!

Gettier as in the Gettier problem with the justified true belief definition of knowledge?

Yep, that's Ed Gettier. He wrote that paper as an undergrad. He's a pretty cool guy--really nice.

~TT