Re:Doing Mathematics Differently
by catnaroek on Friday February 26, 2016 @11:17PM
(#11186042)
Ah, lovely! You just arrived exactly where I was trying to get.
> I'm saying the meaning behind statements are different.
Yes, exactly! And, just like a single C program can have two different meanings under two different implementations, the same axiomatic system can have two different meanings when deducing its consequences (proving theorems) using different rules of inference.
> I'm saying the meaning behind statements are different.
Yes, exactly! And, just like a single C program can have two different meanings under two different implementations, the same axiomatic system can have two different meanings when deducing its consequences (proving theorems) using different rules of inference.