Re:Doing Mathematics Differently
by catnaroek on Friday February 26, 2016 @09:38PM
(#11185802)
What you're saying is more or less equivalent to “two C implementations targeting different [architectures / operating systems / whatever] are actually implementations of two different programming languages”.
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No, I'm saying the meaning behind statements are different. On some architectures, an int is 16-bit, on others 32-bit.
Anyway, this analogy was pushed too far a long time ago.
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.