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 singl

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.