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Let's Define 'rules'

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Posted by Paul R. Martin on May 8, 2001 00:48:51 UTC

Hi Alex,

I want to correct my mistakes, even if they are very common ones, so help me out.

Mathematics consists of four things: undefined terms, defined terms, axioms, and theorems.

Which of these are the 'rules'? The undefined terms are just symbols for who-knows-what. The defined terms are arbitrary and can be anything we (inventor, founder, alien, ape, etc.) choose. The axioms are also arbitrary and can be anything we choose.

The theorems are not arbitrary. They are unavoidable consequences of the definitions and axioms. Are the theorems the 'rules'?

Then there are the rules of logic that constrain how we derive theorems. Maybe these are the 'rules'?

Let me know.

Warm regards,

Paul

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