Paul,

I think it is slightly a misconception to say that the rules of logic/mathematics exist unless we define the term 'exist'. By that term in this instance I am saying that they exert causal powers onto phenomenal reality (for a certain class this phenomenal reality may not be physical but in the minds of mathematicans and logicians). The rules themselves are not phenomenal.

Thus, the rules that 'exist' (i.e., exert causal function) are simply those rules that obtain. That is, a rule obtains if it properly corresponds to the picture that it creates (for example, the equation of a circle properly corresponds to the phenomenal depiction of a circle). It should also cohere with all the other rules that 'exist'. If it cannot be found to cohere, then of course the rule becomes at least questionable. If the lack of cohering becomes sharp enough, then it becomes paradoxial which may or may not be resolvable (at least by humans). If genuine paradoxes of math and logic hold (i.e., not resolvable by any effort conceivable) then this would imply that the logic that disacknowledges paradoxes is either a restricted case of a much more permissive logic reality or that my whole platonist concept is totally thrown in the dumpster!

Warm regards, Harv

• Hoyle has done it - paulm - May 9, 2001 - 00:02 UTC