Re: What is a proof, exactly?

From: Han de Bruijn (Han.deBruijn_at_DTO.TUDelft.NL)
Date: 11/23/04 

Date: Tue, 23 Nov 2004 12:27:57 +0100

J.E. wrote:

>> - What is the status of "=" (equality) with respect to proofs? Is there a
>> difference between "meaning of" and "definition of"? Is "=" defined or does
>> it only have a (logical) meaning? Can we equate any two mathematical
>> objects?
>
> Honest people disagree on this issue. I prefer to define "=" as "x=y
> <=> (Az (zex <=> zey))", the main rationale for having a different
> status for "=" is that in general set theory axioms aren't enough [ ... ]

I suppose you mean: x equals y iff for all z (z is an element of x iff
z is an element of y). But how then do you equal objects which are not
sets? And what do you mean by "Honest people disagree on this issue" ?

Han de Bruijn

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