Destroy the list's faith in Mike? Easier might one try to destroy its faith in the Law of the Excluded Middle.
Well, thank God. Of course, constructive mathematicians do indeed reject the Law of the Extended Middle (LEM). But this does not mean they accept its negation! Unfortunately, many ordinary mathematicians seem to think precisely that, and so naturally they conclude that constructive mathematics is garbage. In fact, both classical and constructive mathematics prove quite easily that the negation of LEM is false. So what do constructive mathematicians believe?
Thanks for the instructive account of what those crazy folks do believe. (They seem to believe that mathematics is set theory when you get right down to it.) Constructivists, I understand, don't allow reductio proofs either, proofs that prove a proof by assuming the negation of the conclusion and then deriving a contradiction. They probably don't allow them because if you write the word 'proof' over and over it begins to look like a senseless string of marks and not like a real word, a phenomenon which I have often noticed. Proof. Proof proof proof.
No, I'm with Frege, who was with Plato, in thinking that numbers are objects. The numeral 7, or VII, both have the same referent, namely, the NUMBER seven. If these numerals don't refer to anything then the sky's the limit and we can look at mathematics as no more than the manipulation of marks on a page (stone tablet, chalk board), so that half of four would be 'fo' or 'ur,' and so on. Let the constructivists construct away; their labors are to reality as the shadows on the wall of the cave are to a real pig in real clover.
Besides, if mathematics consisted of what I could construct, there would be no mathematics. QED.
Robert Paul Cantor Professor of Really Big Numbers Mutton College Sheepskin NE ------------------------------------------------------------------ To change your Lit-Ideas settings (subscribe/unsub, vacation on/off, digest on/off), visit www.andreas.com/faq-lit-ideas.html
