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Date: Mon, 14 Nov 1994 04:14:05 -0500 (EST)
From: Lyle Burkhead <LYBRHED@delphi.com>
Subject: Thin-skinned Platonists
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I am amazed that Platonists of any variety would actually *take 
offense* at Dr. de Bruijn's remarks.  "What, Sir, you call us 
cheats?"  

Dr. DB has cleverly put the ball in the Platonists' court.  A Platonist 
has to admit that some mathematical creatures are not real, since 
he constructs unreal objects himself whenever he produces a proof 
by contradiction.  If he tries to retreat to D-Platonism, he has to 
say where to draw the line between what "exists" and what "does 
not exist."  The line was clear to Dedekind but it is not clear to me. 
When are you talking "about" something?  It isn't merely a 
question of integers vs. real numbers. Dr. de Bruijn has pointed out 
that there is another dimension to the problem.  Even "natural" 
numbers occur in hypothetical constructions which are designed to 
be impossible, like ants in an M.C. Escher drawing.  And yet it's all 
supposed to be part of _the real world_ !

Is it abuse to ask a Platonist to acknowledge this problem?   

Lyle