FOM: Krönecker...Reply to Schuster

Matt Insall montez at
Thu Feb 24 11:59:10 EST 2000

Peter Schuster said:

>Therefore I think that Kronecker's
> view is by no means a purely historical matter.

I agree.  No prominent Mathematician's view on what is ``given'', what is
or what is or is not Mathematics is a ``purely historical matter''.  (Almost
nothing is purely
anything when you get down to talking about what is, or should be,
considered Mathematics,
or Foundations of Mathematics.)  The effect that Krönecker had on
Mathematics during his life was enormous, and this is not just historical
material, but helps determine what the Mathematical Community is like today.
Such ``historical matters'' have significance for FOM also because his
comment was, I daresay, probably intended as a part of his unrelenting
criticism of Cantor and set theory (cf. Dauben's book about Cantor), which,
again, lends a precendent to today's finitists, who would, I guess, even
deny the rational numbers' existence for similar reasons that Krönecker
denied the real numbers and transfinite ordinals' existence.  The way
Krönecker said what he did may be ``purely historical'', but his intent,
philosophical position, and effects on all of (the foundations of)
mathematics are, IMHO, reflected in this one statement about the rational
numbers as opposed to everything else in Mathematics.

Matt Insall
Associate Professor
Mathematics and Statistics Department
University of Missouri - Rolla
insall at
montez at

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