FOM: 'constructivism' as 'minimalistic platonism' Andrej.Bauer at
Fri Jun 9 09:19:50 EDT 2000

Fred Richman <richman at> writes:

> Jeffrey Ketland wrote in a reply to Peter Schuster:
> How do mathematicians use such statements? At some point in a proof
> they might have an integer n > 1. This will not in general be a
> specific integer, like 88001, about which they might conceivably say,
> "88001 is either prime or composite, but I don't know which". They
> might say, "either n is a prime, or n = ab for integers a,b > 1", then
> proceed to argue in each of those two cases. The idea that they do not
> know which alternative holds would make no sense to them in this
> situation. It's not like the case of 88001. Here they don't even know
> what n is, so how would they know if it were prime or composite?

You chose a bad example. It is constructively valid that every natural
number is prime or a product of numbers larger than 1.

Try something like this instead: every real number x is negative or non-negative.

Andrej Bauer

Graduate Student in Pure and Applied Logic
School of Computer Science
Carnegie Mellon University

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