Re: Mathematical Logic, Podnieks'page ...

From: Kory Heath <kory.heath.domain.name.hidden>
Date: Fri, 02 Jul 2004 16:10:19 -0400

At 02:45 PM 7/2/2004, Jesse Mazer wrote:
>As for the non-constructivism definition, is it possible to be a
>non-constructivist but not a mathematical realist? If not then these
>aren't really separate definitions.

It may be that all non-constructivists are mathematical realists, but some
constructivists are mathematical realists as well (by my definition of
"mathematical realism"). So "Platonism == mathematical realism" and
"Platonism == non-constructivism" are two different statements. I can
imagine a non-constructivist asking "Are you a Platonist?" (thinking "Do
you accept the law of excluded middle?"), and a constructivist answering
"Yes." (thinking, "yes, valid constructive proofs are valid whether or not
any human knows them or believes them.") This miscommunication will lead to
confusion later in their conversation.

-- Kory
Received on Fri Jul 02 2004 - 16:21:58 PDT