Dear Kory, an appeal to your open mind: in the question whether
...."we discovered math or invented it"...,
many state that the first version is 'true'.
Beside the fact that anybody's 'truth' is a first person decision, the fact
that anything we may "know" (believe or find), is interpreted by the ways
how our 'human' mind works - including comp and all kinds of computers, as
we 'imagine' (interpret, even formulate) the thoughts.
I find the above distinction illusorical. We may FIND math as existing
'before' we constructed it, or we may FIND math a most ingenious somersault
of our thinking.
To 'believe' that 17 is prime? of course, within the ways as we know (and
formulate) the concept 'prime'. Axioms, conventions.
With the ideas about 'quite' different universes why are we closed to the
idea of 'quite' different mathematical thinking?
We don't have to go to another universe: the Romans subtracted in their
calendar (counting backwards from the 3 fixed dates in a month) like "minus
1 = today, minus 2 = yesterday and so on.
I wonder how would've done that Plato (before the invention of 0)?
Our list-collegues think about math(s) in quite different concepts from the
classic 'constructivist(?)' arithmetical equational thinking.
how far can go a quite differently composed mind - maybe in an
organizational thinking/observing system of a universe NOT based on space -
What can be called 'mathematics'? (Theory(s) of Everything?)
Vive le 'scientific agnosticism'!
(Bruno: am I still in your corner?)
----- Original Message -----
From: "Kory Heath" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Friday, July 02, 2004 4:10 PM
Subject: Re: Mathematical Logic, Podnieks'page ...
> 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
> confusion later in their conversation.
> -- Kory