Re: Logic and math and the world

From: Dan Christensen (dchris_at_netcom.ca)
Date: 10/25/04 

Date: 24 Oct 2004 21:36:16 -0700

emailangel@gmail.com (angel b.) wrote in message news:<51d16196.0410241035.45fae0a8@posting.google.com>...
> dchris@netcom.ca (Dan Christensen) wrote in message news:<4b0c747b.0410212009.17c6fdd3@posting.google.com>...
> > "Craig Franck" <craig.franck@verizon.net> wrote in message news:<d4_cd.5166$B34.3441@trndny02>...
> > > I recently read an argument that since most people are not surprised we
> > > live in a universe in which simple logic holds true, they shouldn't be
> > > surprised math can describe the universe because math reduces to logic.
> > >
> >
> > Math and logic are purely mental constructs and are, therefore, not
> > infallible. At most, you can say only that if certain aspects of the
> > real world can be modelled by a formal symbolic system (math or
> > logic), then you can draw some fairly reliable conclusions about that
> > world.
> >
> > If you want absolute certainty, I suggest you try religion and
> > politics. ;^)
> >
> > Dan
>
> From what I've learned, it seems that logical systems which are sound
> and complete are indeed infallible. So if you can 'model' some real
> world concept using a sound and complete logical system, and you prove
> something using that system, then the semantic counterpart of that
> proof which refers to the real world concept has been proven. In
> fact, that is the definition of soundness as I understand it. Feel
> free to correct me if I am wrong.
>

Axiomatic set theory (ZFC), to my knowledge, has never been proven to
be consistent. As far as we know it works, but still there is room for
some doubt. Maybe there is another Russell's Paradox still lurking in
the shadows.

Dan
Download DC Proof 1.0 at http://www.dcproof.com

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