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SB = Sean Barker
PH = Pat Hayes (02)
Re: http://ontolog.cim3.net/forum/ontolog-forum/2007-08/msg00269.html
CC: Arisbe List, Inquiry List, Ontolog Forum, Semantic Web List (03)
SB, addressing PH: (04)
SB: You evidently have not done a course in geometry where every
theorem starts with the assumption "if 2 not-equal-to 0".
This leaves mathematicians permanently scared [scarred?]
with the idea that pure mathematics is a formal system
independent of reality -- "a game played this way" if
you like -- and it is the job of applied mathematicians
to identify the formal apparatus that can be used to
model some aspects of reality. This is not to say
that the mathematics cannot apply to reality,
but rather that it is sometimes tricky to
work out which parts it applies to. (05)
SB: Perhaps the question keeps arising because there is
a fundamental difference in assumptions/perceptions
between the different religions of mathematics and
logic (to wander into another thread)? (06)
Sean, (07)
Funny you should mention it, because I happen to have spent the
last quarter century working in a branch of geometry where 2 = 0,
and it has a lot to do with the "ecclesiastical rapprochement" of
logic and mathematics. (08)
Vide: http://www.centiare.com/Differential_Logic_and_Dynamic_Systems
What I am calling "Differential Logic" here is in many respects just
Differential Geometry in Characteristic 2. (09)
Jon Awbrey (010)
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o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o (011)
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