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Re: [ontolog-forum] Reality Oriented Logic

To: "Pat Hayes" <phayes@xxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Barker, Sean (UK)" <Sean.Barker@xxxxxxxxxxxxxx>
Date: Wed, 29 Aug 2007 09:31:44 +0100
Message-id: <E18F7C3C090D5D40A854F1D080A84CA44981A1@xxxxxxxxxxxxxxxxxxxxxx>

        Three years at Imperial, admittedly doing mostly pure, convinced
me that pure and applied maths are different and have different aims.
The question is, is this disagreement a result of syllabus studied, or
different interpretations of similar experience?    (01)

        Mills Davis cited a table on research perspectives at
spectives.jpg     (02)

I certainly identify with the Design and Interpretive columns, and view
the Positivist view as irrational and discredited (I really do need a
red rag/bull emoticon). My concern is that too many ontologies are
constructed from a naive positivist perspective, and these will lead to
people becoming disillusioned with the Semantic Web - hence also my
questions about risk.    (03)

Sean Barker
0117 302 8184    (04)

> -----Original Message-----
> From: Pat Hayes [mailto:phayes@xxxxxxx] 
> Sent: 10 August 2007 20:19
> To: Barker, Sean (UK)
> Cc: [ontolog-forum] 
> Subject: Re: [ontolog-forum] Reality Oriented Logic
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> >Pat,
> >
> >     You evidently have not done a course in geometry where 
> every theorem 
> >starts with the assumption "if 2 not-equal-to 0".
> Indeed, I have not had that particular experience, though I 
> did learn axiomatic set theory from Quine, which may have 
> been even more unnerving, since we were not even allowed to 
> assume that zero existed until near the end of the semester.
> >  This leaves mathematicians permanently scared with the idea
> Did you mean 'scared' here? If so I cannot quite follow your meaning. 
> Or did you mean 'scarred'?
> >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.
> Well, I spent 3 years at Cambridge learning parts of pure and 
> applied math in about equal amounts, and one of the lasting 
> lessons I took away with me was that they are really one subject.
> >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.
> There is a discipline to thinking about that, indeed. One 
> gets into questions of error, accuracy and dimensionality, as 
> I dimly recall.
> >     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)?
> I don't think that there is much to choose here (ie in this
> discussion) between math and logic, as they are both 
> concerned with necessary truths. And of course neither of 
> them are religions.
> Pat
> --
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