Pat,
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
http://www.project10x.com/downloads/MDdownloads/Methodology/research_per
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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>
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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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>
>
> (05)
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