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Topic: Monk's definition of mathematics
Replies: 15   Last Post: Aug 3, 2013 11:01 PM

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Posts: 910
Registered: 3/9/08
Re: Monk's definition of mathematics
Posted: Jul 30, 2013 3:16 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

> From time to time a definition of what mathematics
> s is is offered or
> requested--I don't know why. Here is one due to
> Donald Monk:
> As a tentative definition of mathematics we may
> may say it is an a
> priori, exact, abstract, absolute, applicable and
> and symbolic scientific
> discipline.
> [Foot of page 1 of J. Donald Monk, Mathematical
> logic, GTM 37]
> It might be amusing to identify seven things which
> aren't mathematics
> that satisfy all but one (a different one in each of
> the seven cases) of
> - a priori,
> - exact,
> - abstract,
> - absolute,
> - applicable,
> - symbolic,
> - scientific;
> thereby demonstrating their independence. Actually,
> the definition of
> scientific is just as controversial. On page 2 op.
> cit. Monk explains
> that by absolute he means 'not revisable on the basis
> of experience.'
> (The book arrived today, and it's going to be a tough
> read. If I need
> any help I will, of course, seek it in one or both of
> the scis dot logic
> and dot math.)
> My second thought (the first related to 'scientific')
> was that
> 'symbolic' is nugatory: every discipline uses written
> language, and the
> special symbols of mathematics are just taking the
> place of words in
> natural language ((i)for reasons of brevity and (ii)
> for
> understandability among people who use different
> natural languages, I
> suppose).
> Third thought: absolute seems to rule out the
> possibility of a published
> result being found to be wrong subsequently. I
> suppose it depends on
> what one means by experience.

As every human activity, mathematics is a "would be"
which is distorted by reality.

Han de Bruijn

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