Re: What's the name for this?
From: Edward G. Nilges (spinoza1111_at_yahoo.com)
Date: 05/01/04
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Date: 1 May 2004 06:40:53 -0700
Torkel Franzen <torkel@sm.luth.se> wrote in message news:<vcb7jvweris.fsf@beta19.sm.ltu.se>...
> Chris Sonnack <Chris@Sonnack.com> writes:
>
> > Not as I understand it. The Philosophy of Intuitionism claims
> > some truths are indefinable.
>
> Who made this nonsensical assertion? Certainly not Brouwer.
Quite the opposite, for it is the Platonist who insists on the
"undefinable" in the sense of "real" infinities. Mathematical
intuitionism is stricter in its insistence on constructive definition.
I am attempting to set Chris straight but as you can see it is quite a
forced march.
My sourcebook on Brouwer and Heyting in particular and Intuitionism in
general was Evert W. Beth's Philosophy of Mathematics and Arthur
Korner's book of the same title. The former is I believe out of print
while the latter is still available as a Dover reprint.
Korner classifies modern philosophies of mathematics into three
general categories: Russell's "logicism", the now known to be false
belief that all of mathematics is derivable from logic, which Korner
shows is Platonism in modern dress, Hilbert's formalism, which is
confronted with serious difficulties by Godel's proof, and
Intuitionism which survives both challenges but is not well understood
in England and America because of Intuitionism's grounding in Kant.
Kant believed that entities are "out there" in the "real world", but
cannot of necessity be comprehended an sich, as such, because it is
internal to their nature to be contents of experience.
Kant's view is universally conflated in Anglo-American philosophy with
what George Edward Moore, British philosopher of the turn of the last
century, called "idealism" and claimed to have refuted in an amusing
paper, called "The Refutation of Idealism". The problem was that
insofar as Kant was concerned, Moore was beating a straw man because
Kant believed that things are "out there", but always as contents of
experience.
A relation to computer science is that hero computer scientist
Dijkstra, and to a great extent hero computer scientist Wirth, were
conscious or unconscious Kantians owing to an Continental education.
Dijkstra, realizing that while mathematical truth is independent of
the mind, also realized how it would no longer exist in a meaningful
way without our experiencing truth through the medium of mathematical
PROOF. This makes the truth of mathematics no different from
scientific truth and sensory experience, for as anti-nuclear activist
Jon Schell pointed out, after a thermonuclear exchange, the sensual
world, a republic in his phrase "of insects and grass" would no longer
exist apart from the experience of the dead.
Wirth's 1974 book Systematic Programming was equally a constructive
effort to show how systematic programs could manifest their own truth,
considered as correctness, in the labor process of their construction
in Pascal.
Both were more or less steam-rollered by Anglo-American domination of
software and anti-intellectualism and it appears neither realized how
philosophical culture in both America and Britain has been corrupted
by slack-jawed, drool streaked empiricism.
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