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Topic: Matheology § 207
Replies: 7   Last Post: Feb 5, 2013 10:12 PM

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Posts: 18,076
Registered: 1/29/05
Matheology § 207
Posted: Feb 2, 2013 4:23 AM
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Matheology § 207

Towards the end of his Address on the Unity of Knowledge, delivered at
the 1954 Columbia University bicentennial celebrations, Weyl
enumerates what he considers to be the essential constituents of
knowledge. At the top of his list comes
?intuition, mind's ordinary act of seeing what is given to it.
(Weyl 1954, 629)
In particular Weyl held to the view that intuition, or insight -
rather than proof - furnishes the ultimate foundation of mathematical
knowledge. {{What else should furnish it? A formal proof can be given
for every stupidity, and be it infinite.}} Thus in his Das Kontinuum
of 1918 he says:

In the Preface to Dedekind (1888) we read that ?In science, whatever
is provable must not be believed without proof.? This remark is
certainly characteristic of the way most mathematicians think.
Nevertheless, it is a preposterous principle. As if such an indirect
concatenation of grounds, call it a proof though we may, can awaken
any ?belief? apart from assuring ourselves through immediate insight
that each individual step is correct. In all cases, this process of
confirmation - and not the proof - remains the ultimate source from
which knowledge derives its authority; it is the ?experience of
truth? (Weyl 1987, 119) {{like Zermelos "proof" of the well-ordering
assertion is the experience of untruth}}.
[John L. Bell: "Hermann Weyl", Stanford Encyclopedia of Philosophy

Regards, WM

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