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Matheology § 207
Posted:
Feb 2, 2013 4:23 AM


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 wellordering assertion is the experience of untruth}}. [John L. Bell: "Hermann Weyl", Stanford Encyclopedia of Philosophy (2009)] http://plato.stanford.edu/entries/weyl/index.html
Regards, WM
For older §§ of Matheology see http://www.hsaugsburg.de/~mueckenh/KB/Matheology.pdf



