Math Forum Discussions

Ralf Bader

Posts: 488
Registered: 7/4/05

Re: Matheology § 125
Posted: Oct 21, 2012 5:31 PM

Plain Text

WM wrote:

>
>
>
>
> Matheology § 125
>
> The leap into the beyond occurs when the sequence of numbers that is
> never complete but remains open toward the infinite is made into a
> closed aggregate of objects existing in themselves. Giving the numbers
> the status of objects becomes dangerous only when this is done. [p.
> 38]
>
> In advancing to higher and more general theories the inapplicability
> of the simple laws of classical logic eventually results in an almost
> unbearable awkwardness. And the mathematician watches with pain the
> larger part of his towering edifice which he believed to be built of
> concrete blocks dissolve into mist before his eyes. [p. 54]
>
> [Hermann Weyl: "Philosophy of Mathematics and Natural Science" (1949);
> reprinted with a new introduction by Frank Wilczek, Princeton Univ.
> Press (2009)]
> http://press.princeton.edu/titles/8960.html
>
> Regards, WM

Pure declarations of opinion are of no value and interest anyway, even if
they come from someone as knowledgeable as Weyl. However,
the second quotation is preceded by the following sentences, translated from
the 4th German edition which is based on the 1949 American edition:

"With Brouwer, mathematics achieves utmost intuitive clarity. He is able to
develop the initial steps of analysis in a natural way, keeping in much
closer contact with intuition than hitherto. But one can not deny that..."

and precisely here follows Mückenheim's quotation "in advancing ..." which
forms, together with my 3 lines, the closing paragraph of §9 of the book.

So, notwithstanding Weyl's general views, the inapplicability of classical
logic as asserted above is not a defectiveness of classical logic for the
purposes of those higher theories, but a consequence of its incompatibility
with intuitionism; Weyl in fact deplores that intuitionism doesn't have
something as easy to handle as classical logic.

To obscure and distort the context of a quotation in such a way, insinuating
that Weyl here states a failure of classical logic in higher branches of
classical mathematics, while in reality Weyl resp. the Brouwerian "ideal
mathematician" admit an awkwardness of their methods as compared to those
based on classical logic, and for this purpose even splitting up what is a
single sentence at least in the German text, I call a lying and defrauding.