Thursday, May 24, 2018

Eric Temple Bell predicted Karl Seldon [sort of].

Eric Temple Bell predicted Karl Seldon [sort of].

Dear Readers,

Eric Temple Bell predicted Karl Seldon!

He did so in 1937, well before Karl Seldon’s birth, but soon after Kurt Gödel’s proofs of the ‘“self-inconsistency OR self-incompleteness”’ of any mathematical axiomatic systems capable of formulating at least “Natural” Numbers arithmetic, or more.  It was such theorems -- by Gödel, by Löwenheim and Skolem, etc. -- that launched what Seldon calls “the [then-inadvertently] dialectical, immanent critique, or self-critique, of modern mathematics.”

Eric Temple Bell stated this prediction in chapter twenty-five of his famous book on mathematics history, and of mathematicians’ short biographies, entitled -- with all of the male chauvinism of his times -- Men of Mathematics:  The Lives and Achievements of the Great Mathematicians from Zeno to Poincare”.  No mention of Hypatia here, not to mention of Sophie Germain, or of Emmy Noether, or of Sofya Kovalevskaya.

Chapter twenty-five, “The Doubter”, contains Bell’s short biography of the arch anti-Cantorian, Leopold Kronecker.

Bell’s prediction of the core ‘biography’ of our Karl Seldon is stated in a single paragraph on page 469 of that book, the third page of that chapter, as follows --

Kronecker’s university career was a repetition on a larger scale of his years at school:  he attended lectures on the classics and the sciences and indulged his bent for philosophy by profounder studies than any he had as yet undertaken, particularly in the system of Hegel.  The last is emphasized because some curious and competent reader may be moved to seek the origin of Kronecker’s mathematical heresies in the abstrusities of Hegel’s dialectic -- a quest wholly beyond the powers of the present writer.  Nevertheless there is a strange similarity between some of the weird unorthodoxies of recent doubts concerning the self-consistency of mathematics -- doubts for which Kronecker’s “revolution” was partly responsible -- and the subtleties of Hegel’s system.  The ideal candidate for such an undertaking would be a Marxian communist with a sound training in Polish many-valued logic, though in what incense tree this rare bird is to be sought God only knows.[italics emphasis added by M.D.].

Thus, Eric Temple Bell predicted Karl Seldon -- sort of.

Indeed, the NQ arithmetic/algebra for dialectics, discovered by Karl Seldon on 7 April 1996, can be well-described, in its interpretation as a contra-Booleanarithmetic, with a contra-Boolean algebra, not merely as a “many-valued logic”, but as a potentially infinivalentalgebraic dialectical logic, and, moreover, as a potentially infinite-dimensional logic, both in terms of something like Aristotle’s concept of potential infinity, not actual infinity à la Cantorian mysticism.

Much of the work of Karl Seldon, and of his collaborators, including work by yours truly, is available for free-of-charge download via --


Miguel Detonacciones,
Member, F.E.D.,
Officer, F.E.D. Office of Public Liaison

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