The invention of non-Cantorian set theory - part 2    [ part 1 ]

What he achieved can be summarized so:

• A. Tertium exclusi does not hold for transfinitudes, nor for finitudes imbedded in them.
• B. Infinities are prior to finitudes: thus mathematics precedes logic.
• C. Infinites lead to insolubilia - hence he radicalised 'arithmetics of the line' by beginning with insolubilia, viz, he substituted the Fourier-Bolzano series (as stated by B. Bolzano) for the natural numbers and positive integers. This gives contradictory sums at infinity and is thus initially paradoxical.
• D. Overbeck recognised that the negation of tertium exclusi negated identity, that is, not only for transfinitudes, but also for finitudes. As a lack of identity implies incomplete entities, it is man - not simply his systems - who is incomplete.
• E. Christ's visit to Jim Overbeck taught him man is only completed by deification - viz, by the restoration of divine energies and divine identity.

Much of the theory of deification is to be found in Overbeck's The Autobiography of God Almighty. The mathematical notebooks are added as a means of demonstrating the way through the abysses of mathematics to divinization. Like other minds ahead of their time, Overbeck is ignored by a cretinous, superficial and vicious world. 'Only horror will undo their vast stupidities, as they descend into hell'. 'They are gods and goddesses entered into subhumans, peopling themselves with rotten demons and murderously mutant impulses'.

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