Striven with the Infinite. Philosophical and religious aspects of the George Cantor set theory genesis

1. Entity type Lemma
2. Original titleБоровшийся с бесконечным. Философско-религиозные аспекты генезиса теории множеств Георга Кантора.
3. Language term Russian
4. lemma author Saprykin, Dmitry
5. lemma category History and philosophy of science
6. Publication date 1999
7. lemma work Striven with the Infinite. Philosophical and religious aspects of the George Cantor set theory genesis
8. lemma manifestations Боровшийся с бесконечным. Философско-религиозные аспекты генезиса теории множеств Георга Кантора. Москва, Мартис, 1999 : Striven with the Infinite. Philosophical and religious aspects of the George Cantor set theory genesis
9. Keywords Cantor, George
10. Lemma body

    1. The work deals with the George Cantor’s set theory history and its philosophical and theological aspects. The set theory underlies school and university math course in many countries including Russia and is considered to be “the foundation” of the math theoretical basis. Many Orthodox theologians and philosophers, particularly those of so called “onomatodox” (e.g. Alexey Fedorovich Losev) took an interest in the set theory. Contradictions revealed in the set theory were viewed in the XX century as one of the most important sign of crisis of math as a science.

       The author responds to the questions: What does the set theory represent to be a “math crisis” core and what is its philosophical and theological meaning? On the other hand, what did George Cantor as the theory creator aim to achieve making his “revolution” in math, and what did he gain?

       Cantor thought of his theory to be perfectly new calculus of the infinite, a “transfinite” (that is “superfinite”) math. According to his idea such a calculus should have turned over not only math, but also metaphysics and theology which were, perhaps, of more Cantor’s interest than scientific investigation itself.

       Indeed, almost all the previous mathematical, philosophical and theological tradition considered attainment of the actually infinite to be unobtainable by the human finite mind. Many great intellects headed by Aristotle went on denying not only cognoscibility, but the very existence of the actually infinite values as well (e.g. infinite spread or infinite number). They admitted only potential infinity consisting e.g. in perpetual adding unity to the numerical series.

       Cantor was the only mathematician and philosopher who considered actual infinity not only existing in the created world, but also being entirely conceivable by man. In order to prove this point of view he carried on struggling over decennaries with almost all the contemporary philosophers and mathematicians, even the great ones, as Helmholz, Kronecker and Cauchy who denied the legitimacy of constructing math on the base of actual infinity.

       What was to inspire Cantor in his struggling? Vladimir Katasonov distinctively displays that a rather odd metaphysical and theological conception formed the basis of the set theory creator intellectual aspirations (by the way, he kept on continuous arguing on it with the famous Catholic theologians, cardinal Franzelin and Gutberiet). Formulating roughly his idea we may say Cantor viewed the deduced in his theory sequence of transfinite numbers – “alefs” – as a sui generis intellectual ladder to the Absolute Infinity. Cantor postulates the existence of the whole world of infinite entities cognizable by man, and comprehension of them to raise both mathematicians and theologians upward and closer to God. Cantor had a firm belief he was chosen by God to make the great upheaval in science, and this belief was encouraged by mystical apparition of a muse who arose to ensure the mathematician in the set theory absolute verity.

       Katasonov demonstrates in his work that the theologians’ accusations of Cantor in pantheism were quite reasonable. And the discovery of the set theory paradoxes led in large part up to collapse of this pantheistic “scientific mysticism” (one of the varieties of so called “natural theology”), which was not in many ways compatible with the traditional Christian dogmatics with its “apophatism”.

       Cantor’s personal fate and his madness at the end of the life also show, according to the author, the problematical character of this route.