Clarification and CorrectionAziz Poonawalla at Unmedia has accused Bill of “lying” because of his mistaken inference about Cantor’s views on the existential reality of actual infinity. While we apologize to all of our readers of good will for this error, I submit that if one mistaken inference debars all further comment about figures or ideas, then the whole blogosphere itself would have to silent across the religious/political/cultural spectrum. I take responsibility for linking to an old “mirror-site” of Bill's that we no longer have direct editing access to, we cannot delete it so we'll make our correction public here. Please follow the new URL that Bill has provided, he’s going to edit out the sentence in question. Just so there is no confusion, let us make it perfectly clear that Cantor was a mathematical Platonist who believed in the possibility of the existential instantiation of the AI. William Lane Craig in the KALAM COSMOLOGICAL ARGUMENT states in Footnote 20 on page 156 of Part II that “Cantor did think the number of atoms in the universe might be denumerably infinite." Aziz, via Troy, posts the following from “The Continuum Hypothesis“ by Cesare Brazza from the History of Mathematics, Rutgers, Spring 2000:
"In 1862 he (Georg) had written to his father (who had just consented to his son's pursuing a career in mathematics) in order to explain that 'My soul, my entire being lives in my calling...' ". (p. 239, Georg Cantor). Cantor first attended the University of Zurich before transferring to the University of Berlin, where he received his doctorate. However, the area of mathematics which he tackled, was not immediately accept ed. Curiously, his theories were also used by the Jesuits to "prove" the existence of G-d. "... Cantor's transfinite numbers were to prove no less revolutionary for philosophers and theologians who were concerned with the problem of infinity." (p. 118, Georg Cantor). However, Cantor, who was also a theologian, did not associate himself with any of these proofs. Cantor did, however, consider himself to be an intermediary through whom G-d could communicate "these great, immutable truths" of mathemat ics. "Cantor saw his own role, as mathematician, in terms of a faithful secretary, receiving and describing what had been revealed to him by G-d." (p. 238-239, Georg Cantor). In fact, much of Cantor's beliefs in his work stemmed directly from his beliefs that the Continuum Hypothesis was derived directly from nature. "The principles of mathematics, of set theory, and the transfinite numbers, followed directly from Nature." (p. 238, Georg Cantor).Dauben goes on in “Georg Cantor and Pope Leo XIII” JOURNAL OF THE HISTORY OF IDEAS Vol. 38 No.1 1977 (pp.82-108) to point out that the Catholic theologian Constantin Gutberlet attempted to meet Kalam-style objections to the existential instantiation of the AI by pointing to the paradoxes of “the infinte duration and eternity of the world,” (p.99) by the following appeal, which Cantor did not make in his published writings:
cited from: Joseph Dauben, Georg Cantor, Harvard University Press, Cambridge, Massachusetts and London England, 1979. 404 pp
...reminiscent of Berkeley’s use of God as a guarantor of the reality of the external world. In short, Gutberlet argued that God himself insured the existence of Cantor’s transfinite numbers.So it can be seen from the events surrounding Cantor’s own life and work that he did not think it illegitimate to employ his mathematical concepts in metaphysical, cosmological or theological areas, Quite the opposite, his supporters did not rule “out of court” as “word-based arguments” objections to their positions such as the one presented by the Kalam, but considered them challenges worthy of being met, whatever one might think of their solutions.
(quoting Gutberlet) ‘But in the absolute mind the entire sequence is always in actual consciousness without any possibility of increase in the knowledge or contemplation of a new member of the sequence.’(endquote) God could similarly be called upon to insure the ideal existence of infinite decimals, the irrational numbers, the true and exact value of pi, and so on. (Dauben, p. 100)