Timeline for answer to When did set theory throw off theology? by Alexandre Eremenko
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| May 1, 2018 at 9:56 | comment | added | Franz Kurz | @Alexander: Cantor discovered potentially infinite sets. He then switched to actual infinity. That includes as most prominent example the exhaustibility and limit $\omega$ of the ordered set (1, 2, 3, ..), often also denoted by $\omega$. Can this set be finished or completed? Take a merry-go-round to model this question. Its revolutions can be counted. Hence, if set theory is right and belongs to usable mathematics, there will be a limit. What is it? | |
| Apr 28, 2018 at 13:10 | comment | added | Alexandre Eremenko | @Wilhelm: on my opinion, set theory belongs to mathematics, and Cantor discovered it when studying a concrete question about Fourier series. That Cantor himself connected it somehow to theology is of some historical interest, but this does not mean that set theory itself was related to theology. | |
| Apr 27, 2018 at 16:41 | comment | added | Franz Kurz | "daß zu dem Begriffe einer Zahl die Endlichkeit derselben gehöre, und daß andrerseits das wahre Unendliche oder Absolute, welches Gott ist, keinerlei Determination gestattet. Was den letzteren Punkt anbetrifft, so stimme ich, wie es nicht anders sein kann, demselben völlig bei" ... "Omnia seu finita seu infinita definita sunt et excepto Deo ab intellectu determinari possunt."... " Thomas von Aquino, Opuscula, XLII de natura generis, cap. 19 et 20; XXXII de natura materiae et de dimensionibus interminatis." (Cantor: Grundlagen einer allgemeinen Mannigfaltigkeitslehre, 1883) | |
| Apr 27, 2018 at 16:19 | comment | added | Franz Kurz | "Mitteilungen zur Lehre vom Transfiniten" is a mathematical paper. It contains an "extended, purely mathematical theory of order types". That is not only my opinion but a quote by Zermelo. It is simply impossible to distinguish set theory and theology (because set theory definitely belongs to metaphysics). | |
| Apr 27, 2018 at 15:54 | comment | added | Alexandre Eremenko | I was talking about his MATHEMATICAL papers. | |
| Apr 27, 2018 at 14:17 | comment | added | Franz Kurz | Newton did a lot of alchemy and theology, but did not base machanics or mathematics on it, contrary to Cantor. "One of the proofs starts from the notion of God and concludes first from the highest perfection of the Supreme Being on the possibility of the creation of a Transfinitum ordinatum, then from God's loving kindness and glory on the necessity of an actually created Transfinitum." (Cantor: Mitteilungen zur Lehre vom Transfiniten.) | |
| Apr 27, 2018 at 13:42 | history | answered | Alexandre Eremenko | CC BY-SA 3.0 |