Yes! That is of interest. I've been trying to understand a claim I've heard that *actual* infinities are required for full 2nd order math. I.e. potential infinities (which I suppose are necessary for intuitionism and/or program-as-proof) limit the 2nd order operators you can use.
I shouldn't be surprised that the Church got involved. Thanks. On 7/23/20 9:47 AM, Prof David West wrote: > maybe of interest: > > In the 1630s, when the Roman Catholic Church was confronting Galileo over the > Copernican system, the Revisors General of the Jesuit order condemned the > doctrine that the continuum is composed of indivisibles. What we now call > Cavalieri’s Principle was thought to be dangerous to religion. > > Why did the Church get involved in evaluating the “new math” of indivisibles, > infinitesimals, and the infinite? The doctrine of indivisibles was on the > side of Galileo. Besides opposing the Church about whether the earth went > around the sun, Galileo treated matter as made of atoms, which are physical > indivisibles. Bonaventura Cavalieri, who pioneered indivisible methods in > geometry, was among Galileo’s followers. Furthermore, Catholic theology owes > much to Aristotle’s philosophy, and Aristotle, arguing for the potentially > infinite divisibility of the continuum, had explicitly ruled out both > indivisibles and the actual infinite. So it is no wonder that Jesuit > intellectuals opposed using indivisibles in geometry. -- ↙↙↙ uǝlƃ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/
