[FRIAM] square land math question

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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.


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