"From the Closed World to the Infinite Universe" by Alexandre Koyre

This is from the 'Easy Reading Series' of Forgotten Books: it is relatively easy to read but the format which fails to easily distinguish between extensive quotations and the author's gloss makes it much more difficult to read than it should be.

Koyre is concerned with the change of world view which occurred about the same time as the Copernican revolution.

He starts with the arguments of Nicholas of Cusa who "denies the finitude of the world and its enclosure by the walls of the heavenly spheres" (p 8) although he won't go so far as to assert the infinity of space, only that the universe is 'interminate', "it is boundless and not terminated by an outside shell" (p 8) but also that it "utterly lacks precision and strict determination" (p 8) so it can never reach the limit; he reaches this conclusion by using his doctrine of '"learned ignorance" (p 8) "the intellectual act ... which transcends discursive, rational thought". He illustrated this by pointing out that an infinitely large circle has straight sides (the curved side at any point will coincide with its tangent) and an infinitely small circle will also have straight sides (the side will correspond to its radius) and that therefore the big infinite and the little infinite are the same.

Unfortunately Koyre does not really explain 'learned ignorance'; I had to find Wikipedia to tell me: "docta ignorantia means that since mankind can not grasp the infinity of a deity through rational knowledge, the limits of science need to be passed by means of speculation. This mode of inquiry blurs the borders between science and ignorantia. In other words, both reason and a supra-rational understanding are needed to understand God. This leads to the coincidentia oppositorum, a union of opposites, a doctrine common in mystic beliefs from the Middle Ages."  https://en.wikipedia.org/wiki/De_Docta_Ignorantia

Next he talks about a poetic philosopher named Palingenius who uses the Principle of Plenitude (again unexplained but which is the idea that God is so brilliant that all possible forms of creation are available in the world) to deny "the finitude of God's creation" (p 21).

Koyre continues to Copernicus which he says "undermined the very foundations of the traditional cosmic world-order with its hierarchical structure and qualitative opposition of the celestial realm of immutable being to the terrestrial or sublunar region of change and decay." (p 23) He points out that "the immediate effect of the Copernican revolution was to  spread scepticism and bewilderment" (pp 23 - 24) Perhaps the most convincing Copernican argument was the fact that it would take much more effort to make the large sphere of the fixed stars rotate than the much smaller Earth.

There is also a chapter on Giordano Bruno, who asserted the infinity of the heliocentric Universe and was burnt at the stake. But he wasn't that modern or perhaps he was, he asserted that since the senses were flawed and could be fooled the intellect was primary.

Then, via Galileo, comes Descartes who starts with the idea of God and therefore starts with infinity and derives the finite from the idea of the infinite. Typically weird. You start to understand where the other French philosophes have got it from.

We next get several chapters on Henry Moore, a Neo-Platonist who disputed with Descartes and taught Newton and therefore a fascinating and often overlooked philosopher of nascent science. He pointed out the daftness of Descartes endeavour to avoid the void because nothing can come of nothing as Lear might have said. |Moore suggests that the primary property of matter is not its extension but its impenetrability; he asks how "can a purely spiritual soul ... which, according to Descartes, has no extension whatever, be joined to a purely material body, that is to say something which is solely and only extension?" By exposing the contradictions inherent in the ramshackle Cartesian system which endeavours to solve scientific problems through the appeal to a wholly biased intellect, Moore laid the foundations for Newtonian science. And for infinity. Because Descartes believed that the Universe was bounded. But Moore asked: "Could Descartes not tell what would happen ... if somebody sitting at the extremity of the world pushed his sword through them limiting wall? On the one hand, indeed, this would seem easy, as there would be nothing to resist it; on the other, impossible, as there would be no place where it could be pushed." (p 89)

Moore, Koyre tells us, was a syncretist who tried to synthesise the new discoveries with the occult, magical and hermetic traditions nut nevertheless "succeeding in grasping the fundamental principle of the new ontology, the infinitization of space." (p 93) And such dabbling in weird stuff was necessary to develop the theory of, for example, gravity. This has a challenging principle of action at a distance. "Gravity cannot be explained by pure mechanics" (p 98) Koyre points out.

And so from Moore to Newton and, in particular, his letters to Mr Richard Bentley in which he states that "the cause of gravity is what I do not pretend to know"; nevertheless Newton realises that he can analyse its effects without knowing its causes. (p 131).

This is an interesting book but it would be an easier read if (a) some of the Latin tags were translated (I managed to work out most of them but I was taught Latin forty five years ago) and (b) if Koyre explained some of the things he mentions such as the Principle of Plenitude.

May 2017, 200 pages