Friday, December 16, 2011

A few Modern Medievals ... and a Tempier to Temper them

"In the same way, God does not know the relation of the diagonal of a square to its side, not that there is a defect in God's knowledge, but because the relationship cannot be known."


"In the same way, God does not know the ratio of the diagonal of a square to its side, not that there is a defect in God's knowledge, but because the ratio cannot be known."

As for ratio, if space is a continuum, I agree. But a relation need not be a strict ratio as in so many units on one side against so many units on the other hand, which the author means, it can also be an irrational relation functioning otherwise as a ratio.

1:1 and 2:1 are ratios, the one smaller and the other greater than the relation. 14:10 and 15:10 (or 7:5 vs 3:2) are also smaller and greater ratios but not same ratio as the relation.141:100 and 142:100, similarily. And so for 1414:1000 and 1415:1000 (these ratios are a spelling out of the shorthands: 1 or 2, 1.4 or 1.5, 1.41 or 1.42, 1.414 or 1.415). God indeed knows every ratio that in its scope approaches to the relation between diagonal and side of a square, but also the relation itself, though we do not know it. And we cannot know it except by simply looking carelessly at a square with a drawn in diagonal or approaching it laboriously through approximations that happen to be ratios, though the relation itself is not.

What was it the author cited was trying to prove? The text, I found it with the wording "relation" and "relationship", tried to prove basically that God cannot know the unknowable nor make the unmakeable (which was the point: the author was saying that there were things even God could not do, because creation could not take it.Like create a multiplicity or infinity of universes.

Now, this author was William of Paris. He closely echoes, on that question, Michael Scot, astrologer of Frederick II, founder of Averroism. Quoted as saying:

"God can do this, but nature cannot withstand it. The impossibility of the plurality of worlds results from the nature of the world itself, from its proximate and essential causes; God, however, can make several worlds if He so wishes it."

Now, knowing the ratio between a side and a diagonal of a falt square is impossible, because there is no such thing to know, a ratio meaning a relation of "if one gets bigger other gets bigger too, and if there is a difference the difference also gets bigg" BUT ALSO OF "measured in counted units on either side". Take both conditions, there is no such thing. Take away the second, and it is a relation but not exactly a ratio, and for certain God knows it. So, the parallel reasoning, taken either way, breaks down.

However saying that proximate and essential causes of creatures are incompatible with God doing something, is denying Divine Omnipotense, and believers in modern science are doing it all the time, claming to be Thomists while following Aquinas' contemporary, an astrologer (bad enough), living at the court of Frederic II (bad too: he was a great scientist in the sense that Mengele was that too, though his experiments were more in the context of digestion than of heredity).

So this man claims God could not make several worlds? He was condemned in 1277 by the bishop of Paris, Tempier.

And his reasoning is odd enough too. How could any quality of this world, except infinity, which he denied and Christians do generally deny about the universe, though pantheists affirm it, giving to creature the attribute (diluted and denatured) of God, be affected by or affect, what God does totally outside it?

But the reasoning that is cited by William says that God could not have created a finite number of worlds, since his goodness is as much expressed in creating a single one with all perfections of creatures assembled as in creating several ones. Therefore the goodness could not prompt him to create any worlds outside this one. Not any finite number, since it would not satisfy his expression of his goodness and generosity any more than a single one (how does William of Paris know that?) nor an infinity, since any actually infinite number is impossible (in this world, but we were talking about God's possibilities, not those within one world). And then he goes on to say: "this impossibility is not a defect in God, or a defect issuing from God, rather it is a defect on part of the world, which cannot exist in multiples". Oops ... ? Well, I have heard theologians claim similar things, as if a certain autonomy on part of proximate causes put limits on God. As if we could from them conclude that even God could not make Young Earth Creationism or Geocentrism function. Of course not, would they add, due to any imperfection in God, but due to the nature of things.

Well, that is a lie. A lie that though contemporary with St Thomas Aquinas among Western Scholastics, was not his thought. A lie that was not the thought of a certain non-scholastic bishop either. Tempier was his name, Paris was his see (if Vingt-Trois is his successor, he might be making that a bit clearer!), and 1277 was the date of his condemnations.

I have been quoting what I quoted from pp.443-444 in Medieval Cosmology by Pierre Duhem, subtitled: Theories of Infinity, Place, Time, Void, and the Plurality of Worlds. Edited and translated by Roger Ariew.

I note that "theories of Mind" and "theories of Spirits" (excepting of course God Himself) are not part of the subtitle, nor of the content, as far as a glance at the Contents list shows. But more than once is the condemnation by Tempier alluded to. And it is shown how St Thomas Aquinas, for the first time that the author knew about in history, in commenting on Aristotle differed from him in direction of a mechanics of Galileo's and Newton's type.

However, I must add, not in such a way as to indicate that theories of lightness as a real substantial opposite of weight were excluded (the one part of Galileo-Newton that I find impious), rather in pioneering (as far as we know) the distinction, at least in abstract thought, between what Newton called force and what Newton called mass. Nor does he do that in such a manner as to exclude that force means the force of angels working on masses rather than purely immanent ones. Indeed, St Thomas affirms both lightness as a real quality of say air or fire, and angels - spiritual substances - as working on particulars down here, where Aristotle thought they were only about the astra.

Of course, John Philopon pioneered another aspect of modern dynamics. He stated the first part of what Newton called his first law of movement. Newton only added "rectilinear movement" as an equivalent to complete stillness in needing no force. And I am not at all sure Newton was right about that. Though God could make that a natural law too, I am not sure that in fact He did.

Back to Bishop Tempier, and sorry, I won't give page references. It is condemned to say "God could not move the heavens, since in that case they would leave a void behind". It is condemned to say "God could not create a plurality of worlds." It is condemned to say that God needed to make a void to create too: here Christian Orthodoxy clashes head on with the cabbalistic theory of Tsimtsum.

Now I am off from this blog to read either Stanley Jaki's foreword (was he already a Dom then, like Perignon?) or to do some other stuff.

Hans-Georg Lundahl
Paris, Georges Pompidou
Library, on the day of Empress
St Adelaide who was nicknamed
Alice, Y o o L 2011