mathematisation of nature in the 17th century

[grahammartinveale]

I'm reading John Henry's "The Scientific Revolution and the Origins of Modern Science". One of the keys to the development of science was the mathematization of our world picture. Mathematics ceased to be viewed as a discipline that was merely useful for making predictions. Instead Mathematical models of the universe were given a realistic interpretation. They could tell us how the universe really was.

Now, my question. How important is Theism to the mathematization of our world picture. It makes sense to see God as an architect using mathematics to construct reality. Dr Hannam talks about this in his "God's philosophers". But is Theism essential? (Henry mentions that Ptolemy was probably a realist.)

[perplexedseeker]

It really depends on who you ask. Certainly being a realist about the laws of physics requires one to adopt at the very least a mild form of Platonism if you want to avoid Aristotelian formal and final causality. I believe that this is the position of many mathematicians. Now, Plato himself and many of his followers were theists of a sort, but naturalistic formulations are no doubt also possible. I very much doubt that theism is essential to mathematical realism, but I personally believe it is at the very least more consistent with theism than alternatives. However, I'd welcome other perspectives on this, since I'm a neo-Aristotelian in my personal convictions, which requires a quite different sort of realism concerning essences.

[grahammartinveale]

Thanks PerplexedS. Perhaps I should focus my questions a little more. The Aristotleianism of the C17th University made realism about mathematical models of nature problematic. Was a resurgence of interest in Platonism sufficient to get the Scientific Revolution up and running? Or was Theism recquired to make it plausible that nature conforms to a mathematical pattern?
In other words, how important was Theism intellectually to, say, Copernicus and Galileo?

[himself]

I think Henry is wrong. Ptolemy was not a realist about astrology. To him it was simply a set of mathematical calculations that would accurately predict the positions of the stars and thereby predict the will of the gods (or, if he was a Neoplatonist, the God). (He was interested in divination, not the empirical study of nature.)

Not until the Copernicans began to claim that their mathematical model was physically real did the late Ptolemaics begin to make similar claims. Even Copernicus' first editor added (as he thought) in defense that the system being described was only to save the appearances.

Remember: the Ptolemaic math model, if physically real, would contradict Aristotelian physics.

[jonkon]

The American philosopher Charles Saunders Pierce cited as proof of the reality of God the fact that people found scientific investigations to be profitable. Conversely Christian theology is foundational to the validity of scientific investigation.

First, John 1:1's identification of Christ as the personification of the Greek philosophical principle of Logos provides an intellectual rationalization and foundation for the validity of logic and mathematical proof. The successful use of logic in reasoning and mathematical proof thus serves as an illustration of Christ's role in redemption. Without this identification, the use of logic relies upon a highly dubious faith in the effectiveness of human reason. This identification occurred at a time that Roman (and current, for that matter!) legal instruction viewed logic as a convenient tool, if it supported your case, but not essential, if it did not.

Secondly, Aristotle taught that observation was the basis of reality and knowledge, while Plato taught that our observations were a distortion of reality, which can only be found in our "idea" of what is being observed. The significance of heliocentrism was in its assertion that the mathematical model represented an underlying physical reality (per Plato) that clearly contradicted observation (per Aristotle). As a consequence of Godel's Proof, valid, reliable scientific conclusions can only be arrived through a merger of Platonic and Aristotelian concepts, patterned on the Christian Doctrine of the Incarnation - Christ as True God (Theory) and True Man (Experience). Thus without a theoretical justification, we cannot legitimately claim that an empirical generalization represents a true physical relationship and not a mere coincidence. Conversely, a theory must have empirical support before we can legitimately accept it as true.

[James Hannam]

Jun 24, 2010 20:11:15 GMT grahammartinveale said:

The Aristotleianism of the C17th University made realism about mathematical models of nature problematic. Was a resurgence of interest in Platonism sufficient to get the Scientific Revolution up and running? Or was Theism recquired to make it plausible that nature conforms to a mathematical pattern?
In other words, how important was Theism intellectually to, say, Copernicus and Galileo?

I don't think 17th century Aristotelianism had all that much to do with the development of science. It was rather a humanist endevour intended to get back to the original ancient thought without the later amendments by medieval scholars. As such, it was a step backwards.

But mathematicians, like Galileo and Descartes, were never taken in by this. They hung onto medieval progress and continued to develop models independentally.

Theism was essential to Copernicus since it justified his entire system. Without it he had no reason to expect the universe to be elegant in its workings. He is quite explicit about this. For Galileo, it is not so clear. He was a devout Christian, but you see much less explicitly theological reasoning in his work than you find in almost all other seventeenth century mathematicians and natural philosophers.

And Platonism was, in my opinion, pretty much irrelevant except possibly for the way its more mystical variants promoted the sun.

Best wishes

James

[jonkon]

Galileo's theism is implicit in his defense of heliocentrism as representing physical reality. Copernicus's placement of the sun at the center of the universe was explicitly to place God, rather than Man, at the center of the universe. Similarly Kepler's replacement of circles, symbolic in Greek philosophy of the mediation between God and Man, with ellipses, explicitly allowed God to be at the true center of the universe. The lack of explicit reference to theism in Galileo's work is explained in a letter (p. 166 "Discoveries and Opinions of Galileo" by Stillman Drake) where Galileo complains that "Yet while I follow the teachings of a book accepted by the church, there come out against me philosophers quite ignorant of such teachings who tell me that they contain propositions contrary to the faith. So far as possible, I should like to show them that they are mistaken, but my mouth is stopped and I am ordered not to go into the Scriptures." Newton, in what his contemporaries considered his greatest achievement, finally settled the issue by pointing out the omnipresence of God.

[grahammartinveale]

Thank you all. These replies are very helpful indeed.

[grahammartinveale]

Thank you all. These replies are very helpful indeed.