Mathematics and Scientific Revolution

A comment in an online forum thread on my post on Laudato Si’ notes the following about mathematical science:

the application of mathematics to nature is not a particularly 17th century thing, but it goes to the beginnings of civilization, to the point that we could even say that mathematics is natural to the mind and making maths is of the same cultural necessity as making music (an activity that, although strictly not necessary, is present in every civilization).

This is obviously true, and the brief account of the new-science in my post wasn’t meant do deny it, but I can see how the post could be read that way.

What is particular to the sort of mathematical application found in the new science of the 17th century is the homogenizing character of the mathematical symbolization used, and the elevation of this application to a mathesis universalis, a universal method which becomes, the dominant approach to reality. I have posted a long explanation of what that means (from a dissertation draft) to It’s the fullest account of the scientific revolution that I have written so-far, but it is still only a partial account. I am planning to expand it into a full-blown treatise at some point.



Charles De Koninck, Jacob Klein, and Socratic Logocentrism

The bi-lingual Quebecois journal Laval théologique et philosophique, has recently uploaded its archives to the web. This was the organ of Laval School Thomism, and the early issues contain lots of fascinating material by Charles De Koninck, the school’s most distinguished thinker, as well as pieces by his students and colleagues. Laval School Thomists have a somewhat ambivalent attitude toward writing and publishing. In the spirit of Socrates’s critique of writing in the Phaedrus,1 they are wary of the ways in which writing can aggravate the tendency of words to lose their connection to things. De Koninck argues that philosophy is rooted in the common conceptions which human reason forms “prior to any deliberate and constructive endeavor to learn.” These common conceptions are the most certain knowledge, but they are vague, indistinct, “confused.” As Aristotle puts it at the beginning of the Physics, “What are first obvious and certain to us are rather confused, and from these, the elements and principles become known later by dividing them.” The role of philosophy, then, is to make clear what is already contained in common conceptions. De Koninck was a great enemy of philosophic “systems” in which concepts are rendered intelligible by their function in the system, rather than by their rootedness in pre-scientific logos. Among his disciples one gets a sense that the problem with writing is that it lends itself to the development of a “technical” vocabulary from which such systems are formed. De Koninck  was especially opposed to any system which would use not words, which by their nature intend the world, but symbols, which replace what they represent. He pointed out the absurdities that followed from conceiving of thought as a method of manipulating symbols according to rules– of replacing “logic” in the ancient sense with philosophical calculus, or characteristic, or symbolic mathematical logic; all of which are not so much logic as grammatology.

In this De Koninck agrees with a philosopher of a quite different tradition: Jacob Klein. A student of Husserl and Heidegger, Klein did not follow his teachers. He understood philosophy in a way very similar to De Koninck. He looked to the Greeks whose account of philosophy he summarizes as follows: Continue reading