Calculus, Certainty, and Monarchism

The Intermediate Value Theorem, an important part of differential calculus, (I would even say an "integral" part, were that not a groaner of a pun) was first clearly stated in a textbook written by an iconoclastic royalist Frenchman, Augustin-Louis Cauchy in 1821.

That intrigues me for a couple of reasons. One, those of us who are pikers in calculus tend to infer from what little we're heard of its history that Newton and Leibniz simultaneously created it fully blown. That what they created was tentative and only gradually developed into the body of work we have today -- that higher mathematics has an intruguing history with a lot of players -- is itself a bit counter-intuitive for some of us.

A more specific reason to think about Cauchy is ... Cauchy. He must have been a fascinating guy.

In Cauchy's own mind, it appears, his contributions to higher math melded with his own monarchical politics. In the introduction to his Cours d'Analyse. he wrote, "It would be a grave error to think that one only finds certainty in geometrical demonstrations, or in the testimony of the senses; and although no person until now has tried to prove by analysis the existence of Augustus or of Louis XIV, every sensible man will agree that this existence is as certain for him as the square of the hypotheneuse or Maclaurin's theorem."

Note that the example of an unquestionable human-world truth here is the existence of great monarchs, and that the renowned pillar of both Bourbon rule and Bourbon memories, Louis XIV, is one of only two of the monarchs named.

Leibniz and the Mind-Body Problem

The trickiest questions in modern philosophy, i.e. those with which I have struggled most for decades, are those that involve the body/mind (or body/soul) connection.

Does the thinking-stuff that is "me" really interact with the material-stuff that the rest of the world sees and knows as me? If not, how can the two "Mes" be said to be one? Yet if they do interact, how is that possible? It seems to "me" that the two are so very different that it is hard to get a grasp on this.

I recently encountered the blog of a self-described "contemplative scholar," a Quaker who teaches philosophy at a small college. You can make this discovery for yourself here.

He said he has recently been teaching Leibniz to his students in the Modern Philosophy class. So I free-associated on Leibniz in his comments section. I'll just reproduce most of that comment below:

Leibniz, if I remember my college years at all, had a drastic solution to [mind body issues], -- preestablished harmony. Mind and body only seem to interact, as two trains running on parallel tracks at the same (predetermined) speed might seem to be moving deliberately in concert.

This calls for a rather distinctive conception of God, one at odds with much of the revelation offered to each of the "peoples of the book," and it all seems a very high price to pay for the resolution of the mind/body muddle.

Just my two cents.

To which the Contemplative Scholar replied with a fuller account of what Leibniz said in that line, and with his own thoughts on the matter. I'm sure that any of my readers who follow the above link will appreciate his reaction.