Mind and Body:
From René Descartes to William James

Writing Descartes:
I Am, and I Can Think, Therefore ...

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an exchange triggered by Grobstein's Writing Descartes ...
13 July 2004

Weaver with interspersed Grobstein

I read over the letter. I don't get the point. It is my impression that if you have something to say that you simply say it and don't involve interpreting historical figures. It muddies the water and leaves you open to irrelevant critical remarks like the following.

Point understood. Others of my colleagues have urged a more "discursive" style. Actually, as you know, much of the point of the letter is actually played out "discursively" elsewhere (cf. Getting It Less Wrong, The Brain's Way: Science, Pragmatism, and Multiplism). The aim here is different. I wanted to see if an important issue, with an "academic" foundation, could be usefully explored in a broader context, with a broader community of people involved in the exploration. Agree that it raises problems in an "academic" context. But that too is interesting and even germane to thinking about "thinking". And I'm less inclined than you to prejudge what might or might not turn out to be irrelevant, critical or otherwise.

I have some problems with your reading of D. It is my impression that he is treated rather differently by historians of philosophy and historians of mathematics. Historians of mathematics start with The Rules for the Direction of the Mind and The Discourse on Method with the three appendices. The historians of philosophy avoid The Rules and while they read The Discourse they don't bother with the appendices (in fact for years you could not get an addition of The Discourse that had the appendices, it having been decided that they were not relevant) and are more likely to start with The Meditations.

I'd say that's quite relevant. It suggests that one's thinking is heavily influenced by one's community, no? Even among academics, who in turn are the transmitters of peoples' thinking to others? Its probably true that most of what I've read comes from historians of philosophy rather than of mathematics.

The mathematical background to D is to my mind pretty interesting. He is generally credited with applying algebraic methods to geometry. These methods were developed in the Arab world and brought to Europe by Cardano and Vieta, their application to geometry seems to have been D's contribution. This is more than just Cartesian coordinates. It involved also the notion that problems could be solved by the discovery and application of rules. (Arguably, the beginning of algorithmic methods in Europe.) There is a sense in which D thought that algebraic/algorithmic methods could be applied generally.

Yep, the history of mathematics perspective is is DEFINITELY relevant. Is a little hard to put oneself (me at least) backwards to a time before one took as a given that there were rules that could be discovered to solve problems. If I'd been among the first to realize that, I sure as hell might have spent the rest of my life trying to apply it to everything in sight (as we still, despite Gödel/Turing/Chaitin still are prone to do today?).

How all of this squares with his "philosophical" work is a difficult story that I don't begin to understand. Clearly he owed a lot to the Euclidean tradition in geometry as interpreted through Proculus. The search for first principles in rationalism was analogous to the search for axioms in geometry. According to Proculus, the axioms were to be self evident. Proculus also recognized a distinctions between problems and theorems in geometry. This was particularly important for D as he is generally credited with solving problems that were not solved previously. You see this geometric influence on philosophy most clearly in Spinoza's Ethics. I have been told by people in a position to know that the geometric model was applied to several disciplines in the middle ages. Briefly, D's idea was to find a method for discovering first principles.

Yeah, that's what I was/am calling into question. Not because it doesn't work sometimes (clearly some useful things have come out of it) but rather because increasingly it looks like sometimes it doesn't work. And for those cases one needs to come up with new ways to "think", new tools, instead of batting one's head against a wall with old tools or denying that the problems exist.

The famous "I think, therefore I am" is subject to some questions. It appears to involve an inference( Why else "therefore"?) and might not be taken as first principle. I think that it is arguable that whatever D's method, it was not just skepticism. By the way the logic that D objected to was the logic of Aristotle as filtered through the middle ages. It was a straight jacket that could not account for the mathematics of the ancient world.

Case in point. Break a straight jacket, find onself in a straight jacket. Am GLAD D broke the straight jacket of Aristotelian logic. And you're right that D was far from a committed skeptic. He was in fact apparently trying to beat two enemies, Aristotelian logic on the one hand and the Greek Pyrrhonian skeptics on the other. Poor guy. No wonder he couldn't get to "profound skepticism".

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