An Ugly Election, Getting Worse

And I know that this is supposed to be about our readings and passions and stuff, but I think on occasion I'll drop in some other things, 'cause it is a blog, and blogs are meant to be tangential. Anyway. Sexism in America is appalling, example 1 . Just the fact that Clinton and Obama are serious candidates for the Presidency will stir up the muck and horrifying nasties will surface. Maybe it will be cathartic, maybe it will provoke positive change, but I'm not holding my breath.

Descartes and Viete

Viete was a French mathematician whose `The Analytic Art' of 1591 was a standard text on algebra. Viete starts the book with a description of mathematical analysis, breaking it into three parts: zetetics, poristics, and rhetics, with the following definitions:

1. Zetetics: setting up an equation or proportion between the unknown and the givens
   
2. Poristics: testing the truth of a theorem by means of an equation or proportion
   
3. Rhetics: determining the value of an unknown term in an equation or proportion
   

As an example, suppose I know that 3 doughnuts cost 2 dollars; how much would 12 doughnuts cost? Saying `2 is to 3 as x is to 12' or '2/3 = x/12' is zetetics, while solving for x to find x = 8 is rhetics. I can generalize this to find a general theorem: N doughnuts cost (2/3)N dollars; plugging in values for N to verify this theorem is poristics (although this is a lame example of poristics; I think it's more along the lines of trying to figure out the truth value of a proposed equation, not a derived one).

One would think that Descartes was familiar with this book, and with this sort of analysis. The sixteenth century was a time of re-definition for mathematics, in which mathematicians included these little prefaces about how to practice mathematics; in a sense, they were establishing professional methodology. Descartes and other early moderns would inherit these explicit statements of methodology; would then they seek to carry mathematical methodology over to other fields? Note in particular that mathematicians of the time claimed that their field led to truths whose certainty was unchallenged (it's annoying that `certain' has two meanings; `certain truths' means either `some, but not all, truths' or 'undoubtable truths', and I want the latter). How was the early modern search for axioms and a deductive system (Descartes wanted to start with just `I think, therefore I am' and deduced from there; Hobbes started with a state of nature and deduced from there) influenced by the professionalization program of 16th century mathematics?

And thanks have to go out to Jeff Mullins at this point; this sort of a question wouldn't have occurred to me without having gone through his History 610 course.

Passion and Literature

I've just started Harold Bloom's `Genius', and he insists that literature helped create perceptions of human nature. Bloom is particularly high on Shakespeare, but he also mentions Montaigne, Cervantes, and Milton as early moderns who helped create the idea (as he puts it) of `overhearing oneself'. He suggests that these authors created characters who looked into themselves and found truth there. This shift, from a medieval focus on external sources for truth to an early modern focus on internal sources for truth, seems to be a common feature across many aspects of early modern thought. Descartes certainly does this. Did Descartes read Montaigne? or Cervantes? I don't know whether Shakespeare was in French by that time, but I'm pretty sure the Essays and Don Quixote were available to Descartes. How much of an impact did these authors have on constructions of the passions? Bloom would argue (I think) that the widespread availability of literature gave people new models for themselves, new ways to explain themselves. Maybe someone more knowledgeable about this could fill us in?

The Figure of Descartes

The figure of Descartes is pivotal for DesChene, because his study of his Aristotelians is focused on their discussion with Descartes. It feels, somewhat, that DesChene's book is a glorified appendix, a long summary of the background to the milieu of Descartes thought. This Aristotelian argument doesn't seem to be
interesting to DesChene in and of itself, but only in context of how it influenced Descartes. What would a book about early 17th century Aristotelian thought look like? I would think there would be more than just a handful of Jesuits named, and I think there would be more discussion of other aspects of thought--materialism, the Reformation, experimentalism. The focus of this book, both on the thinkers and on their texts (mostly analysis of De Anima), seems to me to be too narrow.

In any case, Descartes (to me) hovers over this book like a ghost, informing almost all of the commentary.