Friday, September 25, 2009

Spinoza, mathematics,

A novelist, Kevin van Duuglas, has been doing lovely work on Spinoza's optics in his very attractively designed blog.
Along the way, he has been advertising and commenting on aspects of my (contrarian) views on Spinoza's relationship with both the mechanical science of his day and his attitude toward mathematics. Leaving aside the larger issue of Spinoza's attitude toward the mechanical philosophy, on my view Spinoza is very skeptical about the application of mathematical tools to nature (in measuring or describing nature). (Letter on the Infinite provides best evidence for this claim, but it shows up elsewhere.) This can never lead to stable/secure/highest form of knowledge, it remains in the domain of imaginary (first kind of knowledge). At best he thinks mathematics plays a useful calculating role in study of nature. (On my view Spinoza is also extremely skeptical about our very ability to have knowledge of nature; Della Rocca defends a similar position but on different grounds.)
This is not to deny that Spinoza values mathematics as a topic of investigation in its own right, and finds more geometrico a useful way to present his views (although it is by no means as straightforward as folks believe). Nor is it to deny that Spinoza's views on different kinds of infinite may have inspired later mathematicians (Cantor).


  1. But... in the apendix to Ethic I Spinoza said that mathematics had shown us the criterion of truth and the way of seek the truth.