I am an infinite regress

I was thinking about Kant’s transcendental logic of experience grounding pure reason and I was reminded that (infinitely) many numbers, such as pi (3.14159...) are classed as ‘transcendental’ numbers because they cannot be expressed rationally (as a fraction) or calculated as a polynomial.  There are, however, a lot of ways to calculate pi, and many of them are sums of infinite series of terms.  My favourite was discovered by Bailey, Borwein and Plouffe and is a sum of series of terms that converge because each is less than the last by a factor of 16.  This means that, if you work in hexadecimal notation, you can work out one place at a time the 250^th place of pi, or the 25,000^th place are equally accessible.  You could use this formula to search for the million-digit section of pi that is closest to encoding a Shakespeare play.

I think Kant wanted to show that the reasoning person was no more real and no less real than the faculties by which the manifold realities of the world cohere and are perceived – time and causality; space and number and so on.  The faculties (which Nietzsche mocked, you will recall) have to have this transcendental quality, bootstrapping themselves into contact with things in themselves.  I sit in something of a Cartesian theatre of experience, which sits in a Cartesian theatre of experience, which sits in a Cartesian theatre of experience, and so on out to the very edge of my skin and into the non-me media (air, space).  From our end of the relationship to the world, the faculties have to be self-justifying.

And so I wonder about the disproving power of the infinite regress.  There are a lot of proofs that rely on it, but how many check whether that is an infinite series converging on some definite goal?

* This blog may be a good example of the value of an undergrad philosophy degree.  I will be arguing by analogy, and from word association, about a book which I have only heard read via librivox and listened to some lectures on once and on which I have never had my understanding examined.