mac@uvacs.UUCP (10/10/83)
With regard to loops and consciousness, consider Theorem 66 of Dedekind's book on the foundations of mathematics, "Essays on the Theory of Numbers", translated 1901. This is the book where the Dedekind Cut is invented to characterize irrational numbers. 64. Definition. A system S is said to be infinite when it is similar to a proper part of itself; in the contrary case S is said to be a finite system. 66. Theorem. There exist infinite systems. Proof. My own realm of thoughts, i.e. the totality S of all things, which can be objects of my thought, is infinite. For if s signifies an element of S, then is the thought s', that s can be object of my thought, itself an element of S. If we regard this as transform phi(s) of the element s then has the transformation phi of S, thus determined, the property that the transform S' is part of S; and S' is certainly proper part of S, because there are elements of S (e.g. my own ego) which are different from such thought s' and therefore are not contained in S'. Finally it is clear that if a, b are different elements of S, their transformation phi is a distinct (similar) transformation. Hence S is infinite, which was to be proved. Alex Colvin ARPA: mac.uvacs@UDel-Relay CS: mac@virginia USE: ...uvacs!mac