### Finitary and Infinitary Mathematics,
the Possibility of Possibilities and the Definition of Probabilities.

#### quant-ph/0306201

** Abstract ** Some relations between physics and
finitary and infinitary mathematics are explored in the context of a
many-minds interpretation of quantum theory. The analogy between
mathematical “existence” and physical “existence” is considered from the point of view of philosophical idealism. Some of the ways in which
infinitary mathematics arises in modern mathematical physics are
discussed. Empirical science has led to the mathematics of quantum
theory. This in turn can be taken to suggest a picture of reality
involving possible minds and the physical laws which determine their
probabilities. In this picture, finitary and infinitary mathematics play
separate roles. It is argued that mind, language, and finitary
mathematics have similar prerequisites, in that each depends on the
possibility of possibilities. The infinite, on the other hand, can be
described but never experienced, and yet it seems that sets of
possibilities and the physical laws which define their probabilities can
be described most simply in terms of infinitary mathematics.

TeX source, 21 pages, 73K,

pdf, 21 pages, 232K.

#### Matthew J. Donald

#### The Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, Great
Britain.

#### e-mail :
mjd1014@cam.ac.uk

#### home page:
http://people.bss.phy.cam.ac.uk/~mjd1014