Self-Similar Random Processes and Infinite-Dimensional Configuration Spaces

We discuss various infinite-dimensional configuration spaces that carry measures quasiinvariant under compactly-supported diffeomorphisms of a manifold M corresponding to a physical space. Such measures allow the construction of unitary representations of the diffeomorphism group, which are important to nonrelativistic quantum statistical physics and to the quantum theory of extended objects in d-dimensional Euclidean space. Special attention is given to measurable structure and topology underlying measures on generalized configuration spaces obtained from self-similar random processes (both for d = 1 and d > 1), which describe infinite point configurations having accumulation points

Aristotle on Good and Bad Actualities

This paper is a discussion of one of the more neglected passages in the central books of Aristotle\u27s Metaphysics, Θ 9 105la4~19. In this passage Aristotle makes some assertions concerning relations that hold among potentialities and actualities, both good and bad. These assertions seem to be made as an afterthought, and their relation to the analysis of potentiality and actuality that precedes is unclear. I shall argue that in this passage Aristotle is in effect providing a metaphysical foundation for the normative component of a teleological analysis of composite substance. I consider certain difficulties in reconciling the text with the account of potentiality, and actuality presented earlier in Metaphysics Θ. I then briefly explore some of the implications that this passage has for our understanding of Aristotelian teleology

Atoms, Complexes, and Demonstration: \u3cem\u3ePosterior Analytics\u3c/em\u3e 96b15-25

There is agreement neither concerning the point that is being made in Posterior analytics 96b15-25 nor the issue Aristotle intends to address. There are two major lines of interpretation of this passage. According to one, sketched by Themistius and developed by Philoponus and Eustratius, Aristotle is primarily concerned with determining the definitions of the infimae species that fall under a certain genus. They understand Aristotle as arguing that this requires collating definitional predictions, seeing which are common to which species. Pacius, on the other hand, takes Aristotle to be saying that a genus is studied scientifically through first determining the infimae species that fall under that genus. This interpretation attributes to Aristotle a distinction between primary and derivative subjects. I argue for Pacius\u27s interpretation, defending it against Barnes\u27s objections