14,079 research outputs found
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
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