Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) hr chaos theory, (ii) for paradoxical decompositions of solid three-dimensional objects, (iii) in the theory of effective computability (Church-Turhrg thesis) related to the possible "solution of supertasks," and (iv) for weak solutions. Several approaches to set theory and their advantages and disadvatages for" physical applications are discussed: Cantorian "naive" (i.e., nonaxiomatic) set theory, contructivism, and operationalism, hr the arrthor's ophrion, an attitude of "suspended attention" (a term borrowed from psychoanalysis) seems most promising for progress. Physical and set theoretical entities must be operationalized wherever possible. At the same thne, physicists shouM be open to "bizarre" or "mindboggling" new formalisms, which treed not be operationalizable or testable at the thne of their " creation, but which may successfully lead to novel fields of phenomenology and technology.

James Thomson envisaged a lamp which would be turned on for 1 minute, off for 1/2 minute, on for 1/4 minute, etc. ad infinitum. He asked whether the lamp would be on or off at the end of 2 minutes. Use of "internal set theory" (a version of nonstandard analysis), developed by Edward Nelson, shows Thomson's lamp is chimerical; its copy within set theory yields a contradiction. The demonstration extends to placing restrictions on other "infinite tasks": Zeno's paradoxes of motion; Kant's First Antinomy; and Malament-Hogarth spacetimes in General Relativity. Critique of infinite tasks yields an analysis of motion and space & time; at some scale, motion would appear staccato and the latter pair would appear granular. The critique also shows necessary existence of some degree of "physical law". The suitability of internal set theory for analyzing phenomena is examined, using a paper by Bridger (1 997) to frame the discussion. Dr. William 1. McLaughlin 301-170s Jet Propulsion Laboratory 4800...