Jeffrey A. Barrett
Professor, Logic and Philosophy of Science
Editor-in-Chief, Philosophy of Science
Ph.D. Columbia University 1992
philosophy of science; philosophy of physics; epistemology; game theory, decision theory, and rational choice
Social Science Tower 765
Most of my research falls into one of three areas.
First, I am interested in attempts to resolve the measurement problem in quantum mechanics. The measurement problem arises from the fact that the standard theory’s two dynamical laws are incompatible: one is linear and the other nonlinear. Since they constitute contradictory descriptions of the time-evolution of physical states, they threaten to render the standard theory logically inconsistent if one is unable to specify strictly disjoint conditions for when each applies. The theory tells us that the linear dynamics is to be used in all situations except when a measurement is made in which case the nonlinear collapse dynamics is to be used; but since it does not tell us what constitutes a measurement, we do not know when to apply the linear dynamics and when to apply the collapse dynamics. I am particularly interested in solutions to the measurement problem that drop the collapse dynamics altogether.
Peter Byrne and I recently organized the newly discovered Hugh Everett III manuscripts concerning his relative-state (or, less accurately, many-worlds) formulation of quantum mechanics. Many of these manuscripts can now be found at the UCIspace Everett Archive at http://ucispace.lib.uci.edu/handle/10575/1060. The companion volume of papers was recently published by Princeton University Press.
Second, I am interested in using decision theory and evolutionary game theory to model basic features of empirical and mathematical inquiry. In particular, I have been modeling the coevolution of descriptive language and predictive theory in the context of Skyrms-Lewis sender-receiver games. Such models show how it is possible for agents with very simple prior dispositions, and no conceptual resources, to evolve from random, meaningless signaling and inaccurate predictive dispositions to a meaningful descriptive language and reliable predictive theories.
Finally, Wayne Aitken and I have developed an algorithmic logic for statements of the form “Algorithm A outputs X when given input Z”. It is a feature of the logic that logical connectives and quantifiers are algorithmically defined. Algorithmic logic has an internal truth predicate, provability predicate, and strong principle of abstraction, and it is consistent. Thinking about models for the logic led to a paper on the physical possibility of transfinite cardinal computation. Our most recent work has been to add quantifiers to algorithmic logic. We take the result to be a plausible logic of intensional functions.