The Concept of the Infinite and the Crisis in Modern Physics
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Speculations in Science and Technology 6 (4):413-425 (1983)
The basic thesis is that the problem of infinity underlies the current dilemma in modern theoretical physics. The traditional and set-theoretic conceptions of infinity are considered. It is demonstrated that standard mathematical analysis is dependent on the complete relativity of the infinite. In examining the domains of modern physics, infinity is found to lose its entirely relative character and, therefore, to be less amenable to classical analysis. Complementary aspects of microworld infinity are identified and are associated with the equivalent features (inertial and gravitational mass) of Einstein's macroworld theory. The persisting effort to treat essentially non-classical phenomena in classical terms is critically discussed. A new attitude toward the infinite is recommended, one that might lead to establishing a second principle of the relativity of the infinite. The prospect for implementing the suggested approach through a "trans-analytic" meta-theory of dimensional generation is briefly entertained.
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