The Essential But Implicit Role of Modal Concepts in Science
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When J. C. C. McKinsey and I were working on the foundations of mechanics many years ago, we thought it important to give a rigorous axiomatization within standard set theory, and we therefore resisted any use of modal concepts or counterfactual conditionals in the formulation of the axioms of mechanics. I continue to think that the use of an extensional set-theoretical framework is appropriate and adequate for most, if not all, scientific discourse. As my interests have shifted more to the foundations of probability and the applications of probability concepts in the behavioral sciences, however, I have gradually come to the position that modal concepts, especially as expressed in the use of probability concepts, are essential to standard scientific talk. Yet, in a majority of cases the modal concepts remain implicit in that talk, and their logic is scarcely used in either theoretical or experimental analyses of empirical phenomena. In this paper I expand on these main points under two headings, probability and physical space, each of which raises particular issues about modal concepts.
KeywordsSample Space Modal Character Modal Concept Primitive Concept Infinite Population
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