Abstract
A brief survey of the historical development of rationalism is made. It is shown that neither rationalism nor empiricism satisfy Aristotle's postulates for a science. The development of mathematical statistics shows a direct concern with the relation between theory and observation. Results to date suggest that Aristotle's postulates do not yield a suitable characterization of science. It is concluded that any system of rationalism suitable for science will share the following characteristics with mathematical statistics; (1) basic concepts will involve both theoretical and empirical entities, (2) some aspects of the rationalism will he developed empirically, and (3) some aspects of the rationalism will be developed by “elimination” of “true values” from “self-evident” mathematics. New systems of scientific rationalism may differ from mathematical statistics by (1) prohibiting the use of the “excluded middle,” (2) replacing, or reformulating, the probability concept, and (3) relaxing the requirement of indefinite repetition of experiments.
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