The Monist 79 (1):141-147 (1996)

Cory Juhl
University of Texas at Austin
From one perspective, the fundamental notions of point-set topology have to do with sequences and their limits. A broad class of epistemological questions also appear to be concerned with sequences and their limits. For example, problems of empirical underdetermination—which of a collection of alternative theories is true—have to do with logical properties of sequences of evidence. Underdetermination by evidence is the central problem of Plato’s Meno, of one of Sextus Empiricus’ many skeptical doubts, and arguably it is the idea at work in Kant’s antinomies, for example in his account of the infinite divisibility of matter. Many questions of methodology, or of the logic of discovery, have to do with sequences and their limits. For example, under what conditions do Bayesian procedures, which put a prior probability distribution over alternative hypotheses and possible evidence and form conditional probabilities as new evidence is obtained, converge to the truth? Some analyses of “S knows that p” seem to appeal to properties of actual and possible sequences of something—for example Nozick’s proposal that knowledge of p is belief in p produced by a method that would not produce belief in p if p were false and would produce belief in p if p were true. Even questions about finding the truth under a quite radical relativism, in which truth depends on conceptual scheme and conceptual schemes can be altered, have been analyzed as a kind of limiting property of sequences.
Keywords Analytic Philosophy  Contemporary Philosophy  General Interest  Philosophy of Mind  Philosophy of Science
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ISBN(s) 0026-9662
DOI 10.5840/monist19967916
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