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The Probable and The Provable$
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L. Jonathan Cohen

Print publication date: 1977

Print ISBN-13: 9780198244127

Published to Oxford Scholarship Online: October 2011

DOI: 10.1093/acprof:oso/9780198244127.001.0001

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The Incommensurability of Inductive Support and Mathematical Probability

The Incommensurability of Inductive Support and Mathematical Probability

(p.188) 15 The Incommensurability of Inductive Support and Mathematical Probability
The Probable and The Provable

L. Jonathan Cohen

Oxford University Press

This chapter provides an elaboration on the incommensurability of inductive support and mathematical probability. It begins by presenting the argument from the possibility of anomalies. If inductive support-grading is to allow for the existence of anomalies, it cannot depend on the mathematical probabilities involved. A second argument for the incommensurability of inductive support with mathematical probability may be built up on the basis of the conjunction principle for inductive support. If s[H,E] conforms to this principle, the actual value of pM[H] must be irrelevant to that of s[H,E] unless intolerable constraints are to restrict the mathematical probability of one conjunct on another. Since the actual value of pM[E,H] must also be irrelevant to that of s[H,E], and s[H,E] cannot possibly be a function of pM[E] alone, it follows that s[H,E] cannot be a function of the mathematical probabilities involved.

Keywords:   inductive support, mathematical probability, incommensurability, inductive support-grading, conjunction principle

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