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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

Chapter:
(p.188) 15 The Incommensurability of Inductive Support and Mathematical Probability
Source:
The Probable and The Provable
Author(s):

L. Jonathan Cohen

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198244127.003.0016

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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