Miller, David (2018) A note on small models of relative probability. UNSPECIFIED. (Unpublished)

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Abstract

In the axiomatic theory of relative probability expounded in appendices ∗iv and ∗v of The Logic of Scientific Discovery, the relation a ~ c =Df \-/b[p(a, b) = p(c, b)] of probabilistic indistinguishability on a set S is demonstrably a congruence, and the quotient S = S/∼ is demonstrably a Boolean algebra. The two-element algebra {0, 1} satisfies the axioms if and only if p(1 | 1), p(1 | 0), and p(0 | 0) are assigned the value 1, and p(0, 1) is assigned the value 0 (where p is the interpretation of the quotient p/∼). The four-element models are almost as straightforwardly described. This note sketches a method of construction and authentication that can, in principle, be applied to larger algebras, and identifies all the eight-element models of Popper's system.

Item Type:	Scholarly Text
Subjects:	B Philosophy. Psychology. Religion > BC Logic Q Science > QA Mathematics
Divisions:	Faculty of Social Sciences > Philosophy
Library of Congress Subject Headings (LCSH):	Probabilities -- Philosophy, Logic, Semantics (Philosophy), Science -- Philosophy
Official Date:	2018
Dates:	Date Event 2018 UNSPECIFIED
Number of Pages:	14
Status:	Not Peer Reviewed
Publication Status:	Unpublished
Reuse Statement (publisher, data, author rights):	This paper belongs to the author. Please note that unpublished papers are subject to correction, revision, and modernization, without explicit notice. No version, current or obsolete, of any of these papers and lectures should be cited in print without the author's written permission.
Access rights to Published version:	Restricted or Subscription Access
Copyright Holders:	D. W. Miller
Related URLs:	Other

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