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How does probability theory generalize logic?
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Miller, David (2004) How does probability theory generalize logic? In: Sextas Jornadas Rolando Chuaqui, Santiago, Chile, May 2004 pp. 1-23. (Unpublished)
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Abstract
Nearly half a century ago Popper [1959], appendices *iv and *v, presented a number of related axiomatizations of the theory of probability in each of which p(x | z) is defined for all x and z, even z = yy' (where concatenation turns out to represent meet, and the accent complementation). These systems are too little known amongst mathematicians. Popper went on to claim that his systems provide a context within which it is possible to give fully correct definitions of the relation of derivability between sentences (in the sense of the classical sentential calculus), and of the property of sentential demonstrability, by means of the formulas
z |- x =Df p(x | zx') = 1
|- x =Df p(x | x') = 1.
This claim has been challenged by Stalnaker [1970], Harper [1975], and by Leblanc & van Fraassen [1979]. The challenge has never been properly answered (though a start was made in Popper & Miller [1994], §4). The aim of this talk is to answer it, and to contrast Popper’s enterprise with what is known as probabilistic semantics.
| Item Type: | Conference Item (Other) | ||||
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| Subjects: | B Philosophy. Psychology. Religion > B Philosophy (General) B Philosophy. Psychology. Religion > BC Logic Q Science > QA Mathematics |
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| Divisions: | Faculty of Social Sciences > Philosophy | ||||
| Library of Congress Subject Headings (LCSH): | Probabilities, Logic, Popper, Karl R. (Karl Raimund), 1902-1994, Algebra | ||||
| Official Date: | May 2004 | ||||
| Dates: |
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| Page Range: | pp. 1-23 | ||||
| Status: | Not Peer Reviewed | ||||
| Publication Status: | Unpublished | ||||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 Please note that unpublished papers are subject to correction, revision, and modernization, without explicit notice.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 | ||||
| Conference Paper Type: | Other | ||||
| Title of Event: | Sextas Jornadas Rolando Chuaqui | ||||
| Type of Event: | Other | ||||
| Location of Event: | Santiago, Chile | ||||
| Date(s) of Event: | May 2004 | ||||
| Related URLs: |
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