Bruno de Finetti and the Logic of Conditional Events

This article begins by outlining some of the history—beginning with brief remarks of Quine's—of work on conditional assertions and conditional events. The upshot of the historical narrative is that diverse works from various starting points have circled around a nexus of ideas without convincingly tying them together. Section 3 shows how ideas contained in a neglected article of de Finetti's lead to a unified treatment of the topics based on the identification of conditional events as the objects of conditional bets. The penultimate section explores some of the consequences of the resulting logic of conditional events while the last defends it.

[1]  John Corcoran,et al.  The switches "paradox" and the limits of propositional logic , 1973 .

[2]  D. Lewis Probabilities of Conditionals and Conditional Probabilities , 1976 .

[3]  Willard Van Orman Quine,et al.  Methods of Logic , 1951 .

[4]  Philip G. Calabrese,et al.  An algebraic synthesis of the foundations of logic and probability , 1987, Inf. Sci..

[5]  Hung T. Nguyen,et al.  Mathematical Foundations of Conditionals and their Probabilistic Assignments , 1995, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[6]  Didier Dubois,et al.  The logical view of conditioning and its application to possibility and evidence theories , 1990, Int. J. Approx. Reason..

[7]  Wilfrid S. Sellars,et al.  III.—INFERENCE AND MEANING , 1953 .

[8]  Peter Milne,et al.  Avoiding triviality: Fuzzy implications and conditional events , 1996, Int. J. Approx. Reason..

[9]  B. D. Finetti,et al.  La Logique de la Probabilite , 1937 .

[10]  John Corcoran Meanings of Implication , 1973 .

[11]  E. W. Adams,et al.  Probability and the Logic of Conditionals , 1966 .

[12]  D. C. Makinson Topics in Modern Logic , 1973 .

[13]  Charles G. Morgan,et al.  Conditionals, probability, and non-triviality , 1995, J. Philos. Log..

[14]  Nuel D. Belnap,et al.  Restricted Quantification and Conditional Assertion , 1973 .

[15]  Elbert A. Walker,et al.  Stone Algebras, Conditional Events, and Three Valued Logic , 1994, IEEE Trans. Syst. Man Cybern. Syst..

[16]  Robert Stalnaker A Theory of Conditionals , 2019, Knowledge and Conditionals.

[17]  Theodore Hailperin,et al.  Boole's logic and probability , 1976 .

[18]  Frank Daring On the Probabilities of Conditionals , 1994 .

[19]  R. Armstrong The Switches Paradox , 1970 .

[20]  Masao Mukaidono Algebraic Structures of Truth Values in Fuzzy Logic , 1991, Fuzzy Logic and Fuzzy Control.

[21]  B. D. Finetti La prévision : ses lois logiques, ses sources subjectives , 1937 .

[22]  I. Goodman Conditional Objects and the Modeling of Uncertainties , 1988 .

[23]  John L. Bell,et al.  A course in mathematical logic , 1977 .

[24]  R. I. G. Hughes A philosophical companion to first-order logic , 1993 .

[25]  Bas C. van Fraassen,et al.  Gentlemen's wagers: Relevant logic and probability , 1983 .

[26]  Vann McGee,et al.  Conditional Probabilities and Compounds of Conditionals , 1989 .

[27]  Georg J. W. Dorn Popper’s Laws of the Excess of the Probability of the Conditional over the Conditional Probability , 1992 .

[28]  Nuel D. Belnap,et al.  Entailment : the logic of relevance and necessity , 1975 .

[29]  P. Calabrese Deduction and Inference Using Conditional Logic and Probability , 1991 .

[30]  Hung T. Nguyen,et al.  Conditional inference and logic for intelligent systems - a theory of measure-free conditioning , 1991 .

[31]  E. W. Adams,et al.  The logic of conditionals , 1975 .

[32]  Peter Milne,et al.  Verification, falsification, and the logic of enquiry , 1991 .

[33]  Henry E. Kyburg,et al.  Studies in Subjective Probability , 1965 .

[34]  G. Schay An algebra of conditional events , 1968 .

[35]  Michael Dummett,et al.  The logical basis of metaphysics , 1991 .