Conditionals, probability, and non-triviality
type: Item
instance of: scholarly article
title: Conditionals, probability, and non-triviality
zbMATH Open document ID: 0838.03016
DOI: 10.1007/BF01052599
author: Charles G. Morgan
author: Edwin D. Mares
published in: Journal of Philosophical Logic
publication date: 1996-06-06T00:00:00Z
review text: \textit{David Lewis}, in his ``Probabilities of conditionals and conditional probability'' [Philosophical Review 85, 279-315 (1976)], showed that, on plausible assumptions about probability functions, Adams's project of setting the probability of conditionals equal to the conditional probability trivialises the probability functions [\textit{E. W. Adams}, The logic of conditionals (1975; Zbl 0324.02002)]. Here, the authors prove: (a) That the implication fragment of intuitionist logic is the weakest logic for which the probability of a conditional is the conditional probability; (b) That adding negation (even with very weak assumptions) is sufficient to trivialise the resulting system. The system of \textit{B. C. van Fraassen} [``Probabilities of conditionals'', in: Foundations of probability theory, statistical inference, and statistical theories in science, Vol. I, Proc. Int. Colloq., London/Can. 1973, 261-300 (1976; Zbl 0339.02025)]\ succumbs to triviality of Adams's thesis is added to it; (c) There are various logics with \(\&\), \(\vee\), and \(F\), stronger than minimal logic but weaker than classical logic, which have a probabilistic semantics.
Mathematics Subject Classification ID: 03B48
Mathematics Subject Classification ID: 03B20
zbMATH DE Number: 819339
zbMATH Keywords: probability functions
zbMATH Keywords: probability of conditionals
zbMATH Keywords: conditional probability
zbMATH Keywords: implication fragment of intuitionist logic
zbMATH Keywords: probabilistic semantics
reviewed by: Jim Mackenzie
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01052599
OpenAlex ID: W2078594708
description: scientific article; zbMATH DE number 819339