Note on Probability of Logical Sentences and the Linda Problem

Authors

DOI:

https://doi.org/10.15633/acr.5405

Keywords:

probability, logic, Boolean valuation, Linda problem

Abstract

This paper presents a logical concept of probability which seems to be obvious, as it is, but the author is not aware of any elaboration of a developed studies on the issue or of any special philosophical application of it. Such a probability of the formula A, of the language of the propositional logic, is the quotient of the number of Boolean valuations of formula A of the classical propositional calculus, which takes the logical value 1, to the number of all Boolean valuations of such a formula A. An application of this concept of logical probability to the solution of the Linda problem is given.

References

Carnap R., Logical Foundations of Probability, Chicago 1950.

Hintikka J., On Semantic Information, in: Information and Inference, eds. J. Hintikka, P. Suppses, Dordrecht 1970, p. 3–27.

Lorenz D., Kooi B., Sack J., Logic and Probability, https://plato.stanford.edu/archives/sum2019/entries/logic-probability/ (15.12.2022).

Makinson D., Bridges from Classical to Nonmonotonic Logic, London 2005.

Mazurkiewicz S., Przyczynek do aksjomatyki rachunku prawdopodobieństwa. Zur Axiomatik der Warscheinlichkeitsrechnung, „Sprawozdania z Posiedzeń Towarzystwa Naukowego Warszawskiego. Wydział III nauk matematyczno-fizycznych” 25 (1933) no 1–6, p. 1–4.

Mazurkiewicz S., Über die Grundlagen der Wahrscheinlichkeitsrechnung I, “Monatshefte für Mathematik und Physik” 41 (1934), p. 343–352; https://doi.org/10.1007/BF01697866.

Olszewski A., A Few Comments on the Linda Problem, “Organon F” 24 (2017), p. 184–195.

Olszewski A., Linda Problem – the Tame Solution in Question, “Analecta Cracoviensia” 51 (2019), p. 209–217.

Tversky A., Kahneman D., Extensional versus Intuitive Reasoning: The Conjunction Fallacy in Probability Judgment, “Psychological Review” 90 (1983), p. 293–315; https://doi.org/10.1037/0033-295X.90.4.293.

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Published

2023-06-30

Issue

Vol. 54 (2022)

Section

Filozofia

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