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Logic and Logical Philosophy

Dynamic Probabilistic Entailment. Improving on Adams' Dynamic Entailment Relation
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Dynamic Probabilistic Entailment. Improving on Adams' Dynamic Entailment Relation

Authors

  • Robert van Rooij Institute for Logic, Language and Computation (ILLC), University of Amsterdam https://orcid.org/0000-0001-6819-6685
  • Patricia Mirabile Institute for Logic, Language and Computation (ILLC), University of Amsterdam https://orcid.org/0000-0001-6440-079X

DOI:

https://doi.org/10.12775/LLP.2021.022

Keywords

probabilistic entailment, experimental philosophy

Abstract

The inferences of contraposition (A ⇒ C ∴ ¬C ⇒ ¬A), the hypothetical syllogism (A ⇒ B, B ⇒ C ∴ A ⇒ C), and others are widely seen as unacceptable for counterfactual conditionals. Adams convincingly argued, however, that these inferences are unacceptable for indicative conditionals as well. He argued that an indicative conditional of form A ⇒ C has assertability conditions instead of truth conditions, and that their assertability ‘goes with’ the conditional probability p(C|A). To account for inferences, Adams developed the notion of probabilistic entailment as an extension of classical entailment. This combined approach (correctly) predicts that contraposition and the hypothetical syllogism are invalid inferences. Perhaps less well-known, however, is that the approach also predicts that the unconditional counterparts of these inferences, e.g., modus tollens (A ⇒ C, ¬C ∴ ¬A), and iterated modus ponens (A ⇒ B, B ⇒ C, A ∴ C) are predicted to be valid. We will argue both by example and by calling to the results from a behavioral experiment (N = 159) that these latter predictions are incorrect if the unconditional premises in these inferences are seen as new information. Then we will discuss Adams’ (1998) dynamic probabilistic entailment relation, and argue that it is problematic. Finally, it will be shown how his dynamic entailment relation can be improved such that the incongruence predicted by Adams’ original system concerning conditionals and their unconditional counterparts are overcome. Finally, it will be argued that the idea behind this new notion of entailment is of more general relevance.

Author Biographies

Robert van Rooij, Institute for Logic, Language and Computation (ILLC), University of Amsterdam

Robert van Rooij, Professor Logic and Cognition, director of Institute for Logic, Language and Computation

 

Patricia Mirabile, Institute for Logic, Language and Computation (ILLC), University of Amsterdam

dr in Philosophy and Cognitive Science

References

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Logic and Logical Philosophy

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Published

2021-12-23

How to Cite

1.
VAN ROOIJ, Robert and MIRABILE, Patricia. Dynamic Probabilistic Entailment. Improving on Adams’ Dynamic Entailment Relation. Logic and Logical Philosophy. Online. 23 December 2021. Vol. 31, no. 3, pp. 359-384. [Accessed 5 July 2025]. DOI 10.12775/LLP.2021.022.
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Vol. 31 No. 3 (2022): September

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