Linguistics and Philosophy 45 (3):511-558 (2022)

Authors
Anna Wójtowicz
University of Warsaw
Krzysztof Wójtowicz
University of Warsaw
Abstract
We define a model for computing probabilities of right-nested conditionals in terms of graphs representing Markov chains. This is an extension of the model for simple conditionals from Wójtowicz and Wójtowicz. The model makes it possible to give a formal yet simple description of different interpretations of right-nested conditionals and to compute their probabilities in a mathematically rigorous way. In this study we focus on the problem of the probabilities of conditionals; we do not discuss questions concerning logical and metalogical issues such as setting up an axiomatic framework, inference rules, defining semantics, proving completeness, soundness etc. Our theory is motivated by the possible-worlds approach ; however, our model is generally more flexible. In the paper we focus on right-nested conditionals, discussing them in detail. The graph model makes it possible to account in a unified way for both shallow and deep interpretations of right-nested conditionals. In particular, we discuss the status of the Import-Export Principle and PCCP. We briefly discuss some methodological constraints on admissible models and analyze our model with respect to them. The study also illustrates the general problem of finding formal explications of philosophically important notions and applying mathematical methods in analyzing philosophical issues.
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DOI 10.1007/s10988-021-09324-z
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References found in this work BETA

On Conditionals.Dorothy Edgington - 1995 - Mind 104 (414):235-329.
General Propositions and Causality.Frank Plumpton Ramsey - 1929 - In The Foundations of Mathematics and other Logical Essays. Kegan Paul, Trench, Trübner. pp. 237-255.
The Logic of Conditionals.Ernest Adams - 1965 - Inquiry: An Interdisciplinary Journal of Philosophy 8 (1-4):166 – 197.

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Citations of this work BETA

Dutch Book Against Lewis.Anna Wójtowicz & Krzysztof Wójtowicz - 2021 - Synthese 199 (3-4):9185-9217.

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