Abstract According to Lewis’s Triviality Results (LTR), conditionals cannot satisfy the equation (E) P(C if A) = P(C | A), except in trivial cases. Since 1935 [9], de Finetti showed that by three-valued truth-tables, the equation might be satisfied in a general way (at least for indicative conditionals). This result is not at odds with LTR, because one of its premises, namely that conditionals are two-valued sentences, is dropped. Unfortunately, de Finetti did not equip his truth-tables by a proper notion of logical consequence. Ernst Adams [1], however, provided a probabilistic semantics for the so-called, simple conditionals (that is for those sentences of the form ‘if A then C’ where both A and C are two-valued ordinary sentences) that also satisfies equation (E) and provides a probabilistic counterpart of logical consequence (called pentailment). Adams’s logic is coextensive to Stalnaker’s and Lewis’s logic as far as simple conditionals are concerned. A theorem, proved by McGee [22], shows that no truth-functional many-valued logic allows a relation of logical consequence coextensive with Adams’s p-entailment. This result applies to de Finetti’s truth-functional semantics. This paper presents amodifiedmodal (Kripke-style) version of de Finetti’s semantics that escapesMcGee’s result and provides a general truth-conditional semantics for indicative conditionals, without being affected by LTR. The new framework encompasses and extends Adams’s probabilistic semantics (APS) to compounds of conditionals. Like APS, the present truth-conditional semantics does not deal with counterfactual conditionals. From the philosophical side, this theory challenges the view (endorsed by many authors) that indicative conditionals lack truth-conditions and show that a truth conditional semantics bypassing LTR is possible. Moreover, a comparison of the present theory with Stalnaker’s theories about compounds of conditionals shows that the present theory presents inherent advantages, especially regarding the import-export law.

Bypassing Lewis’s Triviality Results. A Kripke-Style Partial Semantics for Compounds of Adams’s Conditionals / Mura, Alberto Mario. - In: LOGICA UNIVERSALIS. - ISSN 1661-8300. - (In corso di stampa).

Bypassing Lewis’s Triviality Results. A Kripke-Style Partial Semantics for Compounds of Adams’s Conditionals

Alberto Mura
In corso di stampa

Abstract

Abstract According to Lewis’s Triviality Results (LTR), conditionals cannot satisfy the equation (E) P(C if A) = P(C | A), except in trivial cases. Since 1935 [9], de Finetti showed that by three-valued truth-tables, the equation might be satisfied in a general way (at least for indicative conditionals). This result is not at odds with LTR, because one of its premises, namely that conditionals are two-valued sentences, is dropped. Unfortunately, de Finetti did not equip his truth-tables by a proper notion of logical consequence. Ernst Adams [1], however, provided a probabilistic semantics for the so-called, simple conditionals (that is for those sentences of the form ‘if A then C’ where both A and C are two-valued ordinary sentences) that also satisfies equation (E) and provides a probabilistic counterpart of logical consequence (called pentailment). Adams’s logic is coextensive to Stalnaker’s and Lewis’s logic as far as simple conditionals are concerned. A theorem, proved by McGee [22], shows that no truth-functional many-valued logic allows a relation of logical consequence coextensive with Adams’s p-entailment. This result applies to de Finetti’s truth-functional semantics. This paper presents amodifiedmodal (Kripke-style) version of de Finetti’s semantics that escapesMcGee’s result and provides a general truth-conditional semantics for indicative conditionals, without being affected by LTR. The new framework encompasses and extends Adams’s probabilistic semantics (APS) to compounds of conditionals. Like APS, the present truth-conditional semantics does not deal with counterfactual conditionals. From the philosophical side, this theory challenges the view (endorsed by many authors) that indicative conditionals lack truth-conditions and show that a truth conditional semantics bypassing LTR is possible. Moreover, a comparison of the present theory with Stalnaker’s theories about compounds of conditionals shows that the present theory presents inherent advantages, especially regarding the import-export law.
Bypassing Lewis’s Triviality Results. A Kripke-Style Partial Semantics for Compounds of Adams’s Conditionals / Mura, Alberto Mario. - In: LOGICA UNIVERSALIS. - ISSN 1661-8300. - (In corso di stampa).
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11388/230046
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