It is usually considered that \(A \rightarrowtail (B \rightarrowtail C)\) (i) implies and (ii) is implied by \((A \wedge B) \rightarrowtail C\) . (i) is called Import (IM) and (ii) Export (EX). IM seems to be valid for natural language conditionals, but here we present counterexamples to EX, such as: If he uses cocaine every weekend and hides it from his family, he is already addicted, but not: If he uses cocaine every weekend, then if he hides it from his family, he is already addicted. Gibbard’s collapse theorem depends on IM-EX and Simplification (Conjunction Elimination). Here we use the implicative conditional for a logical analysis of IM-EX. We show that possibilistic versions of IM and EX are respectively valid and invalid for the implicative conditional, in accordance with what is observed in natural language conditionals. We conclude that this supports the adequacy of the implicative conditional for analysing the implicative use of natural language conditionals. We also conclude that the implicative conditional is immune to Gibbard’s collapse theorem, since it invalidates both IM-EX and Simplification.

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

Counterexamples to Import-Export in Conditionals: A Logical Analysis

  • Eric Raidl,
  • Gilberto Gomes

摘要

It is usually considered that \(A \rightarrowtail (B \rightarrowtail C)\) (i) implies and (ii) is implied by \((A \wedge B) \rightarrowtail C\) . (i) is called Import (IM) and (ii) Export (EX). IM seems to be valid for natural language conditionals, but here we present counterexamples to EX, such as: If he uses cocaine every weekend and hides it from his family, he is already addicted, but not: If he uses cocaine every weekend, then if he hides it from his family, he is already addicted. Gibbard’s collapse theorem depends on IM-EX and Simplification (Conjunction Elimination). Here we use the implicative conditional for a logical analysis of IM-EX. We show that possibilistic versions of IM and EX are respectively valid and invalid for the implicative conditional, in accordance with what is observed in natural language conditionals. We conclude that this supports the adequacy of the implicative conditional for analysing the implicative use of natural language conditionals. We also conclude that the implicative conditional is immune to Gibbard’s collapse theorem, since it invalidates both IM-EX and Simplification.