Studia Logica

, Volume 103, Issue 3, pp 579–598 | Cite as

Non-deterministic Conditionals and Transparent Truth

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Abstract

Theories where truth is a naive concept fall under the following dilemma: either the theory is subject to Curry’s Paradox, which engenders triviality, or the theory is not trivial but the resulting conditional is too weak. In this paper we explore a number of theories which arguably do not fall under this dilemma. In these theories the conditional is characterized in terms of (infinitely-valued) non-deterministic matrices. These non-deterministic theories are similar to infinitely-valued Łukasiewicz logic in that they are consistent and their conditionals are quite strong. The difference is the following: while Łukasiewicz logic is \({\omega}\)-inconsistent, the non-deterministic theories might turn out to be \({\omega}\)-consistent.

Keywords

Naive truth theory Łukasiewicz logic Curry’s paradox Non-deterministic semantics \({\omega}\)-Inconsistency 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.SADAFConicetBuenos AiresArgentina

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