Conjunction and Disjunction in Infectious Logics
In this paper we discuss the extent to which conjunction and disjunction can be rightfully regarded as such, in the context of infectious logics. Infectious logics are peculiar many-valued logics whose underlying algebra has an absorbing or infectious element, which is assigned to a compound formula whenever it is assigned to one of its components. To discuss these matters, we review the philosophical motivations for infectious logics due to Bochvar, Halldén, Fitting, Ferguson and Beall, noticing that none of them discusses our main question. This is why we finally turn to the analysis of the truth-conditions for conjunction and disjunction in infectious logics, employing the framework of plurivalent logics, as discussed by Priest. In doing so, we arrive at the interesting conclusion that —in the context of infectious logics— conjunction is conjunction, whereas disjunction is not disjunction.
KeywordsConjunction Disjunction Infectious logics Logics of nonsense Plurivalent logics
We would like to thank the anonymous referees for their helpful (and enthusiastic!) comments that improved our paper. Hitoshi Omori is a Postdoctoral Research Fellow of Japan Society for the Promotion of Science (JSPS). Damian Szmuc is enjoying a PhD fellowship of the National Scientific and Technical Research Council of Argentina (CONICET) and his visits to Kyoto when this collaboration took place were partially supported by JSPS KAKENHI Grant Number JP16H03344.
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