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

Dialetheism in Action: A New Strategy for Solving the Equal Validity Paradox

This paper starts from the Equal Validity Paradox, a paradoxical argument connected to the so-called phenomenon of faultless disagreement. It is argued that there are at least six strategies for solving the paradox. After presenting the first five strategies and their main problems, the paper focuses on the sixth strategy which rejects the assumption that every proposition cannot be both true a false. Dialetheism is the natural candidate for developing strategy six. After presenting strategy six in detail, we formulate a normative problem for the dialetheist and offer a tentative solution to it. We then elaborate further considerations connecting strategy six to pluralism about truth and logic. Even if strategy six is a hard path to take, its scrutiny highlights some important points on truth, logic and the norms for acceptance and rejection

Unity through truth

Renewed worries about the unity of the proposition have been taken as a crucial stumbling block for any traditional conception of propositions. These worries are often framed in terms of how entities independent of mind and language can have truth conditions: why is the proposition that Desdemona loves Cassio true if and only if she loves him? I argue that the best understanding of these worries shows that they should be solved by our theory of truth and not our theory of content. Specifically, I propose a version of the redundancy theory according to which ‘it is true that Desdemona loves Cassio’ expresses the same proposition as ‘Desdemona loves Cassio’. Surprisingly, this variant of the redundancy theory treats ‘is true’ as an ordinary predicate of the language, thereby defusing many standard criticisms of the redundancy theory

The Liar Without Truth

Liar sentences say nothing, according to this chapter—which, it claims, we can, in effect, prove. But extending the proof as the chapter does appears to result in revenge. The solution to this problem is to restrict the laws of logic by distinguishing expressing a falsehood from failing to express a truth. But the question that presses is how we can signify that a given sentence—a liar sentence, for example—fails to express a truth without being mired in paradox. To this end, the chapter revisits the sort of bilateral system that Rumfitt (2000) has discussed. The chapter shows that there is a way of developing Aristotle’s conception of truth into a definition of truth that does not yield a contradiction, even when applied to a semantically closed language. If successful, the proposal will enable us to reject a Strengthened Liar as untrue without asserting its negation.</p