Significance logics.

Relevant Logics Obeying Component Homogeneity

“…Another challenge by Routley is to the idea that meaningless expressions do not need a specific logical treatment. Again, Routley shared this challenge with other logicians-mainly, Brady [10,9] and Goddard [33], but also Bochvar [6] and Halldén [35]. This challenge gave rise to the logic of significance.…”

“…Section 3 presents the five-valued logic S * fde as a relevant logic of meaninglessness. Section 4 detours from the focus on meaninglessness by [10,32,33] and explores two logics that obey CH while designating one contaminating value. These include a system dual to S * fde -which we call dS * fdeand a subsystem of S * fde and dS * fde -which we call crossS * fde .…”

“…6 The Principle of Component Homogeneity. The project of the logic of significance by [10,32,33] centers around three tenets: (a) meaninglessness is treated as a truth value alongside truth and falsity; (b) 'one does not want to be committed to sometimes asserting logical nonsense' [9]; (c) meaningful (i.e. true or false) sentences obey classical logic.…”

“…The logic of significance from [10,32,33] is not the only tradition (and many-valued approach) to investigate the impact of meaninglessness on our reasoning. An independent project is that of Bochvar [6], which indeed interprets K w 3 as a logic of meaninglessness.…”

“…For the sake of completeness, notice that the projects related to [33] often include formal devices that express the notion that a sentence is meaningful. In particular, the systems T0 from [10,32] and H 3 from [35] extend standard propositional language with a connective •, with •ϕ reading 'ϕ is meaningful'. 10 Albeit interesting, the connective does not proves relevant here, as dealing with it would lead us far from the main focus of the paper.…”