Pluralisms: Logic, Truth and Domain-Specificity

Abstract

Logicians and Philosophers have developed a large and rich array of logical systems -intuitionistic logic, relevance logics, free logics, a vast assortment of many-valued logics, multiple conclusion logics, extensions of classical logic of various types including temporal and modal logics and many others besides. These are naturally referred to as "logics" and can be considered and studied in the abstract, giving clear-cut notions of what follows from what according to the various different logics. Talk of "logic" (in the singular) often signals something more than a system considered in the abstract. Logic as the study of what follows from what, looks to concern more than what followsfrom what relative to some chosen system. Similarly for talk of, for example, the study of the logic of our language or of the world. Not all of the abstract systems are on a par and philosophers have often provided detailed arguments for regarding their chosen logic as of particular or unique significance, where many of the positions advocated in this way are incompatible. 1 How do we determine which of the candidate logics we should select?It is natural to suppose that we should treat many of the abstract logical systems as just thatperhaps unsuccessful candidates for capturing the genuine logical consequence relation. The possibility of being a logical pluralist seems to allow us to reject none, or at least fewer of such candidates. The pluralist maintains that there is no unique consequence relation.In this paper I will explore one type of logical pluralism. There are other logical pluralist positions that I will not cover here, and, in particular, I will put aside Beall and Restall's form of logical pluralism (2006). They advocate a form of pluralism based on capturing the notion of consequence with (GTT) -an argument is valid iff in every case in which the premises are all true, the conclusion is also true -and recognising multiple acceptable ways to spell out the notion of "case" in this definition. They maintain that this legitimates a wide-ranging logical pluralism, endorsing at the same time a wide range of apparently conflicting logics (including classical, intuitionistic and 1 Uses of logical systems can go beyond capturing logical consequence relations. For example, it might be useful to employ a paraconsistent logic to work with databases that may contain inconsistent data. But that is not to say that there are true contradictions, even though it can be on the record that p and on the record that not-p. See Keefe 2014, footnote 13.