In this paper, we propose Kripke-style models for the logics of evidence and truth LETJ and LETF. These logics extend, respectively, Nelson’s logic N4 and the logic of first-degree entailment (FDE) with a classicality operator ∘ that recovers classical logic for formulas in its scope. According to the intended interpretation here proposed, these models represent a database that receives information as time passes, and such information can be positive, negative, non-reliable, or reliable, and a formula ∘A means that the information about A, either positive or negative, is reliable. This proposal is in line with the interpretation of N4 and FDE as information-based logics, but adds to the four scenarios expressed by them two new scenarios: reliable (or conclusive) information (i) for the truth and (ii) for the falsity of a given proposition.
In this paper I sketch some lines of response to Mark Colyvan’s (2008) indispensability arguments for the existence of inconsistent objects, being mainly concerned with the indispens ability of inconsistent mathematical entities. My response will draw heavily on Jody Azzouni’s (2004) deflationary nominalism.
Priest (2006, Ch.8, 2nd edn. Oxford University Press), argues that classical reasoning can be made compatible with his preferred (paraconsistent) logical theory by proposing a methodological maxim authorizing the use of classical logic in consistent situations. Although Priest has abandoned this proposal in favour of the one in G. Priest (1991, Stud. Log., 50, 321–331), I shall argue that due to the fact that the derivability adjustment theorem holds for several logics of formal (in)consistency (cf. W. A. Carnielli and M. E. Coniglio, 2016, Springer), these paraconsistent logics are particularly well suited to accommodate classical reasoning by means of a version of that maxim, yielding thus an enthymematic account of classical recapture.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.