On metalogical relativism

Vladimir L. Vasyukov

pp. 495-511

in: Arnold Koslow, Arthur Buchsbaum (eds), The road to universal logic I, Basel, Birkhäuser, 2015

Abstract

The conception of logical pluralism claims that there is not one true logic but there are many. The conception of metalogical relativism is based on the assumption that there is not one correct answer as to whether a given argument is deductively valid, but there are many—many non-classical answers depending of which non-classical metalogic we exploit: intuitionistic, relevant, quantum, many-valued, etc. Since this leads to the interplay between logics and metalogics the question arises: What is the nature of this interplay? The Universal Logics approach gives us hints at some answers to this question but at the expense of the exploitation of different combination of non-classical logical systems leading to the transition from metalogical pluralism to metalogical monism. The only problem in this case is the impossibility of the exploitation of an infinite combination of non-classical systems. There are also some semantic keys to the issue under consideration which are connected with the problem of the interplay of classical and non-classical universes: non-classical logics would be interpreted in the classical universe, and vice versa, the classical logic would be interpreted in non-classical universes.