Why classical logic is privileged: justification of logics based on translatability

Abstract

In Sect. 1 it is argued that systems of logic are exceptional, but not a priori necessary. Logics are exceptional because they can neither be demonstrated as valid nor be confirmed by observation without entering a circle, and their motivation based on intuition is unreliable. On the other hand, logics do not express a priori necessities of thinking because alternative non-classical logics have been developed. Section 2 reflects the controversies about four major kinds of non-classical logics—multi-valued, intuitionistic, paraconsistent and quantum logics. Its purpose is to show that there is no particular domain or reason that demands the use of a non-classical logic; the particular reasons given for the non-classical logic can also be handled within classical logic. The result of Sect. 2 is substantiated in Sect. 3, where it is shown (referring to other work) that all four kinds of non-classical logics can be translated into classical logic in a meaning-preserving way. Based on this fact a justification of classical logic is developed in Sect. 4 that is based on its representational optimality. It is pointed out that not many but a few non-classical logics can be likewise representationally optimal. However, the situation is not symmetric: classical logic has ceteris paribus advantages as a unifying metalogic, while non-classical logics can have local simplicity advantages.

Pluralismo lógico, corrección y tolerancia carnapiana

“…Pero sí debemos observar que la lógica clásica, dentro de este programa de investigación, cumple un rol fundamental de lenguaje común, un rol que en principio ninguna otra lógica cumple. Según G. Schurz (2021), esto se debe a que las lógicas no-clásicas más utilizadas pueden traducirse a la lógica clásica, pero usualmente no pueden traducirse entre sí, o a veces ni siquiera pueden contener la lógica clásica. 16 Por ejemplo, la lógica paraconsistente LP es llamativamente débil para desarrollar metateorías, porque carece de una negación fuerte.…”