Abstract
In order to prove the validity of logical rules, one has to assume these rules in the metalogic. However, rule-circular ‘justifications’ are demonstrably without epistemic value (sec. 1). Is a non-circular justification of a logical system possible? This question attains particular importance in view of lasting controversies about classical versus non-classical logics. In this paper the question is answered positively, based on meaning-preserving translations between logical systems. It is demonstrated that major systems of non-classical logic, including multi-valued, paraconsistent, intuitionistic and quantum logics, can be translated into classical logic by introducing additional intensional operators into the language (sec. 2–5). Based on this result it is argued that classical logic is representationally optimal. In sec. 6 it is investigated whether non-classical logics can be likewise representationally optimal. The answer is predominantly negative but partially positive. Nevertheless the situation is not symmetric, because classical logic has important ceteris paribus advantages as a unifying metalogic.
Highlights
The Significance of Non-circular Justifications for Contemporary Philosophy of LogicThe background of this paper is a foundation-theoretic epistemology whose class of ‘basic’ beliefs is minimalistic, consisting only of immediately evident analytical and introspective beliefs
We have shown that major kinds of non-classical logics are translatable into extended classical logic
We even conjecture that all non-classical logics can be translated into a suitably extended classical logic
Summary
The Significance of Non-circular Justifications for Contemporary Philosophy of Logic. In this framework the major epistemic load has to be carried by deductive, inductive or abductive reasoning
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