Metalogical properties, being logical and being formal

Jan Woleński



The predicate ‘being logical’ has at least four applications. We can apply it to concepts, propositions, sets of propositions (systems, theories) and methods. The concepts of quantifier or disjunction are logical but those of horse or water are not. Some propositions, for instance, the principle of excluded middle, are logical, others, for instance the law of gravity, are not. Propositional calculus is a logical theory (belongs to logic), but the theory of evolution is not. In a sense, the problem of logical propositions reduces itself to the question of logical systems, because we can say that A is logical if and only if it belongs to a logical systems (however, see below). Finally, deduction is a logical method of justification, but observation is not.

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