I. preliminary remarks.The writers of text-books of logic commonly take it for granted that there is a single theory, a set of rules embodying what are called the ‘laws of thought’; and that these laws are universally the same. This conception seems scarcely to accord with the present level of knowledge. For we do already possess distinct logics — if this term is used to denote precisely elaborated formalized systems: e.g., logics including or excluding a Theory of Types, systems admitting or barring the law of excluded middle, etc. Perhaps one might add that the rise of a conventionalistic mode of thinking — emanating from mathematics — today favours attempts to construct novel logics. Here two ways present themselves.
KeywordsFree Variable Propositional Calculus Partial Negation Double Negation Strong Negation
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- 1.For a symbolic system with a simple hierarchy of types see: F. P. Ramsey, ‘The Foundations of Mathematics’, Proc. Lond.Math. Soc., vol. 25, 1945.Google Scholar
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