Are There Really Two Logics

As a historian of logic, I am frequently puzzled by the things which people have to say about the relationship between mathematical logic and some other kind of logic which is variously described as ‘intentional’ and ‘traditional.’ Part of my puzzlement arises from my failure to understand precisely what kind of system is being offered under the guise of intentional logic. I have always taken it that logic is concerned with valid inferences, with showing us how we may legitimately derive a conclusion from a set of premisses; yet the validation of inferences seems to be the least of the concerns of the intentional logician. He says that it can be done, but he does not bother to show us how. My purpose in this paper is to list some of the sources of my puzzlement in the hope that an exponent of intentional logic will show me how they can be resolved, and how their resolution will contribute to the building of a system (however informal) in which different types of argument can be validated

Algorithm · Argument (complex analysis) · Cognitive science · Epistemology · Mathematical logic · Programming language · Resolution (logic) · Set (abstract data type) · Artificial Intelligence · Computer Science · History and Theory of Mathematics · Mathematics · Philosophy · Philosophy and History of Science · Psychology

• Intentional Logic, A Logic Based on Philosophical Realism

  Robert M Martins, R M Martin et al.•Philosophy and Phenomenological…•1953

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• Two Logics

  R H Stoothoff, Robert Stoothoff et al.•The Philosophical Quarterly•1970

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