Inference, Consequence, Implication: A Constructivist's Perspective

Philosophia Mathematica 6 (2):178-194 (1998)
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An implication is a proposition, a consequence is a relation between propositions, and an inference is act of passage from certain premise-judgements to another conclusion-judgement: a proposition is true, a consequence holds, whereas an inference is valid. The paper examines interrelations, differences, refinements and linguistic renderings of these notions, as well as their history. The truth of propositions, respectively the holding of consequences, are treated constructively in terms of verification-objects. The validity of an inference is elucidated in terms of the existence of a chain of immediately evident steps linking premises and conclusion.



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