Meanings of Implication

Dialogos 9 (24):59-76 (1973)
Thirteen meanings of 'implication' are described and compared. Among them are relations that have been called: logical implication, material implication,deductive implication, formal implication, enthymemic implication, and factual implication. In a given context, implication is the homogeneous two-place relation expressed by the relation verb 'implies'. For heuristic and expository reasons this article skirts many crucial issues including use-mention, the nature of the entities that imply and are implied, and the processes by which knowledge of these relations are achieved. This paper is better thought of as an early stage of a dialogue than as a definitive treatise.
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Frege, Hilbert, and the Conceptual Structure of Model Theory.William Demopoulos - 1994 - History and Philosophy of Logic 15 (2):211-225.

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