Semantic Penumbra: Concept Similarity in Logic [Book Review]

Topoi 31 (1):121-134 (2011)
Abstract
Logic’s historically central mission has been to provide formally precise descriptions of logical consequence. This was done with two broad expectations in mind. One was that a pre-theoretically recognizable concept of consequence would be present in the ensuing formalization. The other was that the formalization would be mathematically mature. The first expectation calls for conceptual adequacy. The other calls for technical virtuosity. The record of the past century and a third discloses a tension between the two. Accordingly, logicians have sought a reasoned, if delicate, rapprochement, one in which each expectation would be given its due, but well-short of free sway. Recent developments have imperiled this perestroika. One is logic’s massive and often rivalrous pluralism, and the cheapening relativism to which it beckons. This is exacerbated by the long-acknowledged part that the formal representations of logic distort the logical particles of natural language. The present paper discusses what might be done about this
Keywords Analysis  Conceptual adequacy  Consequence  Explication  Generic entailment  Logical particle  Mathematical virtuosity  Semantic penumbra  Similarity  Synthesis
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DOI 10.1007/s11245-012-9118-y
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Word and Object.W. V. Quine - 1960 - MIT Press.
On Denoting.Bertrand Russell - 2005 - Mind 114 (456):873 - 887.

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