Blackwell Reference Online

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Reduction is the absorption or subsumption of one theory, conceptual scheme, or mode of discourse by another. The notion of reduction is employed in a number of family-resemblance ways relevant to metaphysics, involving three interrelated dimensions or axes: ontological, semantic and scientific. Ontologically reductionist positions typically assert that there are systematic identities between entities, kinds, properties and facts posited respectively in the ‘higher-level’ discourse and in the ‘lower-level’, reducing, discourse. Semantically reductionist positions typically assert that there are systematic semantic equivalences between statements in the higher-level and in the lower-level discourse. Scientific reductionist positions typically assert that the laws and phenomena described in some scientific theory or theories are systematically explainable by those described in some other scientific theory. Semantically reductionist projects have often been viewed as a major means of implementing ontological reductions. An example is logicism in philosophy of mathematics. Semantically, the logicist maintains that all the key concepts and terms of classical mathematics are definable via the terms and concepts of logic and set theory, in such a way that all of pure mathematics is derivable (under these definitions) from logic plus fundamental assumptions about classes. (Logicists ... log in or subscribe to read full text