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Poincare, Richard's Paradox and Indefinite Extensibility

Peter Clark
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association
Vol. 1994, Volume Two: Symposia and Invited Papers (1994), pp. 227-235
Stable URL: http://www.jstor.org/stable/192932
Page Count: 9
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Poincare, Richard's Paradox and Indefinite Extensibility
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Abstract

A central theme in the foundational debates in the early Twentieth century in response to the paradoxes was to invoke the notion of the indefinite extensibility of certain concepts e,g. definability (the Richard paradox) and class (the Zermelo-Russell contradiction). Dummett has recently revived the notion, as the real lesson of the paradoxes and the source of Frege's error in basic law five of the Grundgesetze. The paper traces the historical and conceptual evolution of the concept and critices Dummett's argument that the proper lesson of the paradoxes is that set theory is a theory of indefinitely extensible domains.

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