Art, Open-Endedness, and Indefinite Extensibility

Roy T. Cook

in Art and Abstract Objects

Published in print January 2013 | ISBN: 9780199691494
Published online January 2013 | e-ISBN: 9780191746277 | DOI:
Art, Open-Endedness, and Indefinite Extensibility

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It is often claimed that the concept art is open-ended and that this open-endedness prevents there being precise, necessary, and sufficient conditions for application of the concept (a definition of art) and that open-endedness entails that the extension of the concept art will be fuzzy, vague, or otherwise imprecise. After resolving what the open-endedness of the concept amounts to, it is compared to the indefinite extensibility of mathematical concepts. Two notions of are distinguished: the indefinite extensibility of set theoretic notions, i.e. (transfinite) cardinal number, ordinal number, and set and the indefinite extensibility of the concept finite cardinal number. The open-endedness is shown to be more like the indefinite extensibility of the finite cardinal numbers. This implies that the open-endedness of art provides little reason for rejecting the possibility of a definition of art or for concluding that the extension of the concept art must be fuzzy, vague, or imprecise.

Keywords: art concept; definition of art; indefinite extensibility; open-ended; vagueness; sets; cardinality

Chapter.  8578 words. 

Subjects: Aesthetics and Philosophy of Art

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