Art, Open-Endedness, and Indefinite Extensibility

Research output: Chapter in Book/Report/Conference proceedingChapter


It is often claimed that the concept art is open-ended and that this openendedness 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.

Original languageEnglish (US)
Title of host publicationArt and Abstract Objects
PublisherOxford University Press
ISBN (Electronic)9780191746277
ISBN (Print)9780199691494
StatePublished - Jan 24 2013


  • Art concept
  • Cardinality
  • Definition of art
  • Indefinite extensibility
  • Open-ended
  • Sets
  • Vagueness


Dive into the research topics of 'Art, Open-Endedness, and Indefinite Extensibility'. Together they form a unique fingerprint.

Cite this