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Nominalism Meets Indivisibilism
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Nominalists, it is said, are defined by their opposition to the needless multiplication of entities. For most fourteenth-century nominalists, parsimony was in the first instance a logico-semantic matter, raising the question of how one should explain the truth conditions of sentences without assuming any kind of strictly isomorphic relation between individual sentences and what makes them true. 1 In their analyses of the structure of continuous spatial magnitudes, this question was presented in an especially clear and unambiguous form: \"Is it necessary to posit indivisible entities to explain the truth conditions of sentences containing terms such as 'point', 'line', and 'surface'?\" Affirmative answers offered one route to indivisibilism, the thesis that continue are divisible into finitely or infinitely many indivisible parts, or mathematical atoms.2 But negative answers, besides leading to the opposing view that continua are infinitely divisible, also invited some account of how terms such as 'point', 'line', and 'surface' are to be understood, if not as standing for real mathematical points, lines, and surfaces (surfaces being indivisible in one dimension, lines in two dimensions, and points in three). The way in which such parismonious ontologies were achieved in practice, however, shows us that nominalist methodology was anything but static in the later Middle Ages, as more and more sophisticated techniques were introduced and perfected to explain the relation between terms and what they signify. This essay is addressed to one small, though representative, part of that story.
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- Date created
- 1993
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- Article (Published)
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- License
- © 1993 J. Zupko et al. This version of this article is open access and can be downloaded and shared. The original author(s) and source must be cited.