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Recent Debates over the Existence of Abstract Objects: An Overview

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Abstract Objects

Part of the book series: Synthese Library ((SYLI,volume 422))

Abstract

This volume is dedicated to recent debates over the existence of abstract objects. Three relevant questions for such debates are: (1) what is an abstract object? (2) Why is the debate over the existence of abstract objects important? (3) How should we conduct the debate? (See Burgess and Rosen 1997, p. 12 for a list of similar questions).

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Notes

  1. 1.

    It is standard to assume that no abstract object is concrete. However, some authors (Williamson 2013) hold that some objects are neither abstract nor concrete.

  2. 2.

    It is telling that even later in his life, when he changed his mind on the issue of nominalism and came to accept abstract objects, Quine still referred to abstract objects as entia non grata (see Quine 1960, chapter 50).

  3. 3.

    On the possibility of generalizing Field’s challenge beyond the case of abstract mathematical objects, see Liggins (2010) and Enoch (2010). See Rosen (1994) for problems with the distinction between mind-dependent and mind-independent, objects.

  4. 4.

    Compare Zalta’s view that an abstract object encodes exactly those properties that are used in its characterization with Yablo’s idea (Yablo 2010, Introduction) that mathematical objects are preconceived objects, objects that “Either … should have feature F, given their job description, or … don’t have feature F” (Yablo 2010, 7).

  5. 5.

    “In recent times, many philosophers have been attracted to an ‘assimilationist’ model of mathematical knowledge; they have supposed that we know of mathematical objects in something like the way we know of other objects” Fine (2005, p. 108–9).

  6. 6.

    See also Morrison (2007, 552, quoted by Knowles and Liggins (2015), 3406) on the property of spin: according to Morrison, spin is “perhaps best viewed as a curious hybrid of the mathematical and the physical” (Morrison (2007: 552) quoted by Knowles and Liggins (2015: 3406)).

  7. 7.

    Liggins (2008) argues that neither Quine nor Putnam actually endorsed the Quine-Putnam indispensability argument. See also Putnam (2012).

  8. 8.

    Yablo criticizes the argument “we cannot imagine-without-numbers a complex world [therefore] we cannot imagine a complex world lacking in numbers”, Yablo (2012, p. 1014).

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  1. University of Turin, Turin, Italy

    Matteo Plebani

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  1. Matteo Plebani
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  1. Department of Philosophy and Anthropology, University of Santiago de Compostela, Santiago de Compostela, Spain

    José L. Falguera

  2. Department of of Philosophy and Anthropology, University of Santiago de Compostela, Santiago de Compostela, Spain

    Concha Martínez-Vidal

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Plebani, M. (2020). Recent Debates over the Existence of Abstract Objects: An Overview. In: Falguera, J.L., Martínez-Vidal, C. (eds) Abstract Objects. Synthese Library, vol 422. Springer, Cham. https://doi.org/10.1007/978-3-030-38242-1_1

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