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    Platonism and Anti-platonism in Mathematics (Paperback) By (author) Mark Balaguer

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    DescriptionIn this deft and vigorous book, Mark Balaguer demonstrates that there are no good arguments for or against mathematical platonism (i.e., the view that abstract, or non-spatio-temporal, mathematical objects exist, and that mathematical theories are descriptions of such objects). Balaguer does this by establishing that both platonism and anti-platonism are defensible positions. In Part I, he shows that the former is defensible by introducing a novel version of platonism, which he calls full-blooded platonism, or FBP. He argues that if platonists endorse FBP, they can then solve all of the problems traditionally associated with their view, most notably the two Benacerrafian problems (that is, the epistemological problem and the non-uniqueness problem). In Part II, Balaguer defends anti-platonism (in particular, mathematical fictionalism) against various attacks, chief among them the Quine-Putnam indispensability argument. Balaguer's version of fictionalism bears similarities to Hartry Field's, but the arguments Balaguer uses to defend this view are very different. Parts I and II of this book taken together clearly establish that we do not have any good argument for or against platonism. In Part III, Balaguer extends his conclusions, arguing that it is not simply that we do not currently have any good argument for or against platonism, but that we could never have such an argument, and indeed, that there is no fact of the matter as to whether platonism is correct (ie., whether there exist any abstract objects). This lucid and accessibly written book breaks new ground in its area of engagement and makes vital reading for both specialists and anyone else interested in the philosophy of mathematics or metaphysics in general.


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  • Full bibliographic data for Platonism and Anti-platonism in Mathematics

    Title
    Platonism and Anti-platonism in Mathematics
    Authors and contributors
    By (author) Mark Balaguer
    Physical properties
    Format: Paperback
    Number of pages: 240
    Width: 154 mm
    Height: 236 mm
    Thickness: 15 mm
    Weight: 381 g
    Language
    English
    ISBN
    ISBN 13: 9780195143980
    ISBN 10: 0195143981
    Classifications

    BIC E4L: MAT
    Nielsen BookScan Product Class 3: S7.8
    LC subject heading: ,
    Ingram Subject Code: PH
    Libri: I-PH
    Warengruppen-Systematik des deutschen Buchhandels: 26220
    BISAC V2.8: PHI002000, PHI011000
    BIC subject category V2: PBB
    DC21: 510.1
    BISAC V2.8: MAT000000
    DC22: 510.1
    LC subject heading:
    Thema V1.0: PBB
    Edition statement
    Reprint
    Illustrations note
    black & white illustrations
    Publisher
    Oxford University Press Inc
    Imprint name
    Oxford University Press Inc
    Publication date
    19 July 2001
    Publication City/Country
    New York
    Review quote
    "excellent book...exceptionally clear, insightful, and useful critical survey"--The Review of Modern Logic "Platonism and anti-platonism in mathematics is an impressive work. Balaguer presents forceful arguments for the viability of both FBP and fictionalism, and against the feasibility of any substantially different Platonist or anti-Platonist position. ... an admirable achievement."--The Bulletin of Symbolic Logic