Platonism and Anti-Platonism in Mathematics
Seiten
2001
Oxford University Press Inc (Verlag)
978-0-19-514398-0 (ISBN)
Oxford University Press Inc (Verlag)
978-0-19-514398-0 (ISBN)
A demonstration of the value of both platonism and anti-platonism in the solution of mathematical problems. The author solves the important problems associated with both of the views, and demonstrates that it is inherently impossible for us to have a valid argument for or against mathematical platonism.
In 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.
In 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.
| Erscheint lt. Verlag | 9.8.2001 |
|---|---|
| Verlagsort | New York |
| Sprache | englisch |
| Maße | 235 x 154 mm |
| Gewicht | 376 g |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| ISBN-10 | 0-19-514398-1 / 0195143981 |
| ISBN-13 | 978-0-19-514398-0 / 9780195143980 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Von Logik und Mengenlehre bis Zahlen, Algebra, Graphen und …
Buch | Softcover (2024)
De Gruyter Oldenbourg (Verlag)
CHF 104,90
Analysis und Lineare Algebra mit Querverbindungen
Buch | Hardcover (2022)
Springer Spektrum (Verlag)
CHF 89,95
Versteckte Beiträge, die die Welt verändert haben
Buch | Hardcover (2023)
Springer (Verlag)
CHF 41,95
