Platonism and metaphor in the texts of mathematics: GÃ¶del and Frege on mathematical knowledge [Book Review]
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Man and World 30 (4):453-481 (1997)
In this paper, I challenge those interpretations of Frege that reinforce the view that his talk of grasping thoughts about abstract objects is consistent with Russell's notion of acquaintance with universals and with GÃ¶del's contention that we possess a faculty of mathematical perception capable of perceiving the objects of set theory. Here I argue the case that Frege is not an epistemological Platonist in the sense in which GÃ¶del is one. The contention advanced is that GÃ¶del bases his Platonism on a literal comparison between mathematical intuition and physical perception. He concludes that since we accept sense perception as a source of empirical knowledge, then we similarly should posit a faculty of mathematical intuition to serve as the source of mathematical knowledge. Unlike GÃ¶del, Frege does not posit a faculty of mathematical intuition. Frege talks instead about grasping thoughts about abstract objects. However, despite his hostility to metaphor, he uses the notion of âgraspingâ as a strategic metaphor to model his notion of thinking, i.e., to underscore that it is only by logically manipulating the cognitive content of mathematical propositions that we can obtain mathematical knowledge. Thus, he construes âgraspingâ more as theoretical activity than as a kind of inner mental âseeingâ
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Øystein Linnebo (2008). The Nature of Mathematical Objects. In Bonnie Gold & Roger Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematical Association of America. 205--219.
Øystein Linnebo (2009). Platonism in the Philosophy of Mathematics. In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy.
William J. Melanson (2011). Reassessing the Epistemological Challenge to Mathematical Platonism. Croatian Journal of Philosophy 11 (3):295-304.
Mark Colyvan (2007). Mathematical Recreation Versus Mathematical Knowledge. In Mary Leng, Alexander Paseau & Michael D. Potter (eds.), Mathematical Knowledge. Oxford University Press. 109--122.
Mark Balaguer, Fictionalism in the Philosophy of Mathematics. Stanford Encyclopedia of Philosophy.
Otávio Bueno (2008). Truth and Proof. Manuscrito 31 (1).
Christoph C. Pfisterer (2010). Frege and Kitcher on A Priori Knowledge. Conceptus 94:29-43.
Mary Leng, Alexander Paseau & Michael D. Potter (eds.) (2007). Mathematical Knowledge. Oxford University Press.
Mark Balaguer (1995). A Platonist Epistemology. Synthese 103 (3):303 - 325.
Izabela Bondecka-Krzykowska (2004). Strukturalizm jako alternatywa dla platonizmu w filozofii matematyki. Filozofia Nauki 1.
Carlo Cellucci (2000). The Growth of Mathematical Knowledge: An Open World View. In Emily Grosholz & Herbert Breger (eds.), The Growth of Mathematical Knowledge, pp. 153-176. Kluwer. 153--176.
Colin Cheyne (1999). Problems with Profligate Platonism. Philosophia Mathematica 7 (2):164-177.
Colin Cheyne (1997). Getting in Touch with Numbers: Intuition and Mathematical Platonism. Philosophy and Phenomenological Research 57 (1):111-125.
Jennifer Wilson Mulnix (2008). Reliabilism, Intuition, and Mathematical Knowledge. Filozofia 62 (8):715-723.
Added to index2010-09-02
Total downloads17 ( #94,143 of 1,096,856 )
Recent downloads (6 months)4 ( #74,153 of 1,096,856 )
How can I increase my downloads?