David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Philosophia Mathematica (2):233-235 (1989)
In a recent article in this journal Phil. Math., II, v.4 (1989), n.2, pp.? ?] J. Fang argues that we must not be fooled by A.J. Ayer (God rest his soul!) and his cohorts into believing that mathematical knowledge has an analytic a priori status. Even computers, he reminds us, take some amount of time to perform their calculations. The simplicity of Kant's infamous example of a mathematical proposition (7+5=12) is "partly to blame" for "mislead[ing] scholars in the direction of neglecting the temporal element"; yet a brief instant of time is required to grasp even this simple truth. If Kant were alive today, "and if he had had a little more mathematical savvy", Fang explains, he could have used the latest example of the largest prime number (391,581 x 2 216,193 - 1) as a better example of the "synthetic a priori" character of mathematics. The reason Fang is so intent upon emphasizing the temporal character of mathematics is that he wishes to avoid "the uncritical mixing of ... a theology and a philosophy of mathematics." For "in the light of the Computer Age today: finitism is king!" Although Kant's aim was explicitly "to study the 'human' ... faculty", Fang claims that even he did not adequatley emphasize "the clearly and concretely distinguishable line of demarcation between the human and divine faculties."
|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
Sun-joo Shin (1997). Kant's Syntheticity Revisited by Peirce. Synthese 113 (1):1-41.
Joong Fang (1997). Kant and Mathematics Today: Between Epistemology and Exact Sciences. Edwin Mellen Press.
Paul Anthony Wilson, Constructing Numbers Through Moments in Time: Kant's Philosophy of Mathematics.
Lisa Shabel (1998). Kant on the `Symbolic Construction' of Mathematical Concepts. Studies in History and Philosophy of Science Part A 29 (4):589-621.
Kristina Engelhard & Peter Mittelstaedt (2008). Kant's Theory of Arithmetic: A Constructive Approach? [REVIEW] Journal for General Philosophy of Science 39 (2):245 - 271.
Izabela Bondecka-Krzykowska (1999). Dowody komputerowe a status epistemologiczny twierdzeń matematyki. Filozofia Nauki 3.
J. Fang (1965). Kant and Modern Mathematics. Philosophia Mathematica (2):57-68.
Frode Kjosavik (2009). Kant on Geometrical Intuition and the Foundations of Mathematics. Kant-Studien 100 (1):1-27.
Carl Ginet (2010). Self-Evidence. Logos and Episteme 54 (2):325-352.
Hartry Field (2005). Recent Debates About the A Priori. In Tamar Szabo Gendler & John Hawthorne (eds.), Oxford Studies in Epistemology. Oup Oxford.
Pierre Cassou-Nogués (2006). Signs, Figures and Time: Cavaillès on “Intuition” in Mathematics. Theoria 21 (1):89-104.
Added to index2010-08-24
Total downloads10 ( #171,312 of 1,692,577 )
Recent downloads (6 months)1 ( #181,215 of 1,692,577 )
How can I increase my downloads?