David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Grazer Philosophische Studien 75 (1):65-92 (2007)
My aim is to understand the practice of mathematics in a way that sheds light on the fact that it is at once a priori and capable of extending our knowledge. The account that is sketched draws first on the idea, derived from Kant, that a calculation or demonstration can yield new knowledge in virtue of the fact that the system of signs it employs involves primitive parts (e.g., the ten digits of arithmetic or the points, lines, angles, and areas of Euclidean geometry) that combine into wholes (numerals or drawn Euclidean figures) that are themselves parts of larger wholes (the array of written numerals in a calculation or the diagram of a Euclidean demonstration). Because wholes such as numerals and Euclidean figures both have parts and are parts of larger wholes, their parts can be recombined into new wholes in ways that enable extensions of our knowledge. I show that sentences of Frege's Begriffsschrift can also be read as involving three such levels of articulation; because they have these three levels, we can understand in essentially the same way how a proof from concepts alone can extend our knowledge.
|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
Margit Ruffing (2009). Kant-Bibliographie 2007. Kant-Studien 100 (4):526-564.
Similar books and articles
Kris McDaniel (2010). Parts and Wholes. Philosophy Compass 5 (5):412-425.
Danielle Macbeth (2012). Diagrammatic Reasoning in Frege's Begriffsschrift. Synthese 186 (1):289-314.
John MacFarlane (2002). Frege, Kant, and the Logic in Logicism. Philosophical Review 111 (1):25-65.
David-Hillel Ruben (1983). Social Wholes and Parts. Mind 92 (366):219-238.
Kristina Engelhard & Peter Mittelstaedt (2008). Kant's Theory of Arithmetic: A Constructive Approach? [REVIEW] Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 39 (2):245 - 271.
D. Macbeth (2012). Seeing How It Goes: Paper-and-Pencil Reasoning in Mathematical Practice. Philosophia Mathematica 20 (1):58-85.
Added to index2009-01-28
Total downloads36 ( #66,455 of 1,696,294 )
Recent downloads (6 months)1 ( #333,740 of 1,696,294 )
How can I increase my downloads?