David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Philosophy of Science 31 (3):255-264 (1964)
In this paper I shall argue that to a very significant extent mathematics is concept analysis, and that though the analysis of mathematical concepts is in a number of ways different from the analysis of philosophic concepts, the similarities between these two types of concept analyses are as important and far reaching as the differences. I shall argue that because mathematics and philosophy are each concerned with the analysis of concepts, they are much more like one another epistemologically than is often recognized. In insisting upon fundamental similarities between mathematics and philosophy, I shall be agreeing with the classical rationalists, but on a very different conception of both philosophy and mathematics from that held by the rationalists. The rationalists wished to assimilate philosophy to mathematics as understood in their time; viz. as a body of necessary propositions, which followed from self-evident axioms and postulates, revealed to the natural light of reason. As against this rationalistic position, I wish to make a comparison in the reverse direction, in which I shall presuppose a certain conception of philosophy as something given, and then insist that mathematics is in many important respects similar to philosophy as so understood. In particular, I wish to insist that there is a significant comparison between mathematics on the one hand, and philosophy as understood by probably a majority of philosophers today on the other--viz., philosophy understood as concept analysis--, where it is conceded that the analysis of philosophic concepts is inherently a tentative matter, wherein it is impossible--at least in the usual case--to offer any one analysis of a given philosophic concept as absolutely certain and beyond all revision. I shall argue that by virtue of the fact that mathematics, like philosophy, is concerned with the analysis of concepts, many at least of the propositions advanced within it are inherently revisable, and do not possess the kind of certainty the rationalists ascribed to them
|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
Stephen I. Brown (1973). Mathematics and Humanistic Themes: Sum Considerations. Educational Theory 23 (3):191-214.
Similar books and articles
Helen Billinge (2003). Did Bishop Have a Philosophy of Mathematics? Philosophia Mathematica 11 (2):176-194.
Andrew Arana (2007). Review of D. Corfield, Toward a Philosophy of Real Mathematics. [REVIEW] Mathematical Intelligencer 29 (2).
E. Brian Davies (2005). A Defence of Mathematical Pluralism. Philosophia Mathematica 13 (3):252-276.
Warren Schmaus (1982). The Concept of Analysis in Comte's Philosophy of Mathematics. Philosophy Research Archives 8:205-222.
Christopher Pincock (2009). Towards a Philosophy of Applied Mathematics. In Otávio Bueno & Øystein Linnebo (eds.), New Waves in Philosophy of Mathematics. Palgrave Macmillan
Charles S. Chihara (1990). Constructibility and Mathematical Existence. Oxford University Press.
Robert Thomas (2002). Idea Analysis of Algebraic Groups: A Critical Comment on George Lakoff and Rafael Núñez's Where Mathematics Comes From. Philosophical Psychology 15 (2):185 – 195.
Added to index2009-01-28
Total downloads7 ( #292,153 of 1,725,629 )
Recent downloads (6 months)2 ( #268,736 of 1,725,629 )
How can I increase my downloads?