David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Erkenntnis 34 (2):187 - 209 (1991)
This article was written jointly by a philosopher and a mathematician. It has two aims: to acquaint mathematicians with some of the philosophical questions at the foundations of their subject and to familiarize philosophers with some of the answers to these questions which have recently been obtained by mathematicians. In particular, we argue that, if these recent findings are borne in mind, four different basic philosophical positions, logicism, formalism, platonism and intuitionism, if stated with some moderation, are in fact reconcilable, although with some reservations in the case of logicism, provided one adopts a nominalistic interpretation of Plato's ideal objects. This eclectic view has been asserted by Lambek and Scott (LS 1986) on fairly technical grounds, but the present argument is meant to be accessible to a wider audience and to provide some new insights.
|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
Haskell B. Curry (1963/1977). Foundations of Mathematical Logic. Dover Publications.
Jaakko Hintikka (ed.) (1969). The Philosophy of Mathematics. London, Oxford U.P..
W. C. Kneale (1962/1984). The Development of Logic. Oxford University Press.
Dag Prawitz (1965/2006). Natural Deduction: A Proof-Theoretical Study. Dover Publications.
W. V. Quine (1951). Mathematical Logic. Cambridge, Harvard University Press.
Citations of this work BETA
J. Lambek (2004). What is the World of Mathematics? Annals of Pure and Applied Logic 126 (1-3):149-158.
Similar books and articles
Markus Sebastiaan Paul Rogier van Atten (2007). Brouwer Meets Husserl: On the Phenomenology of Choice Sequences. Springer.
Penelope Maddy (1990). Realism in Mathematics. Oxford University Prress.
Kenny Easwaran (2008). The Role of Axioms in Mathematics. Erkenntnis 68 (3):381 - 391.
Miriam Franchella (1994). Heyting's Contribution to the Change in Research Into the Foundations of Mathematics. History and Philosophy of Logic 15 (2):149-172.
Andrew Arana (2007). Review of D. Corfield's Toward A Philosophy Of Real Mathematics. [REVIEW] Mathematical Intelligencer 29 (2).
J. P. Mayberry (2000). The Foundations of Mathematics in the Theory of Sets. Cambridge University Press.
Alan Baker (2003). The Indispensability Argument and Multiple Foundations for Mathematics. Philosophical Quarterly 53 (210):49–67.
Stewart Shapiro (2000). Thinking About Mathematics: The Philosophy of Mathematics. Oxford University Press.
Edward N. Zalta (2007). Reflections on Mathematics. In V. F. Hendricks & Hannes Leitgeb (eds.), Philosophy of Mathematics: Five Questions. Automatic Press/VIP.
Added to index2009-01-28
Total downloads29 ( #70,686 of 1,679,324 )
Recent downloads (6 months)3 ( #78,911 of 1,679,324 )
How can I increase my downloads?