David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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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.
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References found in this work BETA
Stephen Cole Kleene (1952). Introduction to Metamathematics. North Holland.
W. C. Kneale (1962). The Development of Logic. Oxford University Press.
Dag Prawitz (1965). Natural Deduction: A Proof-Theoretical Study. Dover Publications.
W. V. Quine (1951). Mathematical Logic. Cambridge, Harvard University Press.
Haskell B. Curry (1963). Foundations of Mathematical Logic. Dover Publications.
Citations of this work BETA
Jean-Pierre Marquis (1995). Category Theory and the Foundations of Mathematics: Philosophical Excavations. Synthese 103 (3):421 - 447.
J. Lambek (2004). What is the World of Mathematics? Annals of Pure and Applied Logic 126 (1-3):149-158.
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