David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Synthese 134 (1-2):119 - 158 (2003)
The aim I am pursuing here is to describe some general aspects of mathematical proofs. In my view, a mathematical proof is a warrant to assert a non-tautological statement which claims that certain objects (possibly a certain object) enjoy a certain property. Because it is proved, such a statement is a mathematical theorem. In my view, in order to understand the nature of a mathematical proof it is necessary to understand the nature of mathematical objects. If we understand them as external entities whose 'existence' is independent of us and if we think that their enjoying certain properties is a fact, then we should argue that a theorem is a statement that claims that this fact occurs. If we also maintain that a mathematical proof is internal to a mathematical theory, then it becomes very difficult indeed to explain how a proof can be a warrant for such a statement. This is the essential content of a dilemma set forth by P. Benacerraf (cf. Benacerraf 1973). Such a dilemma, however, is dissolved if we understand mathematical objects as internal constructions of mathematical theories and think that they enjoy certain properties just because a mathematical theorem claims that they enjoy them
|Keywords||Philosophy Philosophy Epistemology Logic Metaphysics Philosophy of Language|
|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
Brendan Larvor (2012). How to Think About Informal Proofs. Synthese 187 (2):715-730.
Paolo Mancosu (1991). On the Status of Proofs by Contradiction in the Seventeenth Century. Synthese 88 (1):15 - 41.
Ian J. Dove (2009). Towards a Theory of Mathematical Argument. Foundations of Science 14 (1-2):136-152.
Yehuda Rav (2007). A Critique of a Formalist-Mechanist Version of the Justification of Arguments in Mathematicians' Proof Practices. Philosophia Mathematica 15 (3):291-320.
Imre Lakatos (1976). Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge University Press.
David Sherry (2009). The Role of Diagrams in Mathematical Arguments. Foundations of Science 14 (1-2):59-74.
Edwin Coleman (2009). The Surveyability of Long Proofs. Foundations of Science 14 (1-2):27-43.
John W. Dawson Jr (2006). Why Do Mathematicians Re-Prove Theorems? Philosophia Mathematica 14 (3):269-286.
Jody Azzouni (2009). Why Do Informal Proofs Conform to Formal Norms? Foundations of Science 14 (1-2):9-26.
Jean Paul Van Bendegem (2005). Proofs and Arguments: The Special Case of Mathematics. Poznan Studies in the Philosophy of the Sciences and the Humanities 84 (1):157-169.
Added to index2009-01-28
Total downloads30 ( #68,481 of 1,679,353 )
Recent downloads (6 months)2 ( #112,124 of 1,679,353 )
How can I increase my downloads?