David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Topoi 13 (2):93-100 (1994)
If proofs are nothing more than truth makers, then there is no force in the standard argument against classical logic (there is no guarantee that there is either a proof forA or a proof fornot A). The standard intuitionistic conception of a mathematical proof is stronger: there are epistemic constraints on proofs. But the idea that proofs must be recognizable as such by us, with our actual capacities, is incompatible with the standard intuitionistic explanations of the meanings of the logical constants. Proofs are to be recognizable in principle, not necessarily in practice, as shown in section 1. Section 2 considers unknowable propositions of the kind involved in Fitch''s paradox:p and it will never be known thatp. It is argued that the intuitionist faces a dilemma: give up strongly entrenched common sense intuitions about such unknowable propositions, or give up verificationism. The third section considers one attempt to save intuitionism while partly giving up verificationism: keep the idea that a proposition is true iff there is a proof (verification) of it, and reject the idea that proofs must be recognizable in principle. It is argued that this move will have the effect that some standard reasons against classical semantics will be effective also against intuitionism. This is the case with Dummett''s meaning theoretical argument. At the same time the basic reason for regarding proofs as more than mere truth makers is lost.
|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
Michael Dummett (1973). The Philosophical Basis of Intuitionistic Logic. In Truth and Other Enigmas. Duckworth. 215--247.
Michael A. E. Dummett (2000). Elements of Intuitionism. Oxford University Press.
Dorothy Edgington (1985). The Paradox of Knowability. Mind 94 (376):557-568.
Frederic B. Fitch (1963). A Logical Analysis of Some Value Concepts. Journal of Symbolic Logic 28 (2):135-142.
Arend Heyting (1931). Die Intuitionistische Grundlegung der Mathematik. Erkenntnis 2 (1):106-115.
Citations of this work BETA
No citations found.
Similar books and articles
Melvin Fitting (2005). The Logic of Proofs, Semantically. Annals of Pure and Applied Logic 132 (1):1-25.
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.
Joram Hirshfeld (1988). Nonstandard Combinatorics. Studia Logica 47 (3):221 - 232.
Kenny Easwaran (2009). Probabilistic Proofs and Transferability. Philosophia Mathematica 17 (3):341-362.
R. B. J. T. Allenby (1997). Numbers and Proofs. Copublished in North, South, and Central America by John Wiley & Sons Inc..
Duccio Luchi & Franco Montagna (1999). An Operational Logic of Proofs with Positive and Negative Information. Studia Logica 63 (1):7-25.
Added to index2009-01-28
Total downloads31 ( #77,866 of 1,696,305 )
Recent downloads (6 months)16 ( #31,278 of 1,696,305 )
How can I increase my downloads?