David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
British Journal for the Philosophy of Science 38 (1):1-18 (1987)
Mathematicians often speak of conjectures as being confirmed by evidence that falls short of proof. For their own conjectures, evidence justifies further work in looking for a proof. Those conjectures of mathematics that have long resisted proof, such as Fermat's Last Theorem and the Riemann Hypothesis, have had to be considered in terms of the evidence for and against them. It is argued here that it is not adequate to describe the relation of evidence to hypothesis as `subjective', `heuristic' or `pragmatic', but that there must be an element of what it is rational to believe on the evidence, that is, of non-deductive logic.
|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
A. Paseau (forthcoming). Knowledge of Mathematics Without Proof. British Journal for the Philosophy of Science:axu012.
John R. Welch (2013). New Tools for Theory Choice and Theory Diagosis. Studies in History and Philosophy of Science 44 (3):318-329.
Alan Baker (2008). Experimental Mathematics. Erkenntnis 68 (3):331 - 344.
Ian J. Dove (2013). Towards a Theory of Mathematical Argument. In Andrew Aberdein & Ian J. Dove (eds.), Foundations of Science. Springer 291--308.
Ian J. Dove (2009). Towards a Theory of Mathematical Argument. Foundations of Science 14 (1-2):136-152.
Similar books and articles
Jay Zeman (1986). Peirce's Philosophy of Logic. Transactions of the Charles S. Peirce Society 22 (1):1 - 22.
Matthew McKeon, Logical Consequence, Deductive-Theoretic Conceptions. Internet Encyclopedia of Philosophy.
James Franklin (1996). Proof in Mathematics. Quakers Hill Press.
Melvin Fitting (2008). A Quantified Logic of Evidence. Annals of Pure and Applied Logic 152 (1):67-83.
Tyler Burge (2003). Logic and Analyticity. Grazer Philosophische Studien 66 (1):199-249.
Stewart Shapiro (2009). We Hold These Truths to Be Self-Evident: But What Do We Mean by That? Review of Symbolic Logic 2 (1):175-207.
Michael Otte (2006). Proof-Analysis and Continuity. Foundations of Science 11 (1-2):121-155.
Added to index2009-01-28
Total downloads117 ( #19,210 of 1,725,580 )
Recent downloads (6 months)70 ( #15,055 of 1,725,580 )
How can I increase my downloads?