Authors
James Franklin
University of New South Wales
Abstract
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 Non-deductive logic  Conjectures in mathematics
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DOI 10.1093/bjps/38.1.1
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References found in this work BETA

Logical Foundations of Probability.Rudolf Carnap - 1950 - Chicago]University of Chicago Press.
In Defence of Objective Bayesianism.Jon Williamson - 2010 - Oxford University Press.
Logical Foundations of Probability.Ernest H. Hutten - 1950 - Journal of Symbolic Logic 16 (3):205-207.
A Treatise on Probability.J. M. Keynes - 1989 - British Journal for the Philosophy of Science 40 (2):219-222.

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Citations of this work BETA

Non-Deductive Methods in Mathematics.Alan Baker - 2010 - Stanford Encyclopedia of Philosophy.
Knowledge of Mathematics Without Proof.Alexander Paseau - 2015 - British Journal for the Philosophy of Science 66 (4):775-799.

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