Non-deductive logic in mathematics

British Journal for the Philosophy of Science 38 (1):1-18 (1987)
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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.

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James Franklin
University of New South Wales

Citations of this work

Chance and the Continuum Hypothesis.Daniel Hoek - 2021 - Philosophy and Phenomenological Research 103 (3):639-60.
Knowledge of Mathematics Without Proof.Alexander Paseau - 2015 - British Journal for the Philosophy of Science 66 (4):775-799.

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References found in this work

Logical Foundations of Probability.Rudolf Carnap - 1950 - Chicago, IL, USA: Chicago University of Chicago Press.
In Defence of Objective Bayesianism.Jon Williamson - 2010 - Oxford University Press.
A Treatise on Probability.Harry T. Costello - 1923 - Journal of Philosophy 20 (11):301-306.
A treatise on probability.J. Keynes - 1924 - Revue de Métaphysique et de Morale 31 (1):11-12.

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