Mathematical Proof and Discovery <i>Reductio ad Absurdum</i>

Authors

  • Dale Jacquette

DOI:

https://doi.org/10.22329/il.v28i3.596

Keywords:

algorithm, argumentation, Euclidean, non-Euclidean geometry, mathematics, methodology, proof, Schopenhauer, Arthur

Abstract

The uses and interpretation of reductio ad absurdum argumentation in mathematical proof and discovery are examined, illustrated with elementary and progressively sophisticated examples, and explained. Against Arthur Schopenhauer’s objections, reductio reasoning is defended as a method of uncovering new mathematical truths, and not merely of confirming independently grasped mathematical intuitions. The application of reductio argument is contrasted with purely mechanical brute algorithmic inferences as an art requiring skill and intelligent intervention in the choice of hypotheses and attribution of contradictions deduced to a particular assumption in a contradiction’s derivation base within a reductio proof structure.

Author Biography

Dale Jacquette


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Published

2008-09-02

Issue

Vol. 28 No. 3 (2008)

Section

Articles

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