Abduction and Conjecturing in Mathematics

Philosophica 61 (1):77-94 (1998)

Authors
Ferdinando Arzarello
Università degli Studi di Torino
Abstract
The logic of discovering and that of justifying have been a permanent source of debate in mathematics, because of their different and apparently contradictory features within the processes of production of mathematical sentences. In fact, a fundamental unity appears as soon as one investigates deeply the phenomenology of conjecturing and proving using concrete examples. In this paper it is shown that abduction, in the sense of Peirce, is an essential unifying activity, ruling such phenomena. Abduction is the major ingredient in a theoretical model suitable for describing the tran-sition from the conjecturing to the proving phase. In the paper such a model is introduced and worked out to test Lakatos' machinery of proofs and refutations from a new point of view. Abduction and its categorical counter-part, adjunction, allow to explain within a unifying framework most of the phenomenology of conjectures and proofs, encompassing also the method of Greek analysis-synthesis.
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References found in this work BETA

Collected Papers.Charles S. Peirce - 1931 - Cambridge: Belknap Press of Harvard University Press.
Proofs and Refutations.Imre Lakatos - 1980 - Noûs 14 (3):474-478.
Why Do We Prove Theorems?Y. Rav - 1999 - Philosophia Mathematica 7 (1):5-41.
Why Do We Prove Theorems?Yehuda Rav - 1999 - Philosophia Mathematica 7 (1):5-41.
From Backward Reduction to Configurational Analysis.Petri Mäenpää - forthcoming - Boston Studies in the Philosophy of Science.

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