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Why proofs by mathematical induction are generally not explanatory
Analysis 69 (2):203-211 (2009)
Abstract
Philosophers who regard some mathematical proofs as explaining why theorems hold, and others as merely proving that they do hold, disagree sharply about the explanatory value of proofs by mathematical induction. I offer an argument that aims to resolve this conflict of intuitions without making any controversial presuppositions about what mathematical explanations would beAuthor's Profile
DOI
10.1093/analys/anp002
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Citations of this work
Mathematical Explanations Of Empirical Facts, And Mathematical Realism.Aidan Lyon - 2012 - Australasian Journal of Philosophy 90 (3):559-578.
Viewing-as explanations and ontic dependence.William D’Alessandro - 2020 - Philosophical Studies 177 (3):769-792.
Arithmetic, Set Theory, Reduction and Explanation.William D’Alessandro - 2018 - Synthese 195 (11):5059-5089.
Mathematical Explanation beyond Explanatory Proof.William D’Alessandro - 2017 - British Journal for the Philosophy of Science 71 (2):581-603.
References found in this work
Explanation, independence and realism in mathematics.Michael D. Resnik & David Kushner - 1987 - British Journal for the Philosophy of Science 38 (2):141-158.
Proofs and pictures.James Robert Brown - 1997 - British Journal for the Philosophy of Science 48 (2):161-180.
Philosophy of Mathematics: An Introduction to the World of Proofs and Pictures.James R. Brown - 2001 - Erkenntnis 54 (3):404-407.
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