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Berkeley and Proof in Geometry

Published online by Cambridge University Press:  28 September 2012

RICHARD J. BROOK
RICHARD J. BROOK*
Affiliation:
Bloomsburg University
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Abstract

Berkeley in his Introduction to the Principles of Human knowledge uses geometrical examples to illustrate a way of generating “universal ideas,” which allegedly account for the existence of general terms. In doing proofs we might, for example, selectively attend to the triangular shape of a diagram. Presumably what we prove using just that property applies to all triangles.

I contend, rather, that given Berkeley’s view of extension, no Euclidean triangles exist to attend to. Rather proof, as Berkeley would normally assume, requires idealizing diagrams; treating them as if they obeyed Euclidean constraints. This convention solves the problem of representative generalization.

Dans l’introduction aux Principes de la connaissance humaine, Berkeley emploie des exemples géométriques pour illustrer une façon d’engendrer des «idées universelles» permettant d’expliquer l’existence des termes généraux. En faisant des démonstrations on pourrait, par exemple, porter une attention sélective à la forme triangulaire d’un diagramme. Il est probable que ce que l’on démontrerait en employant cette seule caractéristique s’appliquerait à tous les triangles.

Je soutiens plutôt que, étant donnée la conception berkeleyenne de l’extension, il n’existe aucun triangle euclidien à étudier. La démonstration exige plutôt, comme Berkeley le supposerait normalement, l’idéalisation des diagrammes : leur traitement conforme aux contraintes d’Euclide. Cette convention résoud le problème de la généralisation représentative.

Type
Articles
Information
Dialogue: Canadian Philosophical Review / Revue canadienne de philosophie , Volume 51 , Issue 3 , September 2012 , pp. 419 - 435
Copyright
Copyright © Canadian Philosophical Association 2012

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