Berkeley and Proof in Geometry

Bibliographic Data

ID3891428
AuthorsRichard J Brooks, R J Brook (0000-0002-1811-663X, Bloomsburg University, corresponding author)
Year2012
Volume51
Issue3
Pages419-435
Publication date2012-09-01
Open AccessYes
TypeARTICLE
VenueDialogue (JOURNAL)
Journal identifiersISSN: 0012-2173 • E-ISSN: 1759-0949
PublisherCambridge University Press (CUP) (PUBLISHER)
DOI10.1017/s0012217312000686
OpenAlexW2067759441
LanguageEN
Citations received1
References cited14

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

Algebra over a field · Calculus (dental) · Combinatorial proof · Combinatorics · Diagram · Epistemology · Euclidean geometry · Extension (predicate logic) · Generalization · Geometry · Mathematical analysis · Mathematical proof · Property (philosophy) · Pure mathematics · Computer Science · Historical and Literary Studies · Historical Philosophy and Science · History and Theory of Mathematics · Mathematics · Philosophy

Tools

Open DOISci-HubOpen Access