Why Euclid’s geometry brooked no doubt J H Lamb

Authors: Katherine Dunlop

Publish Date: 2007/12/21

Volume: 167, Issue: 1, Pages: 33-

PDF Link

Abstract

J H Lambert proved important results of what we now think of as nonEuclidean geometries and gave examples of surfaces satisfying their theorems I use his philosophical views to explain why he did not think the certainty of Euclidean geometry was threatened by the development of what we regard as alternatives to it Lambert holds that theories other than Euclid’s fall prey to skeptical doubt So despite their satisfiability for him these theories are not equal to Euclid’s in justification Contrary to recent interpretations then Lambert does not conceive of mathematical justification as semantic According to Lambert Euclid overcomes doubt by means of postulates Euclid’s theory thus owes its justification not to the existence of the surfaces that satisfy it but to the postulates according to which these “models” are constructed To understand Lambert’s view of postulates and the doubt they answer I examine his criticism of Christian Wolff’s views I argue that Lambert’s view reflects insight into traditional mathematical practice and has value as a foil for contemporary modeltheoretic views of justification

Keywords: