Synthese 167 (1):33-65 (2009)

Katherine Dunlop
University of Texas at Austin
J. H. Lambert proved important results of what we now think of as non-Euclidean 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, model-theoretic, views of justification.
Keywords Philosophy   Philosophy of Language   Metaphysics   Epistemology   Logic
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Reprint years 2009
DOI 10.1007/s11229-007-9277-3
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References found in this work BETA

Kant and the Exact Sciences.Michael Friedman - 1990 - Harvard University Press.

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