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Mathematical representation of empirical phenomena : a case study of 18th-century mathematical and mechanical concepts

University of British Columbia

I suggest a theory of scientific models which considers that a model is composed of three parts: an idealized system, a theoretical description and a set of mathematical equations. Each component is connected to the previous one by bridge principles, i.e. any assertion, whether justified or simply postulated, which establishes a correspondence between two parts of a model. The goal of my research was to find within 18th-century mechanics a set of laws that could be considered mediators between the parts of models. The greater part is dedicated to an analysis of the conceptual developments made by Euler and Lagrange in the 18th century both in mathematics and in mechanics. In the conclusion, I show that the relations between the parts of models are too complex to be expressed in a single, unifying assertion.

Text

2011-12-14

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/39701

Philosophy

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/