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Ancient geometrical analysis and modern logic

In R. S. Cohen, P. K. Feyerabend & M. Wartofsky (eds.), Essays in Memory of Imre Lakatos. Reidel. pp. 253--276 (1976)

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  1. Axiomatic Method and Category Theory.Rodin Andrei - unknown
    Lawvere’s axiomatization of topos theory and Voevodsky’s axiomatization of heigher homotopy theory exemplify a new way of axiomatic theory-building, which goes beyond the classical Hibert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in Categorical logic opens new possibilities for using this method in physics and other natural sciences.
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  • Doing and Showing.Andrei Rodin - unknown
    I elaborate in some detail on the First Book of Euclid's ``Elements'' and show that Euclid's theory of geometry is \underline{not} axiomatic in the modern sense but is construed differently. Then I show that the usual commonly accepted notion of axiomatic theory equally fails to account for today's mathematical theories. I provide some polemical arguments against the popular view according to which a good mathematical theory must be axiomatic and point to an alternative method of theory-building. Since my critique of (...)
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  • Publications de la SMF.Marco Panza - 1986 - History of Science 24:125-144.
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  • Pappus of Alexandria in the 20th Century. Analytical Method and Mathematical Practice.Gianluca Longa - 2014 - Dissertation, University of Milan