UNDERSTANDING OF PROOF AND SIMPLICITY OF FOUNDATIONS: AN OUTLINE OF THE METHODOLOGY FOR THE PHILOSOPHY OF MATHEMATICS
Lev Dmitrievich Lamberov
Ural Federal University, 19, Mira st., Yekaterinburg, 620002, Russia
Keywords: доказательство, простота, понимание, основания математики, философия математики, методология, proof, simplicity, understanding, foundations of mathematics, philosophy of mathematics, methodology
Abstract
The article deals with the study of possibilities of applying abductive reasoning within the philosophy of mathematics to choose the best theory of foundations of mathematics. We consider the concept of simplicity of mathematical proof and its relation with convincingness. In the context of foundations of mathematics, we raise the problem of the criterion of foundations simplicity, reveal difficulties of its application, and outline ways for further studies of the methodology of the philosophy of mathematics.
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