Proof, understanding, and computers
https://doi.org/10.17726/philIT.2020.1.5
Abstract
The article analyzes the concept of understanding in mathematical discourse. The role of understanding in two types of proof - traditional conceptual and computer-based-is considered. It is shown that the concept of understanding in the framework of the philosophy of mathematics for the case of computer proof is most interesting in the works of the late Wittgenstein. Next, we consider the question of what should be a philosophical theory in which this kind of understanding can be part of the conceptual apparatus. The requirements for such a theory include explanations of the various types of «competent mathematical behavior» required of computer program creators. Since these programs are not limited to a particular search strategy, but are «understanding» to a certain extent, the desired philosophical theory should bring «human understanding» and «computer understanding» closer together.
Keywords
mathematical proof,
computer proof,
Leibniz,
Descartes,
provincial,
Wittgenstein,
action,
behavior,
practice
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Review
For citations:
Tselishchev V.V. Proof, understanding, and computers. Philosophical Problems of IT & Cyberspace (PhilIT&C). 2020;(1):54-67. (In Russ.) https://doi.org/10.17726/philIT.2020.1.5
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