TY - JOUR

T1 - Программный реализм в физике и основания математики. Часть 1: классическая наука

AU - Родин, Андрей Вячеславович

N1 - Funding Information: Работа поддержана исследовательским грантом Российского фонда фундаментальных исследований (проект N 13 - 06 - 00515). The article is written with the support from RFBR, project No. 13 - 06 - 00515. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2015

Y1 - 2015

N2 - Why mathematics can adequately describe the physical reality? How one can rationally explain the "unreasonable effectiveness" of mathematics in physics and other natural sciences? In the first part of this work we propose an answer to this question within the context of Classical physics and mathematics. Following Hilbert we distinguish between the real and the ideal semantics of syntactic operations in mathematics and show how the excessiveness of mathematical syntax allows one to complement the real semantics with the ideal one. Then on the basis of our analysis of Kepler's astronomy we introduce the notion of realistic physical theory and show that the "unreasonable effectiveness of mathematics" in such theories amounts to the possibility (not granted a priori but often realized in experiments) to replace a part of the standard ideal semantics of mathematical syntax with an appropriate real semantics.

AB - Why mathematics can adequately describe the physical reality? How one can rationally explain the "unreasonable effectiveness" of mathematics in physics and other natural sciences? In the first part of this work we propose an answer to this question within the context of Classical physics and mathematics. Following Hilbert we distinguish between the real and the ideal semantics of syntactic operations in mathematics and show how the excessiveness of mathematical syntax allows one to complement the real semantics with the ideal one. Then on the basis of our analysis of Kepler's astronomy we introduce the notion of realistic physical theory and show that the "unreasonable effectiveness of mathematics" in such theories amounts to the possibility (not granted a priori but often realized in experiments) to replace a part of the standard ideal semantics of mathematical syntax with an appropriate real semantics.

KW - Real and ideal semantics

KW - Realistic theory

KW - Saving phenomena

KW - Unreasonable effectiveness of mathematics

UR - http://www.scopus.com/inward/record.url?scp=85029870518&partnerID=8YFLogxK

M3 - статья

SP - 58

EP - 67

JO - ВОПРОСЫ ФИЛОСОФИИ

JF - ВОПРОСЫ ФИЛОСОФИИ

SN - 0042-8744

IS - 4

ER -