Аксиоматическая архитектура научных теорий Родин Андрей Вячеславович

Короткий опис

Родин, Андрей Вячеславович.Аксиоматическая архитектура научных теорий : диссертация ... доктора философских наук : 09.00.08 / Родин Андрей Вячеславович; [Место защиты: ФГБОУ ВО «Санкт-Петербургский государственный университет»]. - Санкт-Петербург, 2020. - 279 с. : ил.
Аксиоматическая архитектура научных теорий Родин Андрей Вячеславович
ОГЛАВЛЕНИЕ ДИССЕРТАЦИИ
доктор наук Родин Андрей Вячеславович
Introduction

1 From Euclid to Hilbert

1.1 Euclid: Doing and Showing

1.1.1 Demonstration and "Monstration"

1.1.2 Are Euclid's Proofs Logical?

1.1.3 Instantiation, Objecthood and Objectivity

1.1.4 Proto-Logical Deduction and Geometrical Production

1.2 Hilbert: Making It Formal

1.2.1 Thought-things and thought-relations

1.2.2 Logicism and Objectivity

1.2.3 "Axiomatisation of Logic": Intuition Strikes Back

1.3 Axiomatic Method versus Genetic Method

1.3.1 Genetic and Axiomatic Methods in the Theoretical Arithmetic (1900)

1.3.2 Revendication of the Genetic Method

1.4 Conclusion of Chapter

2 The Axiomatic Method at Work in Mathematical and Scientific Practice

2.1 Set Theory

2.2 Bourbaki

2.2.1 Semantic Version of the Formal Axiomatic Method

2.2.2 Mathematical Structure according to Bourbaki

2.2.3 Bourbaki and Mathematics Education

2.2.4 Bourbaki and Euclid

2.3 Axiomatic Approaches in Science and in the Philosophy of Science

2.3.1 Physics

2.3.2 Biology

2.3.3 Semantic View of Theories

2.3.4 Computer Science and Engineering

2.4 Conclusion of Chapter

3 Novel Axiomatic Approaches

3.1 Category-theoretic foundations of mathematics and Topos theory

3.1.1 Language of Categories

3.1.2 Category Theory as a Foundation

3.1.3 Categorical Logic

3.1.4 Toposes and their Internal Logic

3.2 Homotopy Type theory and Univalent Foundations

3.2.1 Rules versus Axioms. Hilbert-style and Gentzen-style formal systems

3.2.2 Model-theoretic and Proof-theoretic Logical Semantics. General Proof theory

3.2.3 MLTT and its Proof-theoretic Semantics

3.2.4 From MLTT to HoTT

3.2.5 Univalent Foundations

4 Conclusion and Further Research

4.1 Summary

4.2 Constructive Axiomatic Method

4.2.1 Motivations

4.2.2 Axiomatic Theories

4.2.3 The Method

4.3 The Constructive View of Theories