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E-raamat: Logical Foundations of Scientific Theories: Languages, Structures, and Models [Taylor & Francis e-raamat]

(Federal University of Santa Catarina, Brazil), (Federal University of Santa Catarina, Brazil)
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This book addresses the logical aspects of the foundations of scientific theories. Even though the relevance of formal methods in the study of scientific theories is now widely recognized and regaining prominence, the issues covered here are still not generally discussed in philosophy of science. The authors focus mainly on the role played by the underlying formal apparatuses employed in the construction of the models of scientific theories, relating the discussion with the so-called semantic approach to scientific theories. The book describes the role played by this metamathematical framework in three main aspects: considerations of formal languages employed to axiomatize scientific theories, the role of the axiomatic method itself, and the way set-theoretical structures, which play the role of the models of theories, are developed. The authors also discuss the differences and philosophical relevance of the two basic ways of aximoatizing a scientific theory, namely Patrick Suppes’ set theoretical predicates and the "da Costa and Chuaqui" approach. This book engages with important discussions of the nature of scientific theories and will be a useful resource for researchers and upper-level students working in philosophy of science.

Figures
ix
Preface xi
Acknowledgments xvii
1 The Quandary on the Characterization of Scientific Theories
1(20)
1.1 The Received View and Syntactical Approaches
3(7)
1.2 The Semantic Approach
10(8)
1.3 Scientific Theories and Philosophical Tools
18(3)
2 Axiomatization
21(21)
2.1 Concrete Axiomatics
25(5)
2.2 Abstract Axiomatics
30(4)
2.3 Formal Axiomatics
34(8)
2.3.1 First-Order Classical Logic With Identity
34(4)
2.3.2 Peano Arithmetics
38(4)
3 A Mathematical Background
42(20)
3.1 The Principle of Constructivity
42(3)
3.2 The ZF(C) Set Theories
45(8)
3.2.1 The Postulates of ZF(C)
48(3)
3.2.2 A Matter of Terminology
51(1)
3.2.3 Inaccessible Cardinals
52(1)
3.2.4 Informal Semantics of 6
52(1)
3.3 `Models' of ZF(C), Again
53(3)
3.4 Urelemente
56(2)
3.4.1 Some Comments
58(1)
3.5 More on the `Models' of ZF(C)
58(4)
4 Criticism of the Axiomatic Method and Its Defense
62(14)
4.1 Does the AM Encompass Heuristics?
62(2)
4.1.1 The Axiomatic Method and Heuristics
63(1)
4.2 Truesdell Against the `Suppesians'
64(4)
4.3 Arnol'd and the Bourbaki Program
68(1)
4.4 Worth Axiomatize?
68(3)
4.5 Does Axiomatization Really Axiomatize?
71(5)
5 Axiomatization and Scientific Theories
76(36)
5.1 External Axiomatizations
77(2)
5.2 Structures
79(4)
5.3 Languages and Algebras
83(3)
5.4 Languages for Speaking of Structures
86(3)
5.4.1 The Language of a Structure
88(1)
5.5 Definability and Expressive Elements
89(3)
5.6 On the New Symbols
92(2)
5.7 Da Costa and Chuaqui--Suppes Predicates
94(5)
5.7.1 A Suppes Predicate for Group Theory
95(1)
5.7.2 A Suppes Predicate for Classical Particle Mechanics
96(3)
5.8 The Approach of Suppes
99(13)
5.8.1 An Axiomatization of Non-relativistic Quantum Mechanics
104(8)
6 Models and Scientific Theories
112(15)
6.1 Again on the Order of Languages and Structures
112(2)
6.2 Further Remarks on the Suppes Approach
114(3)
6.3 Da Costa and Chuaqui, Further Remarks
117(2)
6.4 The Metamathematical Framework
119(8)
Bibliography 127(8)
Index 135
Décio Krause is Professor of Logic and Philosophy of Science in the Department of Philosophy of the Federal University of Santa Catarina, Brazil. His works deal with the logical foundations of science, mainly involving the logical and metaphysical discussions about identity and individuality of quantum entities, and the applications of non-classical logics to sciences.

Jonas R.B. Arenhart is Associate Professor at the Department of Philosophy of the Federal University of Santa Catarina, Brazil. His main research interests are logic and philosophy of logic, philosophy of science, the metaphysics of science, and foundations of science.