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Analysis and Synthesis in Mathematics: History and Philosophy [Kõva köide]

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Analysis and Synthesis in Mathematics: History and PhilosophySuurem pilt
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Püsilink: https://www.kriso.ee/db/9780792345701.html
Märksõnad:
Discusses instances of the analytic-synthetic distinction in relation to the history and philosophy of mathematics, and explores new perspectives in the problem of objectivity as a form of knowledge. Topics include the analytical method in Descartes' work, background to Euler's analysis, styles of argumentation in the late 19th century, mathematical acts of reasoning as synthetic a priori , and classical sources for concepts of analysis and synthesis. For scholars in philosophy of mathematics, logic, and science, and historians of science and mathematics. No index. Annotation c. by Book News, Inc., Portland, Or.
Introduction ix
I. History
The Analytical Method in Descartes' Geometrie
3(32)
Giorgio Israel
Arcanum Artis Inveniendi: Leibniz and Analysis
35(12)
Enrico Pasini
Introduction
35(1)
Truth Conditions
36(1)
There is Method in't
37(1)
The Anatomy of Wit
38(1)
Thought Instruments
39(2)
The Place of Analysis
41(1)
Calculus on My Mind
42(2)
An Engine for Your Thoughts
44(3)
The Background to and Early Emergence of Euler's Analysis
47(32)
Craig G. Fraser
Introduction
47(1)
Analytical Methods in Early Modern Mathematics
47(16)
Euler's Analysis
63(10)
Discussion
73(6)
Jacob Bernoulli on Analysis, Synthesis, and the Law of Large Numbers
79(24)
Edith Dudley Sylla
Introduction
79(2)
Jacob Bernoulli on Analysis and Synthesis
81(2)
A Priori, A Posteriori, and the Law of Large Numbers
83(2)
Bernoulli's Proof of the Law of Large Numbers
85(2)
Cases (casus) and Bernoulli's Conceptions of God and the World
87(6)
Algebra and the Law of Large Numbers
93(1)
Summary
94(9)
Mathematical Analysis and Analytical Science
103(44)
Carlos Alvarez Jimenez
Introduction
103(5)
The Algebraic Foundation of Mathematical Analysis
108(20)
Convergence and Continuity as the Trends of the New Analysis
128(19)
The Analysis of the Synthesis of the Analysis ... Two Moments of a Chiasmus: Viete and Fourier
147(30)
Jean Dhombres
Introduction
147(2)
Viete or Analysis Seen as an Appeal for a Constructive Synthesis
149(5)
Fourier or the Synthesis Appearing as an Analytical Necessity
154(11)
Fourier's Transform: an Erasing of Synthesis
165(4)
The Scientific Sufficiency of a Chiasmus
169(8)
Styles of Argumentation in Late 19th Century Geometry and the Structure of Mathematical Modernity
177(24)
Moritz Epple
Introduction
177(1)
From Synthesis and Analysis to Concrete and Abstract Styles of Mathematical Argumentation
178(5)
A Philosophical Analysis of Concrete and Abstract Arguments
183(7)
The Role of Concrete and Abstract Argumentative Styles in Mathematical Modernity
190(11)
II. Philosophy
From Backward Reduction to Configurational Analysis
201(26)
Petri Maenpaa
Introduction
201(4)
The Directional Interpretation of Analysis: Pappus's Description
205(2)
The Configurational Interpretation of Analysis: Descartes's Description
207(1)
Logical Form in Analysis
208(9)
The Heuristic Role of Auxiliary Constructions
217(4)
The Logical Role of Auxiliary Constructions
221(6)
Analysis, Hermeneutics, Mathematics
227(16)
Jean-Michel Salanskis
Introduction
227(1)
Greek Analytical Suspension: Hermeneutics and Deliberation
227(4)
Transcendental Analysis
231(4)
The Identity of the Branch Analysis of Contemporary Mathematics
235(8)
Science within Reason: Is there a Crisis of the Modern Sciences?
243(18)
Richard Tieszen
Introduction
243(1)
Rationality, Intentionality and Everyday Experience
244(4)
Scientific Rationality
248(3)
The Analytic-Synthetic Distinction
251(2)
Crisis?
253(4)
(Un-) Intentional Knots
257(1)
Conclusion
258(3)
Mathematics as an Activity and the Analytic-Synthetic Distinction
261(12)
Michael Otte
Marco Panza
Intensional and Extensional Theories
261(1)
Analytical and Synthetical Judgments
262(6)
Cassirer and Poincare
268(1)
Mathematics as an Activity
269(4)
Mathematical Acts of Reasoning as Synthetic a priori
273(54)
Marco Panza
Introduction
273(1)
Standard Accounts
273(4)
A Provisional Reformulation of Kant's Distinction
277(6)
Concept, Object and Intuition: the Final Version of Kant's Distinction
283(10)
Kant's Ontologism
293(2)
Analytic and Synthetic Acts of Reasoning
295(7)
Naive Formalism and Conceptualism
302(3)
Madame Bovary as a Pure Object
305(2)
Euclidean Geometry
307(5)
Arithmetical Proofs
312(6)
Concepts of Objects, Concepts of Properties: the Essential Character of Mathematics
318(3)
Concluding Remarks
321(6)
Analysis and Synthesis in Mathematics from the Perspective of Charles S. Peirce's Philosophy
327(38)
Michael Otte
Introduction
327(3)
Analysis and Synthesis from Leibniz to Kant
330(6)
Kant and Forster
336(7)
Some Issues where Peirce and Kant differ
343(10)
The Analytic-Synthetic Distinction according to Peirce is only relative
353(6)
Pure and Applied Mathematics: Some Examples of Non-Kantian Applications of Mathematics
359(6)
III. History and Philosophy
Classical Sources for the Concepts of Analysis and Synthesis
365(50)
Marco Panza
Philology and Literature
367(2)
Plato
369(1)
Aristotle
370(8)
Aristotelian Forms of Analysis
378(5)
Analysis and Synthesis According to Pappus
383(14)
Thomas
397(4)
Viete and Descartes
401(14)
Bibliography 415(20)
Index of Names 435