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Tables of Contents for Analysis and Synthesis in Mathematics
Chapter/Section Title
Page #
Page Count
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