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E-raamat: From Peirce to Skolem: A Neglected Chapter in the History of Logic

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(Department of Computer Science, University of Chicago, 1100 E 58th Street, Chicago, IL 60637 USA)
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From Peirce to Skolem: A Neglected Chapter in the History of LogicSuurem pilt
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Revising a decade later her master's thesis for the University of Chicago, Brady (U. of Chicago) explores the influence on the development of mathematical logic of Charles S. Peirce and his student O. H. Mitchell through the work of Ernst Schroeder, Leopold Loewenheim, and Thoralf Skolem, all in the late 19th century. She delves into such questions as how first-order logic developed, and what the real contributions of his subjects are over and above the better known contributions of Gottlob Frege, Bertrand Russell, and David Hilbert. She concludes that the Loewenheim-Skolem theorem developed directly from Schroeder's Algebra der Logik , itself an avowed elaboration of the work of American Charles S. Peirce and his student O. H. Mitchell. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Arvustused

M. GuillaumeThe book is well written, and written for a ;arge audience. Many very detailed explanations of terminology, notation and proof techniques in the quotations of historicl texts are given.....Mathematical Reviews

Introduction 1(8)
The Early Work of Charles S. Peirce
9(14)
Overview of the Mathematical Systems of Charles S. Peirce
9(2)
Peirce's Influence on the Development of Logic
11(3)
Peirce's Early Approaches to Logic
14(9)
Peirce's Calculus of Relatives: 1870
23(28)
Peirce's Algebra of Relations
24(22)
Inclusion and Equality
27(2)
Addition
29(1)
Multiplication
30(8)
Peirce's First Quantifiers
38(1)
Involution
39(3)
Involution and Mixed-Quantifier Forms
42(2)
Elementary Relatives
44(2)
Quantification in the Calculus of Relatives in 1870
46(2)
Summary
48(3)
Peirce on the Algebra of Logic: 1880
51(24)
Overview of Peirce's ``On the algebra of logic''
51(3)
Discussion
54(19)
The Origins of Logic
54(2)
Syllogism and Illation
56(4)
Forms of Propositions
60(4)
The Algebra of the Copula
64(6)
The Logic of Nonrelative Terms
70(3)
Conclusion
73(2)
Mitchell on a New Algebra of Logic: 1883
75(20)
Mitchell's Rule of Inference
75(3)
Single-Variable Monadic Logic
78(8)
Single-Variable Monadic Propositions
78(2)
Disjunctive Normal Form
80(2)
Rules of Inference for Single-Variable Logic
82(4)
Two-Variable Monadic Logic
86(3)
Mitchell's Dimension Theory
86(2)
Contrast to Peirce
88(1)
Three-Variable Monadic Logic
89(1)
Peirce on Mitchell
90(5)
Peirce on the Algebra of Relatives: 1883
95(18)
Background in Linear Associative Algebras
95(3)
The Algebra of Relatives
98(6)
Types of Relatives
98(2)
Operations on Relatives
100(4)
Syllogistic in the Relative Calculus
104(2)
Prenex Predicate Calculus
106(3)
Summary of Peirce's Accomplishments in 1883
109(2)
Syntax and Semantics
109(1)
Quantifiers
110(1)
Peirce's Appraisal of His Algebra of Binary Relatives
111(2)
Peirce's Logic of Quantifiers: 1885
113(30)
On the Derivation of Logic from Algebra
113(3)
Nonrelative Logic
116(11)
Embedding Boolean Algebra in Ordinary Algebra
116(5)
Five Peirce Icons
121(4)
Truth-functional Interpretations of Propositions
125(2)
First-Order Logic
127(5)
Infinite Sums and Products
127(1)
Mitchell
128(1)
Formulas and Rules
129(3)
Second-Order Logic
132(11)
Schroder's Calculus of Relatives
143(26)
Die Algebra der Logik: Volume 1
144(3)
Die Algebra der Logik: Volume 2
147(2)
Die Algebra der Logik: Volume 3
149(16)
Peirce's Attack on the General Solutions of Schroder
153(2)
Lectures VI-X and Dedekind Chain Theory
155(5)
Lectures XI-XII and Higher Order Logic
160(5)
Norbert Wiener's Ph.D. Thesis
165(4)
Lowenheim's Contribution
169(28)
Overview of Lowenheim's 1915 Paper
171(1)
Lowenheim's Theorem
172(19)
Conclusions
191(4)
Impact of Lowenheim's Paper
195(2)
Skolem's Recasting
197(248)
Appendices
1. Schroder's Lecture I
207(16)
2. Schroder's Lecture II
223(28)
3. Schroder's Lecture III
251(6)
4. Schroder's Lecture V
257(38)
5. Schroder's Lecture IX
295(44)
6. Schroder's Lecture XI
339(40)
7. Schroder's Lecture XII
379(50)
8. Norbert Wiener's Thesis
429(16)
Bibliography 445(16)
Index 461


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