Explanations | |
Sallies | p. 3 |
Scope and limits of the book | p. 3 |
An outline history | p. 3 |
Mathematical aspects | p. 4 |
Historical presentation | p. 6 |
Other logics, mathematics and philosophies | p. 7 |
Citations, terminology and notations | |
References and the bibliography | p. 9 |
Translations, quotations and notations | p. 10 |
Permissions and acknowledgements | p. 11 |
Preludes: Algebraic Logic and Mathematical Analysis up to | p. 1870 |
Plan of the chapter | p. 14 |
`Logique'' and algebras in French mathematics | p. 14 |
The `logique'' and clarity of `ideologie'' | p. 14 |
Lagrange''s algebraic philosophy | p. 15 |
The many senses of `analysis'' | p. 17 |
Two Lagrangian algebras: functional equations and differential operators | p. 17 |
Autonomy for the new algebras | p. 19 |
Some English algebraists and logicians | p. 20 |
A Cambridge revival: the `Analytical Society, Lacroix, and the professing of algebras | p. 20 |
The advocacy of algebras by Babbage, Herschel and Peacock | p. 20 |
An Oxford movement: Whately and the professing of logic | p. 22 |
A London pioneer: De Morgan on algebras and logic | p. 25 |
Summary of his life | p. 25 |
De Morgan''s philosophies of algebra | p. 25 |
De Morgan''s logical career | p. 26 |
De Morgan''s contributions to the foundations of logic | p. 27 |
Beyond the syllogism | p. 29 |
Contretemps over `the quantification of the predicate'' | p. 30 |
The logic of two place relations, 1860 | p. 32 |
Analogies between logic and mathematics | p. 35 |
De Morgan''s theory of collections | p. 36 |
A Lincoln outsider: Boole on logic as applied mathematics | p. 37 |
Summary of his career | p. 37 |
Boole''s `general method in analysis'' 1844 | p. 39 |
The mathematical analysis of logic, 1847. `elective symbols'' and laws | p. 40 |
`Nothing'' and the `Universe'' | p. 42 |
Propositions, expansion theorems, and solutions | p. 43 |
The laws of thought, 1854: modified principles and extended methods | p. 46 |
Boole''s new theory of propositions | p. 49 |
The character of Boole''s system | p. 50 |
Boole''s search for mathematical roots | p. 53 |
The semi-followers of Boole | p. 54 |
Some initial reactions to Boole''s theory | p. 54 |
The reformulation | p. 56 |
Jevons versus Boole | p. 59 |
Followers of Boole and/or Jevons | p. 60 |
Cauchy, Weierstrass and the rise of mathematical analysis | p. 63 |
Different traditions in the calculus | p. 63 |
Cauchy and the Ecole Polytechnique | p. 64 |
The gradual adoption and adaptation of Cauchy''s new tradition | p. 67 |
The refinements of Weierstrass and his followers | p. 68 |
Judgement and supplement | p. 70 |
Mathematical analysis versus algebraic logic | p. 70 |
The places of Kant and Bolzano | p. 71 |
Cantor: Mathematics as Mengenlehre 3.1 Prefaces | p. 75 |
Plan of the chapter | p. 75 |
Cantor''s career | p. 75 |
The launching of the Mengenlehre, 1870-1883 | p. 79 |
Riemann''s thesis: the realm of discontinuous functions | p. 79 |
Heine on trigonometric series and the real line, 1870-1872 | p. 81 |
Cantor''s extension of Heine''s findings, 1870-1872 | p. 83 |
Dedekind on irrational numbers, 1872 | p. 85 |
Cantor on line and plane, 1874-1877 | p. 88 |
Infinite numbers and the topology of linear sets, 1878-1883 | p. 89 |
The Grundlagen, 1883: the construction of number-classes | p. 92 |
The Grundlagen: the definition of continuity | p. 95 |
The successor to the Grundlagen, 1884 | p. 96 |
Cantor''s Acta mathematica phase, 1883-1885 | p. 97 |
Mittag-Lefler and the French translations, 1883 | p. 97 |
Unpublished and published ''communications'' 1884-1885 | p. 98 |
Order-types and partial derivatives in the `communications'' | p. 100 |
Commentators on Cantor, 1883-1885 | p. 102 |
The extension of the Mengenlehre, 1886-1897 | p. 103 |
Dedekind''s developing set theory, 1888 | p. 103 |
Dedekind''s chains of integers | p. 105 |
Dedekind''s philosophy of arithmetic | p. 107 |
Cantor''s philosophy of the infinite, 1886-1888 | p. 109 |
Cantor''s new definitions of numbers | p. 110 |
Cardinal exponentiation: Cantor''s diagonal argument, 1891 | p. 110 |
Transfinite cardinal arithmetic and simply ordered sets, 1895 | p. 112 |
Transfinite ordinal arithmetic and well-ordered sets, 1897 | p. 114 |
Open and hidden questions in Cantor''s Mengenlehre | p. 114 |
Well-ordering and the axioms of choice | p. 114 |
What was Cantor''s `Cantor''s continuum problem''? | p. 116 |
"Paradoxes" and the absolute infinite | p. 117 |
Cantor''s philosophy of mathematics | p. 119 |
A mixed position | p. 119 |
(No) logic and metamathematics | p. 120 |
The supposed impossibility of infinitesimals | p. 121 |
A contrast with Kronecker | p. 122 |
Concluding comments: the character of Cantor''s achievements | p. 124 |
Parallel Processes in Set Theory, Logics and Axiomatics, 1870s-1900s | |
Plans for the chapter | p. 126 |
The splitting and selling of Cantor''s Mengenlehre | p. 126 |
National and international support | p. 126 |
French initiatives, especially from Borel | p. 127 |
Couturat outlining the infinite, 1896 | p. 129 |
German initiatives from Mein | p. 130 |
German proofs of the Schroder-Bernstein theorem | p. 132 |
Publicity from Hilbert, 1900 | p. 134 |
Integral equations and functional analysis | p. 135 |
Kempe on `mathematical form'' | p. 137 |
Kempe-who? | p. 139 |
American algebraic logic: Peirce and his followers | p. 140 |
Peirce, published and unpublished | p. 141 |
Influences on Peirre''s logic: father''s algebras | p. 142 |
Peirce''s first phase: Boolean logic and the categories, 1867-1868 | p. 144 |
Peirce''s virtuoso theory of relatives, 1870 | p. 145 |
Peirce''s second phase, 1880: the propositional calculus | p. 147 |
Peirre''s second phase, 1881: finite and infinite | p. 149 |
Peirce''s students, 1883: duality, and ''Quantifying'' a proposition | p. 150 |
Peirre on ''icons'' and the order of `quantifiers; 1885 153 | |
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