Russell's hidden substitutional theory:
In The Principles of Mathematics, Bertrand Russell set forth his logicist thesis that the concepts of non-applied mathematics are those of pure logic. In this revisionist interpretation. Gregory Landini explores an important central thread that unifies Russell's thoughts on logic in the two wor...
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Oxford Univ. Press
1998
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | In The Principles of Mathematics, Bertrand Russell set forth his logicist thesis that the concepts of non-applied mathematics are those of pure logic. In this revisionist interpretation. Gregory Landini explores an important central thread that unifies Russell's thoughts on logic in the two works. The heart of Landini's book is a careful presentation and exploration of Russell's largely unpublished "substitutional" theory of propositions. |
| Physical Description: | XI, 337 S. |
| ISBN: | 0195116836 |
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| 520 | 3 | |a In The Principles of Mathematics, Bertrand Russell set forth his logicist thesis that the concepts of non-applied mathematics are those of pure logic. In this revisionist interpretation. Gregory Landini explores an important central thread that unifies Russell's thoughts on logic in the two works. The heart of Landini's book is a careful presentation and exploration of Russell's largely unpublished "substitutional" theory of propositions. | |
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Record in the Search Index
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| adam_text | Russell s Hidden
Substitutional Theory
GREGORY LANDINI
New York Oxford
Oxford University Press
Contents
Introduction 3
Quodlibet Ens Est Unum 3
Overview 7
PARTI THE UNRESTRICTED VARIABLE
1 Russell s Logicist Program 13
Two Conceptions of Logicism: Frege and Russell 13
Arithmetization 17
Russell s Principle of Abstraction 21
Logic as a Science 30
2 The Logic of The Principles of Mathematics 42
The Calculus for the Logic Propositions 42
Russell s Definitions 48
The Theory of Implication 52
Quodlibet Ens Est Unum 54
Denoting Concepts 57
The Analysis of the Variable 63
3 The New Theory of the Variable 69
On Fundamentals Against Denoting Concepts 72
An Argument Against Frege? 80
The Variable as Primitive 82
The Road to Substitution 89
PART II TYPES AS LOGICAL GRAMMAR
4 The Logic of Substitution 97
Russell s Original Principles of Substitution 98
The Basic Logic of Propositions 102
Substitutional Principles 106
Identity 109
Proofs of Propositional Identities 112
5 The No Propositional Functions Theory 127
Substitution and Definite Descriptions 128
Multiple Substitutions 132
Comprehension and Identity 135
Types as Logical Grammar 140
6 The No-Classes Theory 146
Classes as Extensional Propositional Functions 147
Complex Prototypes and Extensionality 149
The General Theory of Classes 152
Comparison with Pnncipia Mathematica 165
7 The No-Relationse Theory 176
Relations-in-Extension in Principia Mathematica 177
Relations-in-Extension in the Substitutional Theory 179
Cantor s Paradox of the Greatest Cardinal 183
The Burali-Forti Paradox 190
PART III RAMIFICATION
8 Les Paradoxes de la Logique 199
Three Paradoxes of Propositions 201
Substitutional Manuscripts of April/May 1906 206
Poincare s Vicious Circle Principle 213
Logic without General Propositions 216
The Statement Liar 220
The Konig, Dixon, Berry, Richard, and Grelling Paradoxes 224
Russell s Mitigating Axiom 227
The Demise of Les Paradoxes 231
Contents xi
9 Mathematical Logic as Based on the Theory of Types 234
Orders of Propositions 235
Substitutional Logic cum Orders of Propositions 240
Predicativity and Reducibility 246
Paradoxes of Propositions Avoided 251
10 The Logic of Principia Mathematica 255
The Formal System of Principia (cum *10) 255
The Perils of Typical Ambiguity 258
Orders within Types or Types within Orders? 267
The Doctrine of the Unlimited Variable 272
Poincare s Vicious Circle Principle 275
The Philosophical Justification of the Type Part of an Order/Type
Index 279
The Philosophical Justification of the Order Part of an Order/Type
Index 281
The Multiple-Relation Theory of Judgment 287
What Is Logic? 291
What Logic Is Not 294
Appendix A: Proof of the Peano Postulates 299
Appendix B: Axioms, Theorems, and Definitions 314
Bibliography 325
Index 333
|
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| era | Geschichte 1900-2000 |
| era_facet | Geschichte 1900-2000 |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:22:13Z |
| institution | BVB |
| isbn | 0195116836 |
| language | English |
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| physical | XI, 337 S. |
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| spelling | Landini, Gregory 1955- Verfasser (DE-588)139991123 aut Russell's hidden substitutional theory Gregory Landini New York [u.a.] Oxford Univ. Press 1998 XI, 337 S. txt rdacontent n rdamedia nc rdacarrier In The Principles of Mathematics, Bertrand Russell set forth his logicist thesis that the concepts of non-applied mathematics are those of pure logic. In this revisionist interpretation. Gregory Landini explores an important central thread that unifies Russell's thoughts on logic in the two works. The heart of Landini's book is a careful presentation and exploration of Russell's largely unpublished "substitutional" theory of propositions. Russell, Bertrand <1872-1970> Russell, Bertrand <1872-1970> ram Russell, Bertrand 1872-1970 (DE-588)118604287 gnd rswk-swf Geschichte 1900-2000 Filosofia da matemática larpcal Logique symbolique et mathématique - 20e siècle ram Logique symbolique et mathématique - Histoire - 20e siècle Lógica larpcal Propositielogica gtt Proposition (Logique) - Histoire - 20e siècle Proposition (logique) - 20e siècle ram Wiskunde gtt Geschichte Mathematik Logic, Symbolic and mathematical History 20th century Proposition (Logic) History 20th century Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Russell, Bertrand 1872-1970 (DE-588)118604287 p Mathematische Logik (DE-588)4037951-6 s DE-604 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008215177&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Landini, Gregory 1955- Russell's hidden substitutional theory Russell, Bertrand <1872-1970> Russell, Bertrand <1872-1970> ram Russell, Bertrand 1872-1970 (DE-588)118604287 gnd Filosofia da matemática larpcal Logique symbolique et mathématique - 20e siècle ram Logique symbolique et mathématique - Histoire - 20e siècle Lógica larpcal Propositielogica gtt Proposition (Logique) - Histoire - 20e siècle Proposition (logique) - 20e siècle ram Wiskunde gtt Geschichte Mathematik Logic, Symbolic and mathematical History 20th century Proposition (Logic) History 20th century Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)118604287 (DE-588)4037951-6 |
| title | Russell's hidden substitutional theory |
| title_auth | Russell's hidden substitutional theory |
| title_exact_search | Russell's hidden substitutional theory |
| title_full | Russell's hidden substitutional theory Gregory Landini |
| title_fullStr | Russell's hidden substitutional theory Gregory Landini |
| title_full_unstemmed | Russell's hidden substitutional theory Gregory Landini |
| title_short | Russell's hidden substitutional theory |
| title_sort | russell s hidden substitutional theory |
| topic | Russell, Bertrand <1872-1970> Russell, Bertrand <1872-1970> ram Russell, Bertrand 1872-1970 (DE-588)118604287 gnd Filosofia da matemática larpcal Logique symbolique et mathématique - 20e siècle ram Logique symbolique et mathématique - Histoire - 20e siècle Lógica larpcal Propositielogica gtt Proposition (Logique) - Histoire - 20e siècle Proposition (logique) - 20e siècle ram Wiskunde gtt Geschichte Mathematik Logic, Symbolic and mathematical History 20th century Proposition (Logic) History 20th century Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Russell, Bertrand <1872-1970> Russell, Bertrand 1872-1970 Filosofia da matemática Logique symbolique et mathématique - 20e siècle Logique symbolique et mathématique - Histoire - 20e siècle Lógica Propositielogica Proposition (Logique) - Histoire - 20e siècle Proposition (logique) - 20e siècle Wiskunde Geschichte Mathematik Logic, Symbolic and mathematical History 20th century Proposition (Logic) History 20th century Mathematische Logik |
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