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Russell's hidden substitutional theory

Author: Gregory Landini
Publisher: New York : Oxford University Press, 1998.
Edition/Format:   eBook : EnglishView all editions and formats
Database:WorldCat
Summary:
Explores a central thread unifying Russell's thoughts on logic in two works considered at odds with each other: "Principles of Mathematics" and "Principia Mathematica". The thread states that logic is an absolutely general science and any calculus for it must embrace unrestricted variables.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Landini, Gregory.
Russell's hidden substitutional theory.
New York : Oxford University Press, 1998
(DLC) 97022750
(OCoLC)37246630
Named Person: Bertrand Russell
Material Type: Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Gregory Landini
ISBN: 0585329060 9780585329062 0195353722 9780195353723 1280470291 9781280470295
OCLC Number: 45842545
Description: 1 online resource (xi, 337 p.)
Contents: The unrestricted variable --
Russell's logicist program --
Two conceptions of logicism: Frege and Russell --
Arithmetization --
Russell's principle of abstraction --
Logic as a science --
The logic of the principles of mathematics --
The calculus for the logic propositions --
Russell's definitions --
The theory of implication --
Quodlibet ens est unum --
Denoting concepts --
The analysis of the variable --
The new theory of the variable --
"On fundamentals" against denoting concepts --
An argument against Frege? --
The variable as primitive --
The road to substitution --
Types as logical grammar --
The logic of substitution --
Russell's original principles of substitution --
The basic logic of propositions --
Substitutional principles --
Identity --
Proofs of propositional identities --
The "no propositional functions" theory --
Substitution and definite descriptions --
Multiple substitutions --
Comprehension and identity --
Types as logical grammar --
The "no-classes" theory --
Classes as extensional propositional functions --
Complex prototypes and extensionality --
The general theory of classes --
Comparison with Principia mathematica --
The "no-relations[subscript e]" theory --
Relations-in-extension in Principia mathematica --
Relations-in-extension in the substitutional theory --
Cantor's paradox of the greatest cardinal --
The Burali-Forti paradox --
Ramification --
Les paradoxes de la logique --
Three paradoxes of propositions --
Substitutional manuscripts of April/May 1906 --
Poincare's vicious circle principle.
Responsibility: Gregory Landini.
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Abstract:

Explores a central thread unifying Russell's thoughts on logic in two works considered at odds with each other: "Principles of Mathematics" and "Principia Mathematica". The thread states that logic  Read more...

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The author provides deep insights into a very dynamic period of Russell's tackling with logical systems by stressing the unifying role of the substitutional theory. V.Peckhaus, MATH, Vol.933 Read more...

 
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