Russell's hidden substitutional theory / Gregory Landini.

Includes bibliographical references (pages 325-332) and index.

Print version record.

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.

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 The heart of Landini's book is a careful presentation and exploration of Russell's largely unpublished "substitutional" theory of propositions.

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.

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