9 found

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  1. Irving Anellis (2011). Did Principia Mathematica Precipitate a ‘Fregean Revolution’? Russell 31 (1).
    I begin by asking whether there was a Fregean revolution in logic, and, if so, in what did it consist. I then ask whether, and if so, to what extent, Russell played a decisive role in carrying through the Fregean revolution, and, if so, how. A subsidiary question is whether it was primarily the influence of The Principles of Mathematics or Principia Mathematica, or perhaps both, that stimulated and helped consummate the Fregean revolution. Finally, I examine cases in which logicians (...)
     
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  2. Kenneth Blackwell (2011). The Wit and Humour of Principia Mathematica. Russell 31 (1).
    Except for belatedly proving that “1 + 1 = 2”, Principia Mathematica doesn’t feature in studies of mathematical humour. Yet there is humour in that work, despite the inauspicious conditions under which it was written. Russell, to take one of the authors, had an irrepressible talent for enlivening any subject matter. This paper reports the results of exploring even the “obscure corners” of PM to uncover its humour and wit.
     
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  3. Ryan Christensen (2011). Propositional Quantification. Russell 31 (1).
    Ramsey defined truth in the following way: x is true if and only if ∃p. This definition is ill-formed in standard first-order logic, so it is normally interpreted using substitutional or some kind of higher-order quantifier. I argue that these quantifiers fail to provide an adequate reading of the definition, but that, given certain adjustments, standard objectual quantification does provide an adequate reading.
     
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  4. Nicholas Griffin & Bernard Linsky (2011). Preface. Russell 31 (1).
     
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  5. Brice Halimi (2011). Generality of Logical Types. Russell 31 (1).
    My aim is to examine logical types in Principia Mathematica from two perspectives. The first one pertains to the ambiguity of the notion of logical type as introduced in the Introduction . I claim that a distinction has to be made between types as called for in the context of paradoxes, and types as logical prototypes. The second perspective bears on typical ambiguity as described in Russell and Whitehead’s “Prefatory Statement of Symbolic Conventions”, inasmuch as it lends itself to a (...)
     
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  6. Roman Murawski (2011). On Chwistek’s Philosophy of Mathematics. Russell 31 (1).
    The paper is devoted to the presentation of Chwistek’s philosophical ideas concerning logic and mathematics. The main feature of his philosophy was nominalism, which found full expression in his philosophy of mathematics. He claimed that the object of the deductive sciences, hence in particular of mathematics, is the expression being constructed in them according to accepted rules of construction. He treated geometry, arithmetic, mathematical analysis and other mathematical theories as experimental disciplines, and obtained in this way a nominalistic interpretation of (...)
     
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  7. Ray Perkins Jr (2011). Incomplete Symbols in Principia Mathematica and Russell’s ‘Definite Proof’. Russell 31 (1).
    Early in Principia Mathematica Russell presents an argument that “‘the author of Waverley’ means nothing”, an argument that he calls a “definite proof”. He generalizes it to claim that definite descriptions are incomplete symbols having meaning only in sentential context. This Principia “proof” went largely unnoticed until Russell reaffirmed a near-identical “proof” in his philosophical autobiography nearly 50 years later. The “proof” is important, not only because it grounds our understanding of incomplete symbols in the Principia programme, but also because (...)
     
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  8. Graham Stevens (2011). Logical Form in Principia Mathematica and English. Russell 31 (1).
    The theory of descriptions, presented informally in “On Denoting” and more formally in Principia Mathematica, has been endorsed by many linguists and philosophers of language as a contribution to natural-language semantics. However, the syntax of Principia’s formal language is far from ideal as a tool for the analysis of natural language. Stephen Neale has proposed a reconstruction of the theory of descriptions in a language of restricted quantification that gives a better approximation of the syntax of English . This has (...)
     
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  9. Alexander Paul Bozzo (2011). Functions or Propositional Functions? [REVIEW] Russell 30 (2):161-8.
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