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Propositional Functions in Extension

Robert Trueman

Theoria 77 (4):292-311 (2011)

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On Ramsey’s reason to amend Principia Mathematica’s logicism and Wittgenstein’s reaction.Anderson Nakano - 2020 - Synthese 2020 (1):2629-2646.details In the Foundations of Mathematics, Ramsey attempted to amend Principia Mathematica’s logicism to meet serious objections raised against it. While Ramsey’s paper is well known, some questions concerning Ramsey’s motivations to write it and its reception still remain. This paper considers these questions afresh. First, an account is provided for why Ramsey decided to work on his paper instead of simply accepting Wittgenstein’s account of mathematics as presented in the Tractatus. Secondly, evidence is given supporting that Wittgenstein was not moved (...) Download Export citation Bookmark 1 citation
A Dilemma for Neo-Fregeanism.Robert Trueman - 2014 - Philosophia Mathematica 22 (3):361-379.details Neo-Fregeans need their stipulation of Hume's Principle — $NxFx=NxGx \leftrightarrow \exists R (Fx \,1\hbox {-}1_R\, Gx)$ — to do two things. First, it must implicitly define the term-forming operator ‘Nx…x…’, and second it must guarantee that Hume's Principle as a whole is true. I distinguish two senses in which the neo-Fregeans might ‘stipulate’ Hume's Principle, and argue that while one sort of stipulation fixes a meaning for ‘Nx…x…’ and the other guarantees the truth of Hume's Principle, neither does both. Download Export citation Bookmark 5 citations
Frank Ramsey and the Realistic Spirit.Steven Methven - 2014 - London and Basingstoke: Palgrave Macmillan.details This book attempts to explicate and expand upon Frank Ramsey's notion of the realistic spirit. In so doing, it provides a systematic reading of his work, and demonstrates the extent of Ramsey's genius as evinced by both his responses to the Tractatus Logico-Philosophicus , and the impact he had on Wittgenstein's later philosophical insights. Download Export citation Bookmark 6 citations
Exclusion Problems and the Cardinality of Logical Space.Tim Button - 2017 - Journal of Philosophical Logic 46 (6):611-623.details Wittgenstein’s atomist picture, as embodied in his Tractatus, is initially very appealing. However, it faces the famous colour-exclusion problem. In this paper, I shall explain when the atomist picture can be defended in the face of that problem; and, in the light of this, why the atomist picture should be rejected. I outline the atomist picture in Section 1. In Section 2, I present a very simple necessary and sufficient condition for the tenability of the atomist picture. The condition is: (...) Download Export citation Bookmark 1 citation
Hourya Benis-Sinaceur, Marco Panza, and Gabriel Sandu.Functions and Generality of Logic: Reflections on Dedekind’s and Frege’s Logicisms. [REVIEW]Patricia Blanchette - forthcoming - Philosophia Mathematica:nky021.details Hourya Benis-Sinaceur, Marco Panza, and Gabriel Sandu. Functions and Generality of Logic: Reflections on Dedekind’s and Frege’s Logicisms. Logic, Epistemology, and the Unity of Science; 37. Springer, 2015. ISBN: 978-3-319-17108-1 ; 978-3-319-36782-8, 978-3-319-17109-8.. Pp. xxi + 125. Download Export citation Bookmark

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