Switch to: References

Add citations

You must login to add citations.
  1. Russell's Schema, Not Priest's Inclosure.Gregory Landini - 2009 - History and Philosophy of Logic 30 (2):105-139.
    On investigating a theorem that Russell used in discussing paradoxes of classes, Graham Priest distills a schema and then extends it to form an Inclosure Schema, which he argues is the common structure underlying both class-theoretical paradoxes (such as that of Russell, Cantor, Burali-Forti) and the paradoxes of ?definability? (offered by Richard, König-Dixon and Berry). This article shows that Russell's theorem is not Priest's schema and questions the application of Priest's Inclosure Schema to the paradoxes of ?definability?.1 1?Special thanks to (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  • The Innocence of Truth in Semantic Paradox.Eric Guindon - 2021 - Erkenntnis 86 (1):71-93.
    According to some philosophers, the Liar paradox arises because of a mistaken theory of truth. Its lesson is that we must reject some instances of the naive propositional truth-schema \It is true that \ if and only if \\. In this paper, I construct a novel semantic paradox in which no principle even analogous to the truth-schema plays any role. I argue that this undermines the claim that we ought to respond to the Liar by revising our theory of truth.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
    		•
  • Omnipresence, Multipresence and Ubiquity: Kinds of Generality in and Around Mathematics and Logics. [REVIEW]I. Grattan-Guinness - 2011 - Logica Universalis 5 (1):21-73.
    A prized property of theories of all kinds is that of generality, of applicability or least relevance to a wide range of circumstances and situations. The purpose of this article is to present a pair of distinctions that suggest that three kinds of generality are to be found in mathematics and logics, not only at some particular period but especially in developments that take place over time: ‘omnipresent’ and ‘multipresent’ theories, and ‘ubiquitous’ notions that form dependent parts, or moments, of (...)
    $47.60 new   $52.55 used   $54.99 from Amazon    (collection)    View on Amazon.com
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  • The Indefinability of “One”.Laurence Goldstein - 2002 - Journal of Philosophical Logic 31 (1):29-42.
    Logicism is one of the great reductionist projects. Numbers and the relationships in which they stand may seem to possess suspect ontological credentials – to be entia non grata – and, further, to be beyond the reach of knowledge. In seeking to reduce mathematics to a small set of principles that form the logical basis of all reasoning, logicism holds out the prospect of ontological economy and epistemological security. This paper attempts to show that a fundamental logicist project, that of (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark  
    		•
  • The inclosure scheme and the solution to the paradoxes of self-reference.Jordi Valor Abad - 2008 - Synthese 160 (2):183 - 202.
    All paradoxes of self-reference seem to share some structural features. Russell in 1908 and especially Priest nowadays have advanced structural descriptions that successfully identify necessary conditions for having a paradox of this kind. I examine in this paper Priest’s description of these paradoxes, the Inclosure Scheme (IS), and consider in what sense it may help us understand and solve the problems they pose. However, I also consider the limitations of this kind of structural descriptions and give arguments against Priest’s use (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   4 citations