Switch to: Citations

References in:

Notes on inconsistent set theory

In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Dordrecht, Netherland: Springer. pp. 315--328 (2012)

Add references

You must login to add references.
  1. Paraconsistent Logic: Essays on the Inconsistent.Graham Priest, Richard Routley & Jean Norman (eds.) - 1989 - Philosophia Verlag.
    Download  
     
    Export citation  
     
    Bookmark   105 citations  
  • On the theory of inconsistent formal systems.Newton C. A. da Costa - 1974 - Notre Dame Journal of Formal Logic 15 (4):497-510.
    Download  
     
    Export citation  
     
    Bookmark   177 citations  
  • Transfinite numbers in paraconsistent set theory.Zach Weber - 2010 - Review of Symbolic Logic 3 (1):71-92.
    This paper begins an axiomatic development of naive set theoryin a paraconsistent logic. Results divide into two sorts. There is classical recapture, where the main theorems of ordinal and Peano arithmetic are proved, showing that naive set theory can provide a foundation for standard mathematics. Then there are major extensions, including proofs of the famous paradoxes and the axiom of choice (in the form of the well-ordering principle). At the end I indicate how later developments of cardinal numbers will lead (...)
    Download  
     
    Export citation  
     
    Bookmark   55 citations  
  • Universal Logic.Ross Brady - 2006 - CSLI Publications.
    Throughout the twentieth century, the classical logic of Frege and Russell dominated the field of formal logic. But, as Ross Brady argues, a new type of weak relevant logic may prove to be better equipped to present new solutions to persistent paradoxes. _Universal Logic _begins with an overview of classical and relevant logic and discusses the limitations of both in analyzing certain paradoxes. It is the first text to demonstrate how the main set-theoretic and semantic paradoxes can be solved in (...)
    Download  
     
    Export citation  
     
    Bookmark   59 citations  
  • Logic without contraction as based on inclusion and unrestricted abstraction.Uwe Petersen - 2000 - Studia Logica 64 (3):365-403.
    On the one hand, the absence of contraction is a safeguard against the logical (property theoretic) paradoxes; but on the other hand, it also disables inductive and recursive definitions, in its most basic form the definition of the series of natural numbers, for instance. The reason for this is simply that the effectiveness of a recursion clause depends on its being available after application, something that is usually assured by contraction. This paper presents a way of overcoming this problem within (...)
    Download  
     
    Export citation  
     
    Bookmark   36 citations  
  • (1 other version)Universal Logic.Ross Brady - 2007 - Studia Logica 87 (2-3):359-362.
    Download  
     
    Export citation  
     
    Bookmark   48 citations  
  • Relevant Logic: A Philosophical Interpretation.Edwin Mares - 2004 - New York: Cambridge University Press.
    This book introduces the reader to relevant logic and provides the subject with a philosophical interpretation. The defining feature of relevant logic is that it forces the premises of an argument to be really used in deriving its conclusion. The logic is placed in the context of possible world semantics and situation semantics, which are then applied to provide an understanding of the various logical particles and natural language conditionals. The book ends by examining various applications of relevant logic and (...)
    Download  
     
    Export citation  
     
    Bookmark   110 citations  
  • (1 other version)Exploring Meinong's Jungle and Beyond.Richard Routley - 1983 - Journal of Philosophy 80 (3):173-179.
    Download  
     
    Export citation  
     
    Bookmark   138 citations  
  • (3 other versions)Symbolic Logic.C. I. Lewis & C. H. Langford - 1932 - Erkenntnis 4 (1):65-66.
    Download  
     
    Export citation  
     
    Bookmark   226 citations  
  • The Inconsistency of Certain Formal Logics.Alonzo Church & Haskell B. Curry - 1942 - Journal of Symbolic Logic 7 (4):170.
    Download  
     
    Export citation  
     
    Bookmark   57 citations  
  • The impossibility of certain higher-order non-classical logics with extensionality.J. Michael Dunn - 1988 - In D. F. Austin (ed.), Philosophical Analysis. Kluwer Academic Publishers. pp. 261--279.
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  • The non-triviality of dialectical set theory.Ross T. Brady - 1989 - In Graham Priest, Richard Routley & Jean Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent. Philosophia Verlag. pp. 437--470.
    Download  
     
    Export citation  
     
    Bookmark   54 citations  
  • (1 other version)Dialectical logic, classical logic, and the consistency of the world.Richard Routley & Robert K. Meyer - 1976 - Studies in Soviet Thought 16 (1-2):1-25.
    Download  
     
    Export citation  
     
    Bookmark   49 citations  
  • Philosophical Analysis.D. F. Austin (ed.) - 1988 - Kluwer Academic Publishers.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • (1 other version)Inconsistent models of arithmetic Part II: the general case.Graham Priest - 2000 - Journal of Symbolic Logic 65 (4):1519-1529.
    The paper establishes the general structure of the inconsistent models of arithmetic of [7]. It is shown that such models are constituted by a sequence of nuclei. The nuclei fall into three segments: the first contains improper nuclei: the second contains proper nuclei with linear chromosomes: the third contains proper nuclei with cyclical chromosomes. The nuclei have periods which are inherited up the ordering. It is also shown that the improper nuclei can have the order type of any ordinal, of (...)
    Download  
     
    Export citation  
     
    Bookmark   15 citations  
  • Extensionality and Restriction in Naive Set Theory.Zach Weber - 2010 - Studia Logica 94 (1):87-104.
    The naive set theory problem is to begin with a full comprehension axiom, and to find a logic strong enough to prove theorems, but weak enough not to prove everything. This paper considers the sub-problem of expressing extensional identity and the subset relation in paraconsistent, relevant solutions, in light of a recent proposal from Beall, Brady, Hazen, Priest and Restall [4]. The main result is that the proposal, in the context of an independently motivated formalization of naive set theory, leads (...)
    Download  
     
    Export citation  
     
    Bookmark   24 citations  
  • Curry’s Paradox.Robert K. Meyer, Richard Routley & J. Michael Dunn - 1979 - Analysis 39 (3):124 - 128.
    Download  
     
    Export citation  
     
    Bookmark   68 citations  
  • Relevant Restricted Quantification.J. C. Beall, Ross T. Brady, A. P. Hazen, Graham Priest & Greg Restall - 2006 - Journal of Philosophical Logic 35 (6):587-598.
    The paper reviews a number of approaches for handling restricted quantification in relevant logic, and proposes a novel one. This proceeds by introducing a novel kind of enthymematic conditional.
    Download  
     
    Export citation  
     
    Bookmark   40 citations  
  • Russell's set versus the universal set in paraconsistent set theory.A. I. Arruda - 1982 - Logique Et Analyse 25 (98):121.
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • (1 other version)Exploring Meinong's Jungle and Beyond.Richard Routley - 1984 - Philosophy and Phenomenological Research 44 (4):539-552.
    Download  
     
    Export citation  
     
    Bookmark   121 citations  
  • Models for a paraconsistent set theory.Thierry Libert - 2005 - Journal of Applied Logic 3 (1):15-41.
    Download  
     
    Export citation  
     
    Bookmark   25 citations