Switch to: Citations

Add references

You must login to add references.
  1. Set theory and the continuum problem.Raymond Smullyan - 1996 - Clarendon Press.
    A lucid, elegant, and complete survey of set theory, this three-part treatment explores axiomatic set theory, the consistency of the continuum hypothesis, and forcing and independence results. 1996 edition.
    Download  
     
    Export citation  
     
    Bookmark   10 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  
  • 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  
  • (3 other versions)Our knowledge of mathematical objects.Kit Fine - 2005 - In Tamar Szabó Gendler & John Hawthorne (eds.), Oxford Studies in Epistemology. Oxford University Press. pp. 89-109.
    Download  
     
    Export citation  
     
    Bookmark   51 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  
  • (1 other version)Towards non-being: the logic and metaphysics of intentionality.Graham Priest - 2005 - New York: Oxford University Press.
    Graham Priest presents a ground-breaking account of the semantics of intentional language--verbs such as "believes," "fears," "seeks," or "imagines." Towards Non-Being proceeds in terms of objects that may be either existent or non-existent, at worlds that may be either possible or impossible. The book will be of central interest to anyone who is concerned with intentionality in the philosophy of mind or philosophy of language, the metaphysics of existence and identity, the philosophy of fiction, the philosophy of mathematics, or cognitive (...)
    Download  
     
    Export citation  
     
    Bookmark   161 citations  
  • Set Theory and its Philosophy: A Critical Introduction.Michael D. Potter - 2004 - Oxford, England: Oxford University Press.
    Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set (...)
    Download  
     
    Export citation  
     
    Bookmark   88 citations  
  • Relatively Unrestricted Quantification.Kit Fine - 2006 - In Agustín Rayo & Gabriel Uzquiano (eds.), Absolute generality. New York: Oxford University Press. pp. 20-44.
    There are four broad grounds upon which the intelligibility of quantification over absolutely everything has been questioned—one based upon the existence of semantic indeterminacy, another on the relativity of ontology to a conceptual scheme, a third upon the necessity of sortal restriction, and the last upon the possibility of indefinite extendibility. The argument from semantic indeterminacy derives from general philosophical considerations concerning our understanding of language. For the Skolem–Lowenheim Theorem appears to show that an understanding of quanti- fication over absolutely (...)
    Download  
     
    Export citation  
     
    Bookmark   86 citations  
  • The logic of paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
    Download  
     
    Export citation  
     
    Bookmark   474 citations  
  • (1 other version)The iterative conception of set.George Boolos - 1971 - Journal of Philosophy 68 (8):215-231.
    Download  
     
    Export citation  
     
    Bookmark   202 citations  
  • (1 other version)Modal set theory.Christopher Menzel - 2018 - In Otávio Bueno & Scott A. Shalkowski (eds.), The Routledge Handbook of Modality. New York: Routledge.
    This article presents an overview of the basic philosophical motivations for, and some recent work in, modal set theory.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • (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  
  • Towards Non-Being: The Logic and Metaphysics of Intentionality.Graham Priest - 2005 - Bulletin of Symbolic Logic 14 (1):116-118.
    Download  
     
    Export citation  
     
    Bookmark   196 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  
  • The potential hierarchy of sets.Øystein Linnebo - 2013 - Review of Symbolic Logic 6 (2):205-228.
    Some reasons to regard the cumulative hierarchy of sets as potential rather than actual are discussed. Motivated by this, a modal set theory is developed which encapsulates this potentialist conception. The resulting theory is equi-interpretable with Zermelo Fraenkel set theory but sheds new light on the set-theoretic paradoxes and the foundations of set theory.
    Download  
     
    Export citation  
     
    Bookmark   103 citations  
  • The Iterative Conception of Set: a (Bi-)Modal Axiomatisation.J. P. Studd - 2013 - Journal of Philosophical Logic 42 (5):1-29.
    The use of tensed language and the metaphor of set ‘formation’ found in informal descriptions of the iterative conception of set are seldom taken at all seriously. Both are eliminated in the nonmodal stage theories that formalise this account. To avoid the paradoxes, such accounts deny the Maximality thesis, the compelling thesis that any sets can form a set. This paper seeks to save the Maximality thesis by taking the tense more seriously than has been customary (although not literally). A (...)
    Download  
     
    Export citation  
     
    Bookmark   41 citations  
  • Paraconsistent Logic: Essays on the Inconsistent.Graham Priest, Richard Routley & Jean Norman (eds.) - 1989 - Philosophia Verlag.
    Download  
     
    Export citation  
     
    Bookmark   105 citations  
  • Sets and modality.C. Parsons - 1983 - In Charles Parsons (ed.), Mathematics in philosophy: selected essays. Ithaca, N.Y.: Cornell University Press. pp. 298--341.
    Download  
     
    Export citation  
     
    Bookmark   26 citations  
  • Ultralogic as Universal?: The Sylvan Jungle -.Richard Routley - 2019 - Springer Verlag.
    Ultralogic as Universal? is a seminal text in non-classcial logic. Richard Routley presents a hugely ambitious program: to use an 'ultramodal' logic as a universal key, which opens, if rightly operated, all locks. It provides a canon for reasoning in every situation, including illogical, inconsistent and paradoxical ones, realized or not, possible or not. A universal logic, Routley argues, enables us to go where no other logic—especially not classical logic—can. Routley provides an expansive and singular vision of how a universal (...)
    Download  
     
    Export citation  
     
    Bookmark   24 citations  
  • (1 other version)Universal Logic.Ross Brady - 2007 - Studia Logica 87 (2-3):359-362.
    Download  
     
    Export citation  
     
    Bookmark   51 citations  
  • The philosophical significance and inevitability of paraconsistency.Graham Priest & Richard Routley - 1989 - In Graham Priest, Richard Routley & Jean Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent. Philosophia Verlag. pp. 483--537.
    Download  
     
    Export citation  
     
    Bookmark   15 citations  
  • Non-Well-Founded Sets.Peter Aczel - 1988 - Palo Alto, CA, USA: Csli Lecture Notes.
    Download  
     
    Export citation  
     
    Bookmark   140 citations  
  • Set Theory and Its Philosophy: A Critical Introduction.Stewart Shapiro - 2005 - Mind 114 (455):764-767.
    Download  
     
    Export citation  
     
    Bookmark   24 citations  
  • (2 other versions)First-order modal theories I--sets.Kit Fine - 1981 - Noûs 15 (2):177-205.
    Download  
     
    Export citation  
     
    Bookmark   32 citations  
  • (1 other version)Universal Logic.Ross Brady - 2006 - Bulletin of Symbolic Logic 13 (4):544-547.
    Download  
     
    Export citation  
     
    Bookmark   60 citations  
  • (3 other versions)Our Knowledge of Mathematical Objects.Kit Fine - 2005 - In Tamar Szabo Gendler & John Hawthorne (eds.), Oxford Studies in Epistemology Volume 1. Oxford University Press UK.
    Download  
     
    Export citation  
     
    Bookmark   30 citations  
  • Non-Well-founded Sets.J. L. Bell - 1989 - Journal of Symbolic Logic 54 (3):1111-1112.
    Download  
     
    Export citation  
     
    Bookmark   48 citations  
  • (3 other versions)Our Knowledge of Mathematical Objects.Kit Fine - 2006 - Oxford Studies in Epistemology 1.
    Download  
     
    Export citation  
     
    Bookmark   37 citations