Switch to: Citations

Add references

You must login to add references.
  1. How We Learn Mathematical Language.Vann McGee - 1997 - Philosophical Review 106 (1):35-68.
    Mathematical realism is the doctrine that mathematical objects really exist, that mathematical statements are either determinately true or determinately false, and that the accepted mathematical axioms are predominantly true. A realist understanding of set theory has it that when the sentences of the language of set theory are understood in their standard meaning, each sentence has a determinate truth value, so that there is a fact of the matter whether the cardinality of the continuum is א2 or whether there are (...)
    Download  
     
    Export citation  
     
    Bookmark   70 citations  
  • How We Learn Mathematical Language.Vann McGee - 1997 - Philosophical Review 106 (1):35-68.
    Mathematical realism is the doctrine that mathematical objects really exist, that mathematical statements are either determinately true or determinately false, and that the accepted mathematical axioms are predominantly true. A realist understanding of set theory has it that when the sentences of the language of set theory are understood in their standard meaning, each sentence has a determinate truth value, so that there is a fact of the matter whether the cardinality of the continuum is א2 or whether there are (...)
    Download  
     
    Export citation  
     
    Bookmark   31 citations  
  • Metamathematics of Fuzzy Logic.Petr Hajek - 1998 - Kluwer Academic Publishers.
    Download  
     
    Export citation  
     
    Bookmark   61 citations  
  • Saving Truth From Paradox.Hartry Field - 2008 - Oxford University Press.
    A selective background -- Broadly classical approaches -- Paracompleteness -- More on paracomplete solutions -- Paraconsistent dialetheism.
    Download  
     
    Export citation  
     
    Bookmark   223 citations  
  • Two Flavors of Curry’s Paradox.Jc Beall & Julien Murzi - 2013 - Journal of Philosophy 110 (3):143-165.
    In this paper, we distinguish two versions of Curry's paradox: c-Curry, the standard conditional-Curry paradox, and v-Curry, a validity-involving version of Curry's paradox that isn’t automatically solved by solving c-curry. A unified treatment of curry paradox thus calls for a unified treatment of both c-Curry and v-Curry. If, as is often thought, c-Curry paradox is to be solved via non-classical logic, then v-Curry may require a lesson about the structure—indeed, the substructure—of the validity relation itself.
    Download  
     
    Export citation  
     
    Bookmark   56 citations  
  • Vagueness.Timothy Williamson - 1994 - Routledge.
    Vagueness provides the first comprehensive examination of a topic of increasing importance in metaphysics and the philosophy of logic and language. Timothy Williamson traces the history of this philosophical problem from discussions of the heap paradox in classical Greece to modern formal approaches such as fuzzy logic. He illustrates the problems with views which have taken the position that standard logic and formal semantics do not apply to vague language, and defends the controversial realistic view that vagueness is a kind (...)
    Download  
     
    Export citation  
     
    Bookmark   351 citations  
  • Toward a Theory of Second-Order Consequence.Augustín Rayo & Gabriel Uzquiano - 1999 - Notre Dame Journal of Formal Logic 40 (3):315-325.
    There is little doubt that a second-order axiomatization of Zermelo-Fraenkel set theory plus the axiom of choice (ZFC) is desirable. One advantage of such an axiomatization is that it permits us to express the principles underlying the first-order schemata of separation and replacement. Another is its almost-categoricity: M is a model of second-order ZFC if and only if it is isomorphic to a model of the form Vκ, ∈ ∩ (Vκ × Vκ) , for κ a strongly inaccessible ordinal.
    Download  
     
    Export citation  
     
    Bookmark   62 citations  
  • A Completeness Theorem for Unrestricted First- Order Languages.Agustin Rayo & Timothy Williamson - 2003 - In Jc Beall (ed.), Liars and Heaps. Oxford University Press.
    Here is an account of logical consequence inspired by Bolzano and Tarski. Logical validity is a property of arguments. An argument is a pair of a set of interpreted sentences (the premises) and an interpreted sentence (the conclusion). Whether an argument is logically valid depends only on its logical form. The logical form of an argument is fixed by the syntax of its constituent sentences, the meanings of their logical constituents and the syntactic differences between their non-logical constituents, treated as (...)
    Download  
     
    Export citation  
     
    Bookmark   25 citations  
  • The Conditional in Quantum Logic.Gary M. Hardegree - 1974 - Synthese 29 (1-4):63 - 80.
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  • The Permutation Principle in Quantificational Logic.Kit Fine - 1983 - Journal of Philosophical Logic 12 (1):33 - 37.
    Download  
     
    Export citation  
     
    Bookmark   12 citations  
  • Dialetheism, Logical Consequence and Hierarchy.Bruno Whittle - 2004 - Analysis 64 (4):318–326.
    I argue that dialetheists have a problem with the concept of logical consequence. The upshot of this problem is that dialetheists must appeal to a hierarchy of concepts of logical consequence. Since this hierarchy is akin to those invoked by more orthodox resolutions of the semantic paradoxes, its emergence would appear to seriously undermine the dialetheic treatments of these paradoxes. And since these are central to the case for dialetheism, this would represent a significant blow to the position itself.
    Download  
     
    Export citation  
     
    Bookmark   13 citations  
  • On Weak Completeness of Intuitionistic Predicate Logic.G. Kreisel - 1962 - Journal of Symbolic Logic 27 (2):139-158.
    Download  
     
    Export citation  
     
    Bookmark   18 citations  
  • On the Metatheory of Field's `Solving the Paradoxes, Escaping Revenge'.Hannes Leitgeb - 2007 - In J. C. Beall (ed.), Revenge of the Liar: New Essays on the Paradox. Oxford University Press.
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • Indeterminacy, Degree of Belief, and Excluded Middle.Hartry Field - 2000 - Noûs 34 (1):1–30.
    Download  
     
    Export citation  
     
    Bookmark   47 citations  
  • Ultimate Truth Vis- À- Vis Stable Truth.P. D. Welch - 2008 - Review of Symbolic Logic 1 (1):126-142.
    We show that the set of ultimately true sentences in Hartry Field's Revenge-immune solution model to the semantic paradoxes is recursively isomorphic to the set of stably true sentences obtained in Hans Herzberger's revision sequence starting from the null hypothesis. We further remark that this shows that a substantial subsystem of second-order number theory is needed to establish the semantic values of sentences in Field's relative consistency proof of his theory over the ground model of the standard natural numbers: -CA0 (...)
    Download  
     
    Export citation  
     
    Bookmark   24 citations  
  • On Theorems of Gödel and Kreisel: Completeness and Markov's Principle.D. C. McCarty - 1994 - Notre Dame Journal of Formal Logic 35 (1):99-107.
    In 1957, Gödel proved that completeness for intuitionistic predicate logic HPL implies forms of Markov's Principle, MP. The result first appeared, with Kreisel's refinements and elaborations, in Kreisel. Featuring large in the Gödel-Kreisel proofs are applications of the axiom of dependent choice, DC. Also in play is a form of Herbrand's Theorem, one allowing a reduction of HPL derivations for negated prenex formulae to derivations of negations of conjunctions of suitable instances. First, we here show how to deduce Gödel's results (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Sorites Paradoxes and the Semantics of Vagueness.Michael Tye - 1994 - Philosophical Perspectives 8:189-206.
    Download  
     
    Export citation  
     
    Bookmark   53 citations  
  • Metamathematics of Fuzzy Logic.P. Hájek - 2002 - Studia Logica 72 (3):433-437.
    Download  
     
    Export citation  
     
    Bookmark   57 citations  
  • Review: John Etchemendy, The Concept of Logical Consequence. [REVIEW]Vann McGee - 2001 - Bulletin of Symbolic Logic 7 (3):379-380.
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • Incompleteness in Intuitionistic Metamathematics.David Charles McCarty - 1991 - Notre Dame Journal of Formal Logic 32 (3):323-358.
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • Informal Rigour and Completeness Proofs.Georg Kreisel - 1967 - In Imre Lakatos (ed.), Problems in the Philosophy of Mathematics. North-Holland. pp. 138--157.
    Download  
     
    Export citation  
     
    Bookmark   131 citations  
  • Syntactical Treatments of Modality, with Corollaries on Reflexion Principles and Finite Axiomatizability.Richard Montague - 1975 - Journal of Symbolic Logic 40 (4):600-601.
    Download  
     
    Export citation  
     
    Bookmark   46 citations  
  • .Timothy Williamson - 2006
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark   460 citations  
  • Solving the Paradoxes, Escaping Revenge.Hartry Field - 2007 - In J. C. Beall (ed.), Revenge of the Liar: New Essays on the Paradox. Oxford University Press.
    It is “the received wisdom” that any intuitively natural and consistent resolution of a class of semantic paradoxes immediately leads to other paradoxes just as bad as the first. This is often called the “revenge problem”. Some proponents of the received wisdom draw the conclusion that there is no hope of any natural treatment that puts all the paradoxes to rest: we must either live with the existence of paradoxes that we are unable to treat, or adopt artificial and ad (...)
    Download  
     
    Export citation  
     
    Bookmark   22 citations