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  1. Church‐Rosser Property for Some Extensions of λβ‐Reducibility Relation.Andrei A. Kuzichev - 1991 - Mathematical Logic Quarterly 37 (33-35):547-559.
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  • (1 other version)Effectivizing Inseparability.John Case - 1991 - Mathematical Logic Quarterly 37 (7):97-111.
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  • Troubles with (the concept of) truth in mathematics.Roman Murawski - 2006 - Logic and Logical Philosophy 15 (4):285-303.
    In the paper the problem of definability and undefinability of the concept of satisfaction and truth is considered. Connections between satisfaction and truth on the one hand and consistency of certain systems of omega-logic and transfinite induction on the other are indicated.
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  • (2 other versions)Logic TK: Algebraic Notions from Tarski’s Consequence Operator.Hércules A. Feitosa, Mauri C. Do Nascimento & Maria Claudia C. Grácio - 2010 - Principia: An International Journal of Epistemology 14 (1):47-70.
    Tarski apresentou sua definição de operador de consequência com a intenção de expor as concepções fundamentais da consequência lógica. Um espaço de Tarski é um par ordenado determinado por um conjunto não vazio e um operador de consequência sobre este conjunto. Esta estrutura matemática caracteriza um espaço quase topológico. Este artigo mostra uma visão algébrica dos espaços de Tarski e introduz uma lógica proposicional modal que interpreta o seu operador modal nos conjuntos fechados de algum espaço de Tarski. DOI:10.5007/1808-1711.2010v14n1p47.
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  • Induction and inference to the best explanation.Ruth Weintraub - 2013 - Philosophical Studies 166 (1):203-216.
    In this paper I adduce a new argument in support of the claim that IBE is an autonomous form of inference, based on a familiar, yet surprisingly, under-discussed, problem for Hume’s theory of induction. I then use some insights thereby gleaned to argue for the claim that induction is really IBE, and draw some normative conclusions.
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  • (1 other version)Drawing dichotomies via formal languages.Charles G. Morgan - 1973 - Southern Journal of Philosophy 11 (3):216-227.
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  • Gödel, Tarski, Church, and the Liar.György Serény - 2003 - Bulletin of Symbolic Logic 9 (1):3-25.
    The fact that Gödel's famous incompleteness theorem and the archetype of all logical paradoxes, that of the Liar, are related closely is, of course, not only well known, but is a part of the common knowledge of the community of logicians. Indeed, almost every more or less formal treatment of the theorem makes a reference to this connection. Gödel himself remarked in the paper announcing his celebrated result :The analogy between this result and Richard's antinomy leaps to the eye;there is (...)
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  • Formalized Token Models and Duality in Semantics: An Algebraic Approach.Lars Hansen - 2004 - Journal of Symbolic Logic 69 (2):443 - 477.
    Employing the theory of Birkhoff polarities as a model of model theory yields an inductively defined dual structure which is a formalization of semantics and which allows for simple proofs of some new results for model theory.
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  • Naturalness, intrinsicality, and duplication.Theodore R. Sider - 1993 - Dissertation, University of Massachusetts
    This dissertation explores the concepts of naturalness, intrinsicality, and duplication. An intrinsic property is had by an object purely in virtue of the way that object is considered in itself. Duplicate objects are exactly similar, considered as they are in themselves. The perfectly natural properties are the most fundamental properties of the world, upon which the nature of the world depends. In this dissertation I develop a theory of intrinsicality, naturalness, and duplication and explore their philosophical applications. Chapter 1 introduces (...)
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  • Logika a logiky.Jaroslav Peregrin - manuscript
    Kniha, jako je tato, nemůže být tak docela dílem jediného člověka. Dovést ji do podoby koherentního celku bych nedokázal bez pomoci svých kolegů, kteří po mně text četli a upozornili mě na spoustu chyb a nedůsledností, které se v něm vyskytovaly. Můj dík v tomto směru patří zejména Vojtěchu Kolmanovi, Liboru Běhounkovi a Martě Bílkové. Za připomínky k různým částem rukopisu jsem vděčen i Pavlu Maternovi, Milanu Matouškovi, Prokopu Sousedíkovi, Vladimíru Svobodovi, Petru Hájkovi a Grahamu Priestovi. Kniha vznikla v rámci (...)
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  • Boolos on the justification of set theory.Alexander Paseau - 2007 - Philosophia Mathematica 15 (1):30-53.
    George Boolos has argued that the iterative conception of set justifies most, but not all, the ZFC axioms, and that a second conception of set, the Frege-von Neumann conception (FN), justifies the remaining axioms. This article challenges Boolos's claim that FN does better than the iterative conception at justifying the axioms in question.
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  • On Gödel Sentences and What They Say.Peter Milne - 2007 - Philosophia Mathematica 15 (2):193-226.
    Proofs of Gödel's First Incompleteness Theorem are often accompanied by claims such as that the gödel sentence constructed in the course of the proof says of itself that it is unprovable and that it is true. The validity of such claims depends closely on how the sentence is constructed. Only by tightly constraining the means of construction can one obtain gödel sentences of which it is correct, without further ado, to say that they say of themselves that they are unprovable (...)
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  • In defense of the simplest quantified modal logic.Bernard Linsky & Edward N. Zalta - 1994 - Philosophical Perspectives 8:431-458.
    The simplest quantified modal logic combines classical quantification theory with the propositional modal logic K. The models of simple QML relativize predication to possible worlds and treat the quantifier as ranging over a single fixed domain of objects. But this simple QML has features that are objectionable to actualists. By contrast, Kripke-models, with their varying domains and restricted quantifiers, seem to eliminate these features. But in fact, Kripke-models also have features to which actualists object. Though these philosophers have introduced variations (...)
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  • (1 other version)Redundancies in the Hilbert-Bernays derivability conditions for gödel's second incompleteness theorem.R. G. Jeroslow - 1973 - Journal of Symbolic Logic 38 (3):359-367.
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  • Simplifications of the recursion scheme.M. D. Gladstone - 1971 - Journal of Symbolic Logic 36 (4):653-665.
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  • On Vidal's trivalent explanations for defective conditional in mathematics.Yaroslav Petrukhin & Vasily Shangin - 2019 - Journal of Applied Non-Classical Logics 29 (1):64-77.
    ABSTRACTThe paper deals with a problem posed by Mathieu Vidal to provide a formal representation for defective conditional in mathematics Vidal, M. [. The defective conditional in mathematics. Journal of Applied Non-Classical Logics, 24, 169–179]. The key feature of defective conditional is that its truth-value is indeterminate if its antecedent is false. In particular, we are interested in two explanations given by Vidal with the use of trivalent logics. By analysing a simple argument from plane geometry, where defective conditional is (...)
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  • Enciclopédia de Termos Lógico-Filosóficos.João Miguel Biscaia Branquinho, Desidério Murcho & Nelson Gonçalves Gomes (eds.) - 2006 - São Paulo, SP, Brasil: Martins Fontes.
    Esta enciclopédia abrange, de uma forma introdutória mas desejavelmente rigorosa, uma diversidade de conceitos, temas, problemas, argumentos e teorias localizados numa área relativamente recente de estudos, os quais tem sido habitual qualificar como «estudos lógico-filosóficos». De uma forma apropriadamente genérica, e apesar de o território teórico abrangido ser extenso e de contornos por vezes difusos, podemos dizer que na área se investiga um conjunto de questões fundamentais acerca da natureza da linguagem, da mente, da cognição e do raciocínio humanos, bem (...)
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  • The Logical Contingency of Identity.Hanoch Ben-Yami - 2018 - European Journal of Analytic Philosophy 14 (2):5-10.
    I show that intuitive and logical considerations do not justify introducing Leibniz’s Law of the Indiscernibility of Identicals in more than a limited form, as applying to atomic formulas. Once this is accepted, it follows that Leibniz’s Law generalises to all formulas of the first-order Predicate Calculus but not to modal formulas. Among other things, identity turns out to be logically contingent.
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  • The Methodological Roles of Tolerance and Conventionalism in the Philosophy of Mathematics: Reconsidering Carnap's Logic of Science.Emerson P. Doyle - 2014 - Dissertation, University of Western Ontario
    This dissertation makes two primary contributions. The first three chapters develop an interpretation of Carnap's Meta-Philosophical Program which places stress upon his methodological analysis of the sciences over and above the Principle of Tolerance. Most importantly, I suggest, is that Carnap sees philosophy as contiguous with science—as a part of the scientific enterprise—so utilizing the very same methods and subject to the same limitations. I argue that the methodological reforms he suggests for philosophy amount to philosophy as the explication of (...)
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  • On Berry's paradox and nondiagonal constructions.Dev K. Roy - 1999 - Complexity 4 (3):35-38.
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  • (1 other version)Godel's theorem and mechanism.David Coder - 1969 - Philosophy 44 (September):234-7.
    In “Minds, Machines, and Gödel”, J. R. Lucas claims that Goedel's incompleteness theorem constitutes a proof “that Mechanism is false, that is, that minds cannot be explained as machines”. He claims further that “if the proof of the falsity of mechanism is valid, it is of the greatest consequence for the whole of philosophy”. It seems to me that both of these claims are exaggerated. It is true that no minds can be explained as machines. But it is not true (...)
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  • Collective Choice and Social Welfare: Economics Imperialism in Action and Inaction.Ben Fine - 2018 - Ethics and Social Welfare 12 (4):393-399.
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  • Strong Normalization via Natural Ordinal.Daniel Durante Pereira Alves - 1999 - Dissertation,
    The main objective of this PhD Thesis is to present a method of obtaining strong normalization via natural ordinal, which is applicable to natural deduction systems and typed lambda calculus. The method includes (a) the definition of a numerical assignment that associates each derivation (or lambda term) to a natural number and (b) the proof that this assignment decreases with reductions of maximal formulas (or redex). Besides, because the numerical assignment used coincide with the length of a specific sequence of (...)
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  • A Neighbourhood Semantics for the Logic TK.Cezar A. Mortari & Hércules de Araújo Feitosa - 2011 - Principia: An International Journal of Epistemology 15 (2):287.
    The logic TK was introduced as a propositional logic extending the classical propositional calculus with a new unary operator which interprets some conceptions of Tarski’s consequence operator. TK-algebras were introduced as models to TK . Thus, by using algebraic tools, the adequacy (soundness and completeness) of TK relatively to the TK-algebras was proved. This work presents a neighbourhood semantics for TK , which turns out to be deductively equivalent to the non-normal modal logic EMT4 . DOI:10.5007/1808-1711.2011v15n2p287.
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  • Mathematical Knowledge and Pattern Cognition.Michael D. Resnik - 1975 - Canadian Journal of Philosophy 5 (1):25 - 39.
    This paper is concerned with the genesis of mathematical knowledge. While some philosophers might argue that mathematics has no real subject matter and thus is not a body of knowledge, I will not try to dissuade them directly. I shall not attempt such a refutation because it seems clear to me that mathematicians do know such things as the Mean Value Theorem, The Fundamental Theorem of Arithmetic, Godel's Theorems, etc. Moreover, this is much more evident to me than any philosophical (...)
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  • What is Mathematics: Gödel's Theorem and Around (Edition 2015).Karlis Podnieks - manuscript
    Introduction to mathematical logic. Part 2.Textbook for students in mathematical logic and foundations of mathematics. Platonism, Intuition, Formalism. Axiomatic set theory. Around the Continuum Problem. Axiom of Determinacy. Large Cardinal Axioms. Ackermann's Set Theory. First order arithmetic. Hilbert's 10th problem. Incompleteness theorems. Consequences. Connected results: double incompleteness theorem, unsolvability of reasoning, theorem on the size of proofs, diophantine incompleteness, Loeb's theorem, consistent universal statements are provable, Berry's paradox, incompleteness and Chaitin's theorem. Around Ramsey's theorem.
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  • Issues in the philosophy of logic: an unorthodox approach.Guillermo E. Rosado Haddock - 2007 - Principia: An International Journal of Epistemology 11 (1):25-44.
    In this paper six of the most important issues in the philosophy of logic are examined from a standpoint that rejects the First Commandment of empiricist analytic philosophy, namely, Ockham’s razor. Such a standpoint opens the door to the clarification of such fundamental issues and to possible new solutions to each of them.
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  • (1 other version)Algebraic Semantics for Modal Predicate Logic.James B. Freeman - 1976 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 22 (1):523-552.
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  • How do We Know that the Godel Sentence of a Consistent Theory Is True?G. Sereny - 2011 - Philosophia Mathematica 19 (1):47-73.
    Some earlier remarks Michael Dummett made on Gödel’s theorem have recently inspired attempts to formulate an alternative to the standard demonstration of the truth of the Gödel sentence. The idea underlying the non-standard approach is to treat the Gödel sentence as an ordinary arithmetical one. But the Gödel sentence is of a very specific nature. Consequently, the non-standard arguments are conceptually mistaken. In this paper, both the faulty arguments themselves and the general reasons underlying their failure are analysed. The analysis (...)
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  • On a problem of MacDowell and Specker.Mark Nadel - 1980 - Journal of Symbolic Logic 45 (3):612-622.
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  • Epistemic optimism.Mihai Ganea - 2008 - Philosophia Mathematica 16 (3):333-353.
    Michael Dummett's argument for intuitionism can be criticized for the implicit reliance on the existence of what might be called absolutely undecidable statements. Neil Tennant attacks epistemic optimism, the view that there are no such statements. I expose what seem serious flaws in his attack, and I suggest a way of defending the use of classical logic in arithmetic that circumvents the issue of optimism. I would like to thank an anonymous referee for helpful comments. CiteULike Connotea Del.icio.us What's this?
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  • A universal approach to self-referential paradoxes, incompleteness and fixed points.Noson S. Yanofsky - 2003 - Bulletin of Symbolic Logic 9 (3):362-386.
    Following F. William Lawvere, we show that many self-referential paradoxes, incompleteness theorems and fixed point theorems fall out of the same simple scheme. We demonstrate these similarities by showing how this simple scheme encompasses the semantic paradoxes, and how they arise as diagonal arguments and fixed point theorems in logic, computability theory, complexity theory and formal language theory.
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  • (1 other version)Quantified modal logic with neighborhood semantics.Geir Waagbø & G. Waagbø - 1992 - Mathematical Logic Quarterly 38 (1):491-499.
    The paper presents a semantics for quantified modal logic which has a weaker axiomatization than the usual Kripke semantics. In particular, the Barcan Formula and its converse are not valid with the proposed semantics. Subclasses of models which validate BF and other interesting formulas are presented. A completeness theorem is proved, and the relation between this result and completeness with respect to Kripke models is investigated.
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  • Notions of sameness by default and their application to anaphora, vagueness, and uncertain reasoning.Ariel Cohen, Michael Kaminski & Johann A. Makowsky - 2008 - Journal of Logic, Language and Information 17 (3):285-306.
    We motivate and formalize the idea of sameness by default: two objects are considered the same if they cannot be proved to be different. This idea turns out to be useful for a number of widely different applications, including natural language processing, reasoning with incomplete information, and even philosophical paradoxes. We consider two formalizations of this notion, both of which are based on Reiter’s Default Logic. The first formalization is a new relation of indistinguishability that is introduced by default. We (...)
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  • (1 other version)A Theory of Ambiguous Types and Its Axiomatizations.Andrey A. Kuzichev - 1989 - Mathematical Logic Quarterly 35 (6):495-514.
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  • Boolean sentence algebras: Isomorphism constructions.William P. Hanf & Dale Myers - 1983 - Journal of Symbolic Logic 48 (2):329-338.
    Associated with each first-order theory is a Boolean algebra of sentences and a Boolean space of models. Homomorphisms between the sentence algebras correspond to continuous maps between the model spaces. To what do recursive homomorphisms correspond? We introduce axiomatizable maps as the appropriate dual. For these maps we prove a Cantor-Bernstein theorem. Duality and the Cantor-Bernstein theorem are used to show that the Boolean sentence algebras of any two undecidable languages or of any two functional languages are recursively isomorphic where (...)
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  • (2 other versions)Objetos matemáticos sensibles y objetos Matemáticos inteligibles.Víctor Hugo Chica Pérez, Luis F. Echeverri & Edwin Zarrazola - 2016 - Estudios de Filosofía (Universidad de Antioquia) 54:187-205.
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  • Truth via Satisfaction?Nicholas J. J. Smith - 2017 - In Arazim Pavel & Lávička Tomáš (eds.), The Logica Yearbook 2016. College Publications. pp. 273-287.
    One of Tarski’s stated aims was to give an explication of the classical conception of truth—truth as ‘saying it how it is’. Many subsequent commentators have felt that he achieved this aim. Tarski’s core idea of defining truth via satisfaction has now found its way into standard logic textbooks. This paper looks at such textbook definitions of truth in a model for standard first-order languages and argues that they fail from the point of view of explication of the classical notion (...)
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  • (1 other version)About Nothing.Dale Jacquette - 2013 - Humana Mente 6 (25).
    The possibilities are explored of considering nothing as the intended object of thoughts that are literally about the concept of nothing first, and thereby of nothing. Nothing, on the proposed analysis, turns out to be nothing other than the property of being an intendable object. There are propositions that look to be both true and to be about nothing in the sense of being about the concept and ultimate intended object of what is here formally defined and designated as N-nothing. (...)
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  • Meaning and inference.Jaroslav Peregrin - 2003 - In Timothy Childers & Ondrej Majer (eds.), Logica Yearbook 2002. Filosofia.
    In this paper we first propose an exact definition of the concept of inferential role, and then go on to examine the question whether subscribing to inferentialism necessitates throwing away existing theories of formal semantics, as we know them from logic, or whether these could be somehow accomodated within the inferentialist framework. The conclusion we reach is that it is possible to make an inferentialist sense of even those common semantic theories which are usually considered as incompatible with inferentialism, such (...)
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