Switch to: References

Add citations

You must login to add citations.
  1. Ask not what bilateralist intuitionists can do for Cut, but what Cut can do for bilateralist intuitionism.Bogdan Dicher - forthcoming - Analysis.
    On a bilateralist reading, sequents are interpreted as statements to the effect that, given the assertion of the antecedent it is incoherent to deny the succedent. This interpretation goes against its own ecumenical ambitions, endowing Cut with a meaning very close to that of tertium non datur and thus rendering it intuitionistically unpalatable. This paper explores a top-down route for arguing that, even intuitionistically, a prohibition to deny is as strong as a licence to assert.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Who were the American Postulate Theorists?Michael Scanlan - 1991 - Journal of Symbolic Logic 56 (3):981-1002.
    Articles by two American mathematicians, E. V. Huntington and Oswald Veblen, are discussed as examples of a movement in foundational research in the period 1900-1930 called American postulate theory. This movement also included E. H. Moore, R. L. Moore, C. H. Langford, H. M. Sheffer, C. J. Keyser, and others. The articles discussed exemplify American postulate theorists' standards for axiomatizations of mathematical theories, and their investigations of such axiomatizations with respect to metatheoretic properties such as independence, completeness, and consistency.
    Download  
     
    Export citation  
     
    Bookmark   41 citations  
  • Zermelo and set theory.Akihiro Kanamori - 2004 - Bulletin of Symbolic Logic 10 (4):487-553.
    Ernst Friedrich Ferdinand Zermelo transformed the set theory of Cantor and Dedekind in the first decade of the 20th century by incorporating the Axiom of Choice and providing a simple and workable axiomatization setting out generative set-existence principles. Zermelo thereby tempered the ontological thrust of early set theory, initiated the delineation of what is to be regarded as set-theoretic, drawing out the combinatorial aspects from the logical, and established the basic conceptual framework for the development of modern set theory. Two (...)
    Download  
     
    Export citation  
     
    Bookmark   11 citations  
  • Nonmonotonic reasoning: From finitary relations to infinitary inference operations.Michael Freund & Daniel Lehmann - 1994 - Studia Logica 53 (2):161 - 201.
    A. Tarski [22] proposed the study of infinitary consequence operations as the central topic of mathematical logic. He considered monotonicity to be a property of all such operations. In this paper, we weaken the monotonicity requirement and consider more general operations, inference operations. These operations describe the nonmonotonic logics both humans and machines seem to be using when infering defeasible information from incomplete knowledge. We single out a number of interesting families of inference operations. This study of infinitary inference operations (...)
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  • Existential-Import Mathematics.John Corcoran & Hassan Masoud - 2015 - Bulletin of Symbolic Logic 21 (1):1-14.
    First-order logic haslimitedexistential import: the universalized conditional ∀x[S(x) → P(x)] implies its corresponding existentialized conjunction ∃x[S(x) & P(x)] insome but not allcases. We prove theExistential-Import Equivalence:∀x[S(x) → P(x)] implies ∃x[S(x) & P(x)] iff ∃xS(x) is logically true.The antecedent S(x) of the universalized conditional alone determines whether the universalized conditionalhas existential import: implies its corresponding existentialized conjunction.Apredicateis a formula having onlyxfree. Anexistential-importpredicate Q(x) is one whose existentialization, ∃xQ(x), is logically true; otherwise, Q(x) isexistential-import-freeor simplyimport-free. Existential-import predicates are also said to beimport-carrying.How (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Address at the Princeton University Bicentennial Conference on Problems of Mathematics (December 17–19, 1946), By Alfred Tarski. [REVIEW]Alfred Tarski & Hourya Sinaceur - 2000 - Bulletin of Symbolic Logic 6 (1):1-44.
    This article presents Tarski's Address at the Princeton Bicentennial Conference on Problems of Mathematics, together with a separate summary. Two accounts of the discussion which followed are also included. The central topic of the Address and of the discussion is decision problems. The introductory note gives information about the Conference, about the background of the subjects discussed in the Address, and about subsequent developments to these subjects.
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Philosophy in Poland: Varieties of Anti-Irrationalism. A Commitment to Reason without the Worship of Reason.Konrad Werner - 2020 - Philosophia 48 (1):1-32.
    I shall elaborate more on the idea of anti-irrationalism proposed by the Polish analytic philosopher Kazimierz Ajdukiewicz, a prominent member of the Lvov-Warsaw School of philosophy and logic. In my reading, anti-irrationalism stands in opposition not only to overt irrationalism, which is made clear by the term itself, but also to all forms of rationalism that tip toward something like worship of reason. Having characterized anti-irrationalism as it originally appeared in Ajdukiewicz’s works, I shall propose a certain reformulation of it, (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Embracing the technicalities: Expressive completeness and revenge.Nicholas Tourville & Roy T. Cook - 2016 - Review of Symbolic Logic 9 (2):325-358.
    The Revenge Problem threatens every approach to the semantic paradoxes that proceeds by introducing nonclassical semantic values. Given any such collection Δ of additional semantic values, one can construct a Revenge sentence:This sentence is either false or has a value in Δ.TheEmbracing Revengeview, developed independently by Roy T. Cook and Phlippe Schlenker, addresses this problem by suggesting that the class of nonclassical semantic values is indefinitely extensible, with each successive Revenge sentence introducing a new ‘pathological’ semantic value into the discourse. (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Tarski's system of geometry.Alfred Tarski & Steven Givant - 1999 - Bulletin of Symbolic Logic 5 (2):175-214.
    This paper is an edited form of a letter written by the two authors (in the name of Tarski) to Wolfram Schwabhäuser around 1978. It contains extended remarks about Tarski's system of foundations for Euclidean geometry, in particular its distinctive features, its historical evolution, the history of specific axioms, the questions of independence of axioms and primitive notions, and versions of the system suitable for the development of 1-dimensional geometry.
    Download  
     
    Export citation  
     
    Bookmark   44 citations  
  • Post completeness in modal logic.Krister Segerberg - 1972 - Journal of Symbolic Logic 37 (4):711-715.
    Download  
     
    Export citation  
     
    Bookmark   14 citations  
  • The Naïve Conception of Properties.Benjamin Schnieder - 2017 - Philosophical Issues 27 (1):322-342.
    The semantic rules that govern ordinary property discourse appear to give rise to a version of Russell's antinomy. Do we therefore have an inconsistent conception of properties? This paper firstly develops a consistent conception of properties and secondly argues that we may indeed interpret ordinary property discourse as expressing the consistent conception rather than an inconsistent one.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Truth and Meaning.Ian Rumfitt - 2014 - Aristotelian Society Supplementary Volume 88 (1):21-55.
    Download  
     
    Export citation  
     
    Bookmark   17 citations  
  • Undefinability of truth. the problem of priority:tarski vs gödel.Roman Murawski - 1998 - History and Philosophy of Logic 19 (3):153-160.
    The paper is devoted to the discussion of some philosophical and historical problems connected with the theorem on the undefinability of the notion of truth. In particular the problem of the priority of proving this theorem will be considered. It is claimed that Tarski obtained this theorem independently though he made clear his indebtedness to Gödel’s methods. On the other hand, Gödel was aware of the formal undefinability of truth in 1931, but he did not publish this result. Reasons for (...)
    Download  
     
    Export citation  
     
    Bookmark   17 citations  
  • Quick and Easy Recipes for Hypergunk.Patrick Reeder - 2020 - Australasian Journal of Philosophy 98 (1):178-191.
    I argue for the possibility of hypergunk: that is, it is possible that there exists an x such that every part of x has a proper part and, for any set S of parts of x, there is a set S′ of parts of...
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • On Why Mathematics Can Not be Ontology.Shiva Rahman - 2019 - Axiomathes 29 (3):289-296.
    The formalism of mathematics has always inspired ontological theorization based on it. As is evident from his magnum opus Being and Event, Alain Badiou remains one of the most important contemporary contributors to this enterprise. His famous maxim—“mathematics is ontology” has its basis in the ingenuity that he has shown in capitalizing on Gödel’s and Cohen’s work in the field of set theory. Their work jointly establish the independence of the continuum hypothesis from the standard axioms of Zermelo–Fraenkel set theory, (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Structured Propositions in a Generative Grammar.Bryan Pickel - 2019 - Mind (510):329-366.
    Semantics in the Montagovian tradition combines two basic tenets. One tenet is that the semantic value of a sentence is an intension, a function from points of evaluations into truth-values. The other tenet is that the semantic value of a composite expression is the result of applying the function denoted by one component to arguments denoted by the other components. Many philosophers object to intensional semantics on the grounds that intensionally equivalent sentences do not substitute salva veritate into attitude ascriptions. (...)
    Download  
     
    Export citation  
     
    Bookmark   17 citations  
  • Generalized Revenge.Julien Murzi & Lorenzo Rossi - 2020 - Australasian Journal of Philosophy 98 (1):153-177.
    Since Saul Kripke’s influential work in the 1970s, the revisionary approach to semantic paradox—the idea that semantic paradoxes must be solved by weakening classical logic—has been increasingly popular. In this paper, we present a new revenge argument to the effect that the main revisionary approaches breed new paradoxes that they are unable to block.
    Download  
     
    Export citation  
     
    Bookmark   24 citations  
  • The work of Kurt gödel.Stephen C. Kleene - 1976 - Journal of Symbolic Logic 41 (4):761-778.
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • II—Hyperintensional Truth Conditions.Gary Kemp - 2014 - Aristotelian Society Supplementary Volume 88 (1):57-68.
    A response to certain parts of Rumfitt : I defend Davidson's project in semantics, suggest that Rumfitt's use of sentential quantification renders his definition of truth needlessly elaborate, and pose a question for Rumfitt's handling of the strengthened Liar.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Dialectical Contradictions and Classical Formal Logic.Inoue Kazumi - 2014 - International Studies in the Philosophy of Science 28 (2):113-132.
    A dialectical contradiction can be appropriately described within the framework of classical formal logic. It is in harmony with the law of noncontradiction. According to our definition, two theories make up a dialectical contradiction if each of them is consistent and their union is inconsistent. It can happen that each of these two theories has an intended model. Plenty of examples are to be found in the history of science.
    Download  
     
    Export citation  
     
    Bookmark  
  • The mathematical development of set theory from Cantor to Cohen.Akihiro Kanamori - 1996 - Bulletin of Symbolic Logic 2 (1):1-71.
    Set theory is an autonomous and sophisticated field of mathematics, enormously successful not only at its continuing development of its historical heritage but also at analyzing mathematical propositions cast in set-theoretic terms and gauging their consistency strength. But set theory is also distinguished by having begun intertwined with pronounced metaphysical attitudes, and these have even been regarded as crucial by some of its great developers. This has encouraged the exaggeration of crises in foundations and of metaphysical doctrines in general. However, (...)
    Download  
     
    Export citation  
     
    Bookmark   19 citations  
  • Complete additivity and modal incompleteness.Wesley H. Holliday & Tadeusz Litak - 2019 - Review of Symbolic Logic 12 (3):487-535.
    In this article, we tell a story about incompleteness in modal logic. The story weaves together an article of van Benthem, “Syntactic aspects of modal incompleteness theorems,” and a longstanding open question: whether every normal modal logic can be characterized by a class of completely additive modal algebras, or as we call them, ${\cal V}$-baos. Using a first-order reformulation of the property of complete additivity, we prove that the modal logic that starred in van Benthem’s article resolves the open question (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • The härtig quantifier: A survey.Heinrich Herre, Michał Krynicki, Alexandr Pinus & Jouko Väänänen - 1991 - Journal of Symbolic Logic 56 (4):1153-1183.
    A fundamental notion in a large part of mathematics is the notion of equicardinality. The language with Hartig quantifier is, roughly speaking, a first-order language in which the notion of equicardinality is expressible. Thus this language, denoted by LI, is in some sense very natural and has in consequence special interest. Properties of LI are studied in many papers. In [BF, Chapter VI] there is a short survey of some known results about LI. We feel that a more extensive exposition (...)
    Download  
     
    Export citation  
     
    Bookmark   11 citations  
  • The Substitutional Analysis of Logical Consequence.Volker Halbach - 2019 - Noûs 54 (2):431-450.
    A substitutional account of logical validity for formal first‐order languages is developed and defended against competing accounts such as the model‐theoretic definition of validity. Roughly, a substitution instance of a sentence is defined as the result of uniformly substituting nonlogical expressions in the sentence with expressions of the same grammatical category and possibly relativizing quantifiers. In particular, predicate symbols can be replaced with formulae possibly containing additional free variables. A sentence is defined to be logically true iff all its substitution (...)
    Download  
     
    Export citation  
     
    Bookmark   10 citations  
  • Carnap’s Defense of Impredicative Definitions.Vera Flocke - 2019 - Review of Symbolic Logic 12 (2):372-404.
    A definition of a property P is impredicative if it quantifies over a domain to which P belongs. Due to influential arguments by Ramsey and Gödel, impredicative mathematics is often thought to possess special metaphysical commitments. It seems that an impredicative definition of a property P does not have the intended meaning unless P already exists, suggesting that the existence of P cannot depend on its explicit definition. Carnap (1937 [1934], p. 164) argues, however, that accepting impredicative definitions amounts to (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Uniqueness, definability and interpolation.Kosta Došen & Peter Schroeder-Heister - 1988 - Journal of Symbolic Logic 53 (2):554-570.
    Download  
     
    Export citation  
     
    Bookmark   10 citations  
  • Deductive completeness.Kosta Došen - 1996 - Bulletin of Symbolic Logic 2 (3):243-283.
    This is an exposition of Lambek's strengthening and generalization of the deduction theorem in categories related to intuitionistic propositional logic. Essential notions of category theory are introduced so as to yield a simple reformulation of Lambek's Functional Completeness Theorem, from which its main consequences can be readily drawn. The connections of the theorem with combinatory logic, and with modal and substructural logics, are briefly considered at the end.
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  • Variations on intra-theoretical logical pluralism: internal versus external consequence.Bogdan Dicher - 2020 - Philosophical Studies 177 (3):667-686.
    Intra-theoretical logical pluralism is a form of meaning-invariant pluralism about logic, articulated recently by Hjortland :355–373, 2013). This version of pluralism relies on it being possible to define several distinct notions of provability relative to the same logical calculus. The present paper picks up and explores this theme: How can a single logical calculus express several different consequence relations? The main hypothesis articulated here is that the divide between the internal and external consequence relations in Gentzen systems generates a form (...)
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  • The original sin of proof-theoretic semantics.Bogdan Dicher & Francesco Paoli - 2020 - Synthese:1-26.
    Proof-theoretic semantics is an alternative to model-theoretic semantics. It aims at explaining the meaning of the logical constants in terms of the inference rules that govern their behaviour in proofs. We argue that this must be construed as the task of explaining these meanings relative to a logic, i.e., to a consequence relation. Alas, there is no agreed set of properties that a relation must have in order to qualify as a consequence relation. Moreover, the association of a consequence relation (...)
    Download  
     
    Export citation  
     
    Bookmark   15 citations  
  • Arithmetical Reflection and the Provability of Soundness.Walter Dean - 2015 - Philosophia Mathematica 23 (1):31-64.
    Proof-theoretic reflection principles are schemas which attempt to express the soundness of arithmetical theories within their own language, e.g., ${\mathtt{{Prov}_{\mathsf {PA}} \rightarrow \varphi }}$ can be understood to assert that any statement provable in Peano arithmetic is true. It has been repeatedly suggested that justification for such principles follows directly from acceptance of an arithmetical theory $\mathsf {T}$ or indirectly in virtue of their derivability in certain truth-theoretic extensions thereof. This paper challenges this consensus by exploring relationships between reflection principles (...)
    Download  
     
    Export citation  
     
    Bookmark   18 citations  
  • Schemata: The concept of schema in the history of logic.John Corcoran - 2006 - Bulletin of Symbolic Logic 12 (2):219-240.
    The syllogistic figures and moods can be taken to be argument schemata as can the rules of the Stoic propositional logic. Sentence schemata have been used in axiomatizations of logic only since the landmark 1927 von Neumann paper [31]. Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski’s 1933 Convention T [42]. Mathematical logicians recognize the role of schemata in first-order number theory where Peano’s second-order Induction Axiom is approximated by Herbrand’s Induction-Axiom (...)
    Download  
     
    Export citation  
     
    Bookmark   16 citations  
  • Kazimierz Ajdukiewicz on transcendental idealism from a semantic point of view.Arkadiusz Chrudzimski - 2016 - Studies in East European Thought 68 (1):63-74.
    In a paper entitled A Semantical Version of the Problem of Transcendental Idealism, Kazimierz Ajdukiewicz gives a very impressive analysis of transcendental idealism. He approaches the matter using the tools of formal semantics developed by Alfred Tarski and draws a rather surprising conclusion. According to Ajdukiewicz, the idealist position, claiming that the world around us is ontologically dependent on our cognitive activity can be shown to be implausible on purely logical grounds. It is worth taking a closer look at this (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • The simple argument for subclassical logic.Jc Beall - 2018 - Philosophical Issues 28 (1):30-54.
    This paper presents a simple but, by my lights, effective argument for a subclassical account of logic—an account according to which logical consequence is (properly) weaker than the standard, so‐called classical account. Alas, the vast bulk of the paper is setup. Because of the many conflicting uses of ‘logic’ the paper begins, following a disclaimer on logic and inference, by fixing the sense of ‘logic’ in question, and then proceeds to rehearse both the target subclassical account of logic and its (...)
    Download  
     
    Export citation  
     
    Bookmark   33 citations  
  • Idealism, Empiricism, Pluralism, Law: Legal truth after modernity.Luke Mason - forthcoming - In Angela Condello & Tiziana Andina (eds.), Post-Truth, Law and Philosophy. Routledge.
    Making a connection between ‘post-modernism’ and post-truth has by now become a standard trope, both within academia and popular discourse, despite post-truth’s only recent emergence as a concept. Such claims are often rather vague and fanciful and lack an altogether credible account of either phenomenon in many cases. This Chapter argues however that within a legal context, there is the emergence of a legal post-truth which is the direct consequence of a concrete form of post-modernity within legal practice and thought. (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Symbolic logic.Greg Restall - unknown
    Symbolic logic is sited at intersection of philosophy, mathematics, linguistics and computer science. It deals with the structure of reasoning, and the formal features of information. Work in symbolic logic has almost exclusively treated the deductive validity of arguments: those arguments for which it is impossible for the premises to be true and the conclusion false. However, techniques from twentieth-century logic have found a place in the study of inductive or probabilistic reasoning, in which premises need not render their conclusions (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Existence Assumptions and Logical Principles: Choice Operators in Intuitionistic Logic.Corey Edward Mulvihill - 2015 - Dissertation, University of Waterloo
    Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program in the (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • An Objection to Naturalism and Atheism from Logic.Christopher Gregory Weaver - 2019 - In Graham Oppy (ed.), Blackwell Companion to Atheism and Philosophy. Malden: Blackwell Publishers. pp. 451-475.
    I proffer a success argument for classical logical consequence. I articulate in what sense that notion of consequence should be regarded as the privileged notion for metaphysical inquiry aimed at uncovering the fundamental nature of the world. Classical logic breeds necessitism. I use necessitism to produce problems for both ontological naturalism and atheism.
    Download  
     
    Export citation  
     
    Bookmark  
  • Truthmakers, Truthbearers and the Objectivity of Truth.Artur Rojszczak & Barry Smith - 2003 - In Jaako Hintikka (ed.), Philosophy and Logic: In Search of the Polish Tradition. Boston: Kluwer. pp. 229-268.
    The aim of this paper is to show that the account of objective truth taken for granted by logicians at least since the publication in 1933 of Tarski’s “The Concept of Truth in Formalized Languages” arose out of a tradition of philosophical thinking initiated by Bolzano and Brentano. The paper shows more specifically that certain investigations of states of affairs and other objectual correlates of judging acts, investigations carried out by Austrian and Polish philosophers around the turn of the century, (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • The Tangled Derivative Logic of the Real Line and Zero-Dimensional Space.Robert Goldblatt & Ian Hodkinson - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 342-361.
    Download  
     
    Export citation  
     
    Bookmark   2 citations