Switch to: References

Citations of:

Categoricity

History and Philosophy of Logic 1 (1):187-207 (1980)

Add citations

You must login to add citations.
  1. Carnap’s Early Semantics.Georg Schiemer - 2013 - Erkenntnis 78 (3):487-522.
    This paper concerns Carnap’s early contributions to formal semantics in his work on general axiomatics between 1928 and 1936. Its main focus is on whether he held a variable domain conception of models. I argue that interpreting Carnap’s account in terms of a fixed domain approach fails to describe his premodern understanding of formal models. By drawing attention to the second part of Carnap’s unpublished manuscript Untersuchungen zur allgemeinen Axiomatik, an alternative interpretation of the notions ‘model’, ‘model extension’ and ‘submodel’ (...)
    Download  
     
    Export citation  
     
    Bookmark   10 citations  
  • Omnipresence, Multipresence and Ubiquity: Kinds of Generality in and Around Mathematics and Logics. [REVIEW]I. Grattan-Guinness - 2011 - Logica Universalis 5 (1):21-73.
    A prized property of theories of all kinds is that of generality, of applicability or least relevance to a wide range of circumstances and situations. The purpose of this article is to present a pair of distinctions that suggest that three kinds of generality are to be found in mathematics and logics, not only at some particular period but especially in developments that take place over time: ‘omnipresent’ and ‘multipresent’ theories, and ‘ubiquitous’ notions that form dependent parts, or moments, of (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Structure and Categoricity: Determinacy of Reference and Truth Value in the Philosophy of Mathematics.Tim Button & Sean Walsh - 2016 - Philosophia Mathematica 24 (3):283-307.
    This article surveys recent literature by Parsons, McGee, Shapiro and others on the significance of categoricity arguments in the philosophy of mathematics. After discussing whether categoricity arguments are sufficient to secure reference to mathematical structures up to isomorphism, we assess what exactly is achieved by recent ‘internal’ renditions of the famous categoricity arguments for arithmetic and set theory.
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  • Information Recovery Problems.John Corcoran - 1995 - Theoria 10 (3):55-78.
    An information recovery problem is the problem of constructing a proposition containing the information dropped in going from a given premise to a given conclusion that folIows. The proposition(s) to beconstructed can be required to satisfy other conditions as well, e.g. being independent of the conclusion, or being “informationally unconnected” with the conclusion, or some other condition dictated by the context. This paper discusses various types of such problems, it presents techniques and principles useful in solving them, and it develops (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Structuralism and Representation Theorems.George Weaver - 1998 - Philosophia Mathematica 6 (3):257-271.
    Much of the inspiration for structuralist approaches to mathematics can be found in the late nineteenth- and early twentieth-century program of characterizing various mathematical systems upto isomorphism. From the perspective of this program, differences between isomorphic systems are irrelevant. It is argued that a different view of the import of the differences between isomorphic systems can be obtained from the perspective of contemporary discussions of representation theorems and that from this perspective both the identification of isomorphic systems and the reduction (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Logical Consequence Revisited.José M. Sagüillo - 1997 - Bulletin of Symbolic Logic 3 (2):216-241.
    Download  
     
    Export citation  
     
    Bookmark   14 citations  
  • Completeness Before Post: Bernays, Hilbert, and the Development of Propositional Logic.Richard Zach - 1999 - Bulletin of Symbolic Logic 5 (3):331-366.
    Some of the most important developments of symbolic logic took place in the 1920s. Foremost among them are the distinction between syntax and semantics and the formulation of questions of completeness and decidability of logical systems. David Hilbert and his students played a very important part in these developments. Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923. The aim of this paper is to describe these results, focussing (...)
    Download  
     
    Export citation  
     
    Bookmark   30 citations  
  • A New–Old Characterisation of Logical Knowledge.Ivor Grattan-Guinness - 2012 - History and Philosophy of Logic 33 (3):245 - 290.
    We seek means of distinguishing logical knowledge from other kinds of knowledge, especially mathematics. The attempt is restricted to classical two-valued logic and assumes that the basic notion in logic is the proposition. First, we explain the distinction between the parts and the moments of a whole, and theories of ?sortal terms?, two theories that will feature prominently. Second, we propose that logic comprises four ?momental sectors?: the propositional and the functional calculi, the calculus of asserted propositions, and rules for (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • A Logical Approach to Philosophy: Essays in Memory of Graham Solomon.David DeVidi & Tim Kenyon (eds.) - 2006 - Dordrecht, Netherland: Springer.
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Carnap, Completeness, and Categoricity:The Gabelbarkeitssatz OF 1928. [REVIEW]S. Awodey & A. W. Carus - 2001 - Erkenntnis 54 (2):145-172.
    In 1929 Carnap gave a paper in Prague on Investigations in General Axiomatics; a briefsummary was published soon after. Its subject lookssomething like early model theory, and the mainresult, called the Gabelbarkeitssatz, appears toclaim that a consistent set of axioms is complete justif it is categorical. This of course casts doubt onthe entire project. Though there is no furthermention of this theorem in Carnap''s publishedwritings, his Nachlass includes a largetypescript on the subject, Investigations inGeneral Axiomatics. We examine this work here,showing (...)
    Download  
     
    Export citation  
     
    Bookmark   26 citations  
  • Choice of Primitives: A Note on Axiomatizing Intuitionistic Logic.I. L. Humberstone - 1998 - History and Philosophy of Logic 19 (1):31-40.
    A purported axiomatization, by P. Gärdenfors, of intuitionistic propositional logic is shown to be incomplete, and that the mistaken claim to completeness is seen to result from carelessness in the choice of primitive logical vocabulary. This leads to a consideration of various ways of conceiving the distinction between primitive and defined vocabularies, along with the bearing of these differences on such matters as are discussed in connection with Gärdenfors.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Completeness and Categoricity. Part I: Nineteenth-Century Axiomatics to Twentieth-Century Metalogic.Steve Awodey & Erich H. Reck - 2002 - History and Philosophy of Logic 23 (1):1-30.
    This paper is the first in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully extend the usual set-theoretic semantics (...)
    Download  
     
    Export citation  
     
    Bookmark   40 citations  
  • Domains of Sciences, Universes of Discourse and Omega Arguments.Jose M. Saguillo - 1999 - History and Philosophy of Logic 20 (3-4):267-290.
    Each science has its own domain of investigation, but one and the same science can be formalized in different languages with different universes of discourse. The concept of the domain of a science and the concept of the universe of discourse of a formalization of a science are distinct, although they often coincide in extension. In order to analyse the presuppositions and implications of choices of domain and universe, this article discusses the treatment of omega arguments in three very different (...)
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  • Mathematics and Symbolic Logics: Some Notes on an Uneasy Relationship.I. Grattan-Guinness - 1999 - History and Philosophy of Logic 20 (3-4):159-167.
    Symbolic logics tend to be too mathematical for the philosophers and too philosophical for the mathematicians; and their history is too historical for most mathematicians, philosophers and logicians. This paper reflects upon these professional demarcations as they have developed during the century.
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Pasch entre Klein et Peano: empirisme et idéalité en géométrie.Sébastien Gandon - 2005 - Dialogue 44 (4):653-692.
    RÉSUMÉ: Pasch est généralement considéré comme le premier à avoir proposé une axiomatisation de la géométrie. Mais ses Vorlesungen über neure Geometrie contiennent plusieurs éléments étrangers au paradigme hilbertien. Pasch soutient ainsi que la « géométrie élémentaire », dont il propose une axiomatisation complète, est une théorie empiriquement vraie. Les commentateurs considèrent généralement les différences entre la méthode de Pasch et celle qui deviendra standard après Hilbert comme autant de défauts affectant une pensée encore inaboutie. Notre but consiste au contraire (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark   5 citations  
  • On the categoricity of quantum mechanics.Iulian D. Toader - 2021 - European Journal for Philosophy of Science 11 (1):1-14.
    The paper offers an argument against an intuitive reading of the Stone-von Neumann theorem as a categoricity result, thereby pointing out that this theorem does not entail any model-theoretical difference between the theories that validate it and those that don't.
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark   1 citation  
  • On Generalization of Definitional Equivalence to Non-Disjoint Languages.Koen Lefever & Gergely Székely - 2019 - Journal of Philosophical Logic 48 (4):709-729.
    For simplicity, most of the literature introduces the concept of definitional equivalence only for disjoint languages. In a recent paper, Barrett and Halvorson introduce a straightforward generalization to non-disjoint languages and they show that their generalization is not equivalent to intertranslatability in general. In this paper, we show that their generalization is not transitive and hence it is not an equivalence relation. Then we introduce another formalization of definitional equivalence due to Andréka and Németi which is equivalent to the Barrett–Halvorson (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • تحلیل منطقی فلسفی پارادوکس اسکولم. Mansooreh - 2015 - Dissertation,
    ریاضیدانان هرروز با مجموعههای ناشمارا، مجموعهی توانی، خوشترتیبی، تناهی و ... سروکار دارند و با این تصور که این مفاهیم همان چیزهایی هستند که در ذهن دارند، کتابها و اثباتهای ریاضی را میخوانند و میفهمند و درمورد آنها صحبت میکنند. اما آیا این مفاهیم همان چیزهایی هستند که ریاضیدانان تصور میکنند؟ اولینبار اسکولم با بیان یک پارادوکس شک خود را به این موضوع ابراز کرد. بنابر قضیهی لوونهایم اسکولم رو به پایین، نظریه مجموعهها مدلی شمارا دارد. این مدل قضیهی کانتور (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  • Completeness and Categoricity (in Power): Formalization Without Foundationalism.John T. Baldwin - 2014 - Bulletin of Symbolic Logic 20 (1):39-79.
    We propose a criterion to regard a property of a theory as virtuous: the property must have significant mathematical consequences for the theory. We then rehearse results of Ajtai, Marek, Magidor, H. Friedman and Solovay to argue that for second order logic, ‘categoricity’ has little virtue. For first order logic, categoricity is trivial; but ‘categoricity in power’ has enormous structural consequences for any of the theories satisfying it. The stability hierarchy extends this virtue to other complete theories. The interaction of (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Objectivity Sans Intelligibility. Hermann Weyl's Symbolic Constructivism.Iulian D. Toader - 2011 - Dissertation, University of Notre Dame
    A new form of skepticism is described, which holds that objectivity and understanding are incompossible ideals of modern science. This is attributed to Weyl, hence its name: Weylean skepticism. Two general defeat strategies are then proposed, one of which is rejected as a failure.
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • Completeness and Categoricity: Frege, Gödel and Model Theory.Stephen Read - 1997 - History and Philosophy of Logic 18 (2):79-93.
    Frege?s project has been characterized as an attempt to formulate a complete system of logic adequate to characterize mathematical theories such as arithmetic and set theory. As such, it was seen to fail by Gödel?s incompleteness theorem of 1931. It is argued, however, that this is to impose a later interpretation on the word ?complete? it is clear from Dedekind?s writings that at least as good as interpretation of completeness is categoricity. Whereas few interesting first-order mathematical theories are categorical or (...)
    Download  
     
    Export citation  
     
    Bookmark   11 citations  
  • Scientific Representation and Theoretical Equivalence.James Nguyen - 2017 - Philosophy of Science 84 (5):982-995.
    In this article I connect two debates in the philosophy of science: the questions of scientific representation and both model and theoretical equivalence. I argue that by paying attention to how a model is used to draw inferences about its target system, we can define a notion of theoretical equivalence that turns on whether models license the same claims about the same target systems. I briefly consider the implications of this for two questions that have recently been discussed in the (...)
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  • Fraenkel's Axiom of Restriction: Axiom Choice, Intended Models and Categoricity.Georg Schiemer - 2010 - In Benedikt L.öwe & Thomas Müller (eds.), PhiMSAMP. Philosophy of Mathematics: Sociological Aspects and Mathematical Practice. College Publications. pp. 307{340.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Hilbert's Finitism: Historical, Philosophical, and Metamathematical Perspectives.Richard Zach - 2001 - Dissertation, University of California, Berkeley
    In the 1920s, David Hilbert proposed a research program with the aim of providing mathematics with a secure foundation. This was to be accomplished by first formalizing logic and mathematics in their entirety, and then showing---using only so-called finitistic principles---that these formalizations are free of contradictions. ;In the area of logic, the Hilbert school accomplished major advances both in introducing new systems of logic, and in developing central metalogical notions, such as completeness and decidability. The analysis of unpublished material presented (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Completeness and Categoricity, Part II: Twentieth-Century Metalogic to Twenty-First-Century Semantics.Steve Awodey & Erich H. Reck - 2002 - History and Philosophy of Logic 23 (2):77-94.
    This paper is the second in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully extend the usual set-theoretic semantics (...)
    Download  
     
    Export citation  
     
    Bookmark   13 citations  
  • Husserl and Hilbert on Completeness, Still.Jairo Jose da Silva - 2016 - Synthese 193 (6).
    In the first year of the twentieth century, in Gottingen, Husserl delivered two talks dealing with a problem that proved central in his philosophical development, that of imaginary elements in mathematics. In order to solve this problem Husserl introduced a logical notion, called “definiteness”, and variants of it, that are somehow related, he claimed, to Hilbert’s notions of completeness. Many different interpretations of what precisely Husserl meant by this notion, and its relations with Hilbert’s ones, have been proposed, but no (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • Towards Completeness: Husserl on Theories of Manifolds 1890–1901.Mirja Helena Hartimo - 2007 - Synthese 156 (2):281-310.
    Husserl’s notion of definiteness, i.e., completeness is crucial to understanding Husserl’s view of logic, and consequently several related philosophical views, such as his argument against psychologism, his notion of ideality, and his view of formal ontology. Initially Husserl developed the notion of definiteness to clarify Hermann Hankel’s ‘principle of permanence’. One of the first attempts at formulating definiteness can be found in the Philosophy of Arithmetic, where definiteness serves the purpose of the modern notion of ‘soundness’ and leads Husserl to (...)
    Download  
     
    Export citation  
     
    Bookmark   17 citations  
  • A General Setting for Dedekind's Axiomatization of the Positive Integers.George Weaver - 2011 - History and Philosophy of Logic 32 (4):375-398.
    A Dedekind algebra is an ordered pair (B, h), where B is a non-empty set and h is a similarity transformation on B. Among the Dedekind algebras is the sequence of the positive integers. From a contemporary perspective, Dedekind established that the second-order theory of the sequence of the positive integers is categorical and finitely axiomatizable. The purpose here is to show that this seemingly isolated result is a consequence of more general results in the model theory of second-order languages. (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Second-Order Languages and Mathematical Practice.Stewart Shapiro - 1985 - Journal of Symbolic Logic 50 (3):714-742.
    Download  
     
    Export citation  
     
    Bookmark   27 citations  
  • 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   34 citations  
  • Carnap on Extremal Axioms, "Completeness of the Models," and Categoricity.Georg Schiemer - 2012 - Review of Symbolic Logic 5 (4):613-641.
    This paper provides a historically sensitive discussion of Carnaps theory will be assessed with respect to two interpretive issues. The first concerns his mathematical sources, that is, the mathematical axioms on which his extremal axioms were based. The second concerns Carnapcompleteness of the modelss different attempts to explicate the extremal properties of a theory and puts his results in context with related metamathematical research at the time.
    Download  
     
    Export citation  
     
    Bookmark   7 citations