Switch to: References

Citations of:

Introduction to mathematical logic

Princeton,: Princeton University Press. Edited by C. Truesdell (1944)

Add citations

You must login to add citations.
  1. Personal Identity and Subjective Time: Readings in From Brain to Cosmos.Mark F. Sharlow - manuscript
    This document consists primarily of an excerpt (chapter 5) from the author’s book From Brain to Cosmos. That excerpt presents an analysis of personal identity through time, using the concept of subjective fact that the author developed earlier in the book. (Readers unfamiliar with that concept are strongly advised to read chapters 2 and 3 of From Brain to Cosmos first. See the last page of this document for details on how to obtain those chapters.).
    Download  
     
    Export citation  
     
    Bookmark  
  • Subjective Facts and Other Minds: Readings in From Brain to Cosmos.Mark F. Sharlow - manuscript
    This document consists primarily of an excerpt (chapter 6) from the author’s book From Brain to Cosmos. That excerpt presents an analysis of the problem of knowledge of other minds, using the concept of subjective fact that the author developed earlier in the book. (Readers unfamiliar with that concept are strongly advised to read chapters 2 and 3 of From Brain to Cosmos first. See the last page of this document for details on how to obtain those chapters.).
    Download  
     
    Export citation  
     
    Bookmark  
  • Time and Subjective Facts: Readings in From Brain to Cosmos.Mark F. Sharlow - manuscript
    This document consists primarily of excerpts (chapters 5 and 7-9) from the author’s book From Brain to Cosmos. These excerpts address some traditional philosophical problems about temporal flux and identity through time, using the concept of subjective fact that the author developed earlier in the book. (Readers unfamiliar with that concept are strongly advised to read chapters 2 and 3 of From Brain to Cosmos first. See the last page of this document for details on how to obtain those chapters.).
    Download  
     
    Export citation  
     
    Bookmark  
  • Completeness and Hauptsatz for second order logic.Dag Prawitz - 1967 - Theoria 33 (3):246-258.
    Download  
     
    Export citation  
     
    Bookmark   10 citations  
  • (1 other version)On the Concept of Following Logically.Alfred Tarski - 2002 - History and Philosophy of Logic 23 (3):155-196.
    We provide for the first time an exact translation into English of the Polish version of Alfred Tarski's classic 1936 paper, whose title we translate as ?On the Concept of Following Logically?. We also provide in footnotes an exact translation of all respects in which the German version, used as the basis of the previously published and rather inexact English translation, differs from the Polish. Although the two versions are basically identical, to an extent that is even uncanny, we note (...)
    Download  
     
    Export citation  
     
    Bookmark   63 citations  
  • Metaphysics, substitution salva veritate and the slingshot argument.Robert J. Stainton - 2005 - In Keith Brown (ed.), Encyclopedia of Language and Linguistics. Elsevier. pp. 73--82.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Formalizations après la lettre: Studies in Medieval Logic and Semantics.Catarina Dutilh Novaes - 2006 - Dissertation, Leiden University
    This thesis is on the history and philosophy of logic and semantics. Logic can be described as the ‘science of reasoning’, as it deals primarily with correct patterns of reasoning. However, logic as a discipline has undergone dramatic changes in the last two centuries: while for ancient and medieval philosophers it belonged essentially to the realm of language studies, it has currently become a sub-branch of mathematics. This thesis attempts to establish a dialogue between the modern and the medieval traditions (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • On the concept of material consequence.Tomis Kapitan - 1982 - History and Philosophy of Logic 3 (2):193-211.
    Everyday reasoning is replete with arguments which, though not logically valid, nonetheless harbor a measure of credibility in their own right. Here the claim that such arguments force us to acknowledge material validity, in addition to logical validity, is advanced, and criteria that attempt to unpack this concept are examined in detail. Of special concern is the effort to model these criteria on explications of logical validity that rely on notions of substitutivity and logical form. It is argued, however, that (...)
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  • Rereading Tarski on logical consequence.Mario Gómez-Torrente - 2009 - Review of Symbolic Logic 2 (2):249-297.
    I argue that recent defenses of the view that in 1936 Tarski required all interpretations of a language to share one same domain of quantification are based on misinterpretations of Tarski’s texts. In particular, I rebut some criticisms of my earlier attack on the fixed-domain exegesis and I offer a more detailed report of the textual evidence on the issue than in my earlier work. I also offer new considerations on subsisting issues of interpretation concerning Tarski’s views on the logical (...)
    Download  
     
    Export citation  
     
    Bookmark   12 citations  
  • Why do informal proofs conform to formal norms?Jody Azzouni - 2009 - Foundations of Science 14 (1-2):9-26.
    Kant discovered a philosophical problem with mathematical proof. Despite being a priori , its methodology involves more than analytic truth. But what else is involved? This problem is widely taken to have been solved by Frege’s extension of logic beyond its restricted (and largely Aristotelian) form. Nevertheless, a successor problem remains: both traditional and contemporary (classical) mathematical proofs, although conforming to the norms of contemporary (classical) logic, never were, and still aren’t, executed by mathematicians in a way that transparently reveals (...)
    Download  
     
    Export citation  
     
    Bookmark   30 citations  
  • (1 other version)Gottlob Frege.Kevin C. Klement - 2001 - Internet Encyclopedia of Philosophy.
    Gottlob Frege (1848-1925) was a German logician, mathematician and philosopher who played a crucial role in the emergence of modern logic and analytic philosophy. Frege's logical works were revolutionary, and are often taken to represent the fundamental break between contemporary approaches and the older, Aristotelian tradition. He invented modern quantificational logic, and created the first fully axiomatic system for logic, which was complete in its treatment of propositional and first-order logic, and also represented the first treatment of higher-order logic. In (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Conceptual realism versus Quine on classes and higher-order logic.Nino B. Cocchiarella - 1992 - Synthese 90 (3):379 - 436.
    The problematic features of Quine's set theories NF and ML are a result of his replacing the higher-order predicate logic of type theory by a first-order logic of membership, and can be resolved by returning to a second-order logic of predication with nominalized predicates as abstract singular terms. We adopt a modified Fregean position called conceptual realism in which the concepts (unsaturated cognitive structures) that predicates stand for are distinguished from the extensions (or intensions) that their nominalizations denote as singular (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Semantical analyses of propositional systems of Fitch and Nelson.Richard Routley - 1974 - Studia Logica 33 (3):283 - 298.
    Download  
     
    Export citation  
     
    Bookmark   22 citations  
  • The indispensability of farbung.Michael W. Pelczar - 2004 - Synthese 138 (1):49 - 77.
    I offer a theory of propositional attitudeascriptions that reconciles a number of independently plausiblesemantic principles. At the heart of the theory lies the claim thatpsychological verbs (such as ``to believe'' and ``to doubt'') vary incontent indexically. After defending this claim and explaining how itrenders the aforementioned principles mutually compatible, I arguethat my account is superior to currently popular hidden indexicaltheories of attitude ascription. To conclude I indicate a number oframifications that the proposed theory has for issues in epistemology,philosophy of mind, (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Plural descriptions and many-valued functions.Alex Oliver & Timothy Smiley - 2005 - Mind 114 (456):1039-1068.
    Russell had two theories of definite descriptions: one for singular descriptions, another for plural descriptions. We chart its development, in which ‘On Denoting’ plays a part but not the part one might expect, before explaining why it eventually fails. We go on to consider many-valued functions, since they too bring in plural terms—terms such as ‘4’ or the descriptive ‘the inhabitants of London’ which, like plain plural descriptions, stand for more than one thing. Logicians need to take plural reference seriously (...)
    Download  
     
    Export citation  
     
    Bookmark   26 citations  
  • First-order indefinite and uniform neighbourhood semantics.Arnold Nat - 1979 - Studia Logica 38 (3):277 - 296.
    The main purpose of this paper is to define and study a particular variety of Montague-Scott neighborhood semantics for modal propositional logic. We call this variety the first-order neighborhood semantics because it consists of the neighborhood frames whose neighborhood operations are, in a certain sense, first-order definable. The paper consists of two parts. In Part I we begin by presenting a family of modal systems. We recall the Montague-Scott semantics and apply it to some of our systems that have hitherto (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • (1 other version)Sein und heißen.Hans-Ulrich Hoche - 1985 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 16 (2):287-303.
    If identity is to be taken as a relation, not between any object and itself, nor between expressions , but between "intensions" or Fregean "Sinnen" of individual constants , then not only definite descriptions but also grammatically proper names ought to have intensions. This, however, has been repudiated by J. St. Mill and, more recently and more persuasively, by Saul Kripke. So an attempt will be made to interpret proper names as definite descriptions sui generis, namely, "rigid" descriptions referring to (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Carnapian extensions of S.Herbert E. Hendry & M. L. Pokriefka - 1985 - Journal of Philosophical Logic 14 (2):111 - 128.
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • The Logical Basis of the Tractarian Ontology.Natan Berber - 2007 - Axiomathes 17 (2):185-196.
    This paper focuses on the relation between logic and ontology. In particular, it demonstrates how classical logical theory can clarify the ontological part of Ludwig Wittgenstein’s Tractatus Logico-Philosophicus. To this end, the work examines the adequacy of a formal system that was devised by the Polish logician, mathematician and philosopher Roman Suszko (1919–1979) as a model for the Tractatus. Following a brief explanation of the Tractarian ontology, the main ideas of Suszko’s system and its philosophical significance will be considered. The (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Ramified structure.Gabriel Uzquiano - 2022 - Philosophical Studies 180 (5-6):1651-1674.
    The Russell–Myhill theorem threatens a familiar structured conception of propositions according to which two sentences express the same proposition only if they share the same syntactic structure and their corresponding syntactic constituents share the same semantic value. Given the role of the principle of universal instantiation in the derivation of the theorem in simple type theory, one may hope to rehabilitate the core of the structured view of propositions in ramified type theory, where the principle is systematically restricted. We suggest (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Truth and Falsehood: An Inquiry Into Generalized Logical Values.Yaroslav Shramko & Heinrich Wansing - 2011 - Dordrecht, Netherland: Springer.
    The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and most notably, (...)
    Download  
     
    Export citation  
     
    Bookmark   26 citations  
  • The Cogito Paradox.Arnold Cusmariu - forthcoming - Symposion. Theoretical and Applied Inquiries in Philosophy and Social Sciences.
    Arnold Cusmariu ABSTRACT: The Cogito formulation in Discourse on Method attributes properties to one conceptual category that belong to another. Correcting the error ends up defeating Descartes’ response to skepticism. His own creation, the Evil Genius, is to blame. Download PDF.
    Download  
     
    Export citation  
     
    Bookmark  
  • Using Kreisel’s Way Out to Refute Lucas-Penrose-Putnam Anti-Functionalist Arguments.Jeff Buechner - 2020 - Studia Semiotyczne 34 (1):109-158.
    Georg Kreisel suggested various ways out of the Gödel incompleteness theorems. His remarks on ways out were somewhat parenthetical, and suggestive. He did not develop them in subsequent papers. One aim of this paper is not to develop those remarks, but to show how the basic idea that they express can be used to reason about the Lucas-Penrose-Putnam arguments that human minds are not finitary computational machines. Another aim is to show how one of Putnam’s two anti-functionalist arguments avoids the (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Syntactic Description of Reported Speech in Categorial Grammar.Witold Marciszewski - 1977 - Studia Semiotyczne—English Supplement 7:112-136.
    Download  
     
    Export citation  
     
    Bookmark  
  • Text and Its Structure.Andrzej Łachwa - 1990 - Studia Semiotyczne—English Supplement 19:118-137.
    Download  
     
    Export citation  
     
    Bookmark  
  • Notational Differences.Francesco Bellucci & Ahti-Veikko Pietarinen - 2020 - Acta Analytica 35 (2):289-314.
    Expressively equivalent logical languages can enunciate logical notions in notationally diversified ways. Frege’s Begriffsschrift, Peirce’s Existential Graphs, and the notations presented by Wittgenstein in the Tractatus all express the sentential fragment of classical logic, each in its own way. In what sense do expressively equivalent notations differ? According to recent interpretations, Begriffsschrift and Existential Graphs differ from other logical notations because they are capable of “multiple readings.” We refute this interpretation by showing that there are at least three different kinds (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Gödel on Deduction.Kosta Došen & Miloš Adžić - 2019 - Studia Logica 107 (1):31-51.
    This is an examination, a commentary, of links between some philosophical views ascribed to Gödel and general proof theory. In these views deduction is of central concern not only in predicate logic, but in set theory too, understood from an infinitistic ideal perspective. It is inquired whether this centrality of deduction could also be kept in the intensional logic of concepts whose building Gödel seems to have taken as the main task of logic for the future.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • (1 other version)Conceptual realism and the nexus of predication.Nino Cocchiarella - 2003 - Metalogicon 16 (2):45-70.
    The nexus of predication is accounted for in different ways in different theories of universals. We briefly review the account given in nominalism, logical realism , and natural realism. Our main goal is to describe the account given in a modern form of conceptualism extended to include a theory of intensional objects as the contents of our predicable and referential concepts.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Necessity and the Ontological Argument.Joel I. Friedman - 1980 - Erkenntnis 15 (3):301-331.
    Download  
     
    Export citation  
     
    Bookmark  
  • (1 other version)Funkce–Procedura–Konstrukce.Pavel Materna - 2012 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 19 (3):283-305.
    The purpose of this paper can be described as follows. The contemporary philosophical logic cannot work without using some terms well-known from mathematics and logic. Among such terms that play an important role in logical and philosophical analyses of language, meaning and the like we can find function, procedure and construction. One problem is that various authors use these terms in various ways, another problem consists in the well-known fact that many philosophers do not have any idea of what those (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • (1 other version)On some interpretations of classical logic.Branislav R. Boričić & B. R. Boričić - 1992 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 38 (1):409-412.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • (1 other version)Quantified propositional calculi and fragments of bounded arithmetic.Jan Krajíček & Pavel Pudlák - 1990 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (1):29-46.
    Download  
     
    Export citation  
     
    Bookmark   24 citations  
  • (1 other version)A Constructive Proof of a Theorem in Relevance Logic.Aleksandar Kron - 1985 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 31 (25-28):423-430.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • (1 other version)Probabilistic Semantics for First-Order Logic.Hugues Leblanc - 1979 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 25 (32):497-509.
    Download  
     
    Export citation  
     
    Bookmark   16 citations  
  • (1 other version)An Extension of the Notion of Relativization to Hilbert's ϵ‐Symbol.Masazumi Hanazawa - 1980 - Mathematical Logic Quarterly 26 (31):491-496.
    Download  
     
    Export citation  
     
    Bookmark  
  • (1 other version)The Strong Completeness of a System for Kleene's Three‐Valued Logic.John T. Kearns - 1979 - Mathematical Logic Quarterly 25 (3-6):61-68.
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • (1 other version)The Logic of Calculation.John T. Kearns - 1977 - Mathematical Logic Quarterly 23 (1-6):45-58.
    Download  
     
    Export citation  
     
    Bookmark  
  • (1 other version)The Logic of Calculation.John T. Kearns - 1976 - Mathematical Logic Quarterly 23 (1‐6):45-58.
    Download  
     
    Export citation  
     
    Bookmark  
  • (1 other version)Minimal Axioms for Peirce's Triadic Logic.Atwell R. Turquette - 1976 - Mathematical Logic Quarterly 22 (1):169-176.
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • (1 other version)Minimal Axioms for Peirce's Triadic Logic.Atwell R. Turquette - 1976 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 22 (1):169-176.
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • (1 other version)Übersetzung von algorithmischen Formelsprachen in die Programmsprachen von Rechenmaschinen.H. Bottenbruch - 1958 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 4 (12-16):180-221.
    Download  
     
    Export citation  
     
    Bookmark  
  • Transparent quantification into hyperintensional objectual attitudes.Bjørn Jespersen & Marie Duží - 2015 - Synthese 192 (3):635-677.
    We demonstrate how to validly quantify into hyperintensional contexts involving non-propositional attitudes like seeking, solving, calculating, worshipping, and wanting to become. We describe and apply a typed extensional logic of hyperintensions that preserves compositionality of meaning, referential transparency and substitutivity of identicals also in hyperintensional attitude contexts. We specify and prove rules for quantifying into hyperintensional contexts. These rules presuppose a rigorous method for substituting variables into hyperintensional contexts, and the method will be described. We prove the following. First, it (...)
    Download  
     
    Export citation  
     
    Bookmark   15 citations  
  • (1 other version)On Some Subsystems of Dummett's LC.Branislav R. Boričić - 1985 - Mathematical Logic Quarterly 31 (14-18):243-247.
    Download  
     
    Export citation  
     
    Bookmark  
  • Sheffer’s stroke: A study in proof-theoretic harmony.Stephen Read - 1999 - Danish Yearbook of Philosophy 34 (1):7-23.
    In order to explicate Gentzen’s famous remark that the introduction-rules for logical constants give their meaning, the elimination-rules being simply consequences of the meaning so given, we develop natural deduction rules for Sheffer’s stroke, alternative denial. The first system turns out to lack Double Negation. Strengthening the introduction-rules by allowing the introduction of Sheffer’s stroke into a disjunctive context produces a complete system of classical logic, one which preserves the harmony between the rules which Gentzen wanted: all indirect proof reduces (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Equivalence of Problems (An Attempt at an Explication of Problem).Pavel Materna - 2013 - Axiomathes 23 (4):617-631.
    On the one hand, Pavel Tichý has shown in his Transparent Intensional Logic (TIL) that the best way of explicating meaning of the expressions of a natural language consists in identification of meanings with abstract procedures. TIL explicates objective abstract procedures as so-called constructions. Constructions that do not contain free variables and are in a well-defined sense ´normalized´ are called concepts in TIL. On the second hand, Kolmogorov in (Mathematische Zeitschrift 35: 58–65, 1932) formulated a theory of problems, using NL (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Frege on identity, cognitive value, and subject matter.John Perry - 2019 - In Studies in language and information. Stanford, California: Center for the Study of Language and Information.
    Frege continues by explaining what bothered him in the Begriffsschrift, and motivated his treatment of identity in that work.2 He goes on to criticize that account. By the end of the paragraph, he has introduced his key concept of sinn, abandonning not only the Begriffsschrift account of identity, but its basical semantical framework. In the Begriffsschrift Frege’s main semantic concept was content [Inhalt ]. Already in the Begriffsschrift, he is struggling with this concept. In §3 he..
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • (1 other version)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   49 citations  
  • Zero-place operations and functional completeness, and the definition of new connectives.I. L. Humberstone - 1993 - History and Philosophy of Logic 14 (1):39-66.
    Tarski 1968 makes a move in the course of providing an account of ?definitionally equivalent? classes of algebras with a businesslike lack of fanfare and commentary, the significance of which may accordingly be lost on the casual reader. In ?1 we present this move as a response to a certain difficulty in the received account of what it is to define a function symbol (or ?operation symbol?). This difficulty, which presents itself as a minor technicality needing to be got around (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • Concepts and recipes.Pavel Materna - 2009 - Acta Analytica 24 (1):69-90.
    If concepts are explicated as abstract procedures, then we can easily show that each empirical concept is a not an effective procedure. Some, but not all empirical concepts are shown to be of a special kind: they cannot in principle guarantee that the object they identify satisfies the intended conditions.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Some problems of perception in navya-nyāya.Pradyot Mandal - 1987 - Journal of Indian Philosophy 15 (2):125-148.
    Download  
     
    Export citation  
     
    Bookmark