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. Variation on a Trivialist Argument of Paul Kabay.Lloyd Humberstone - 2011 - Journal of Logic, Language and Information 20 (1):115-132.
    Impossible worlds are regarded with understandable suspicion by most philosophers. Here we are concerned with a modal argument which might seem to show that acknowledging their existence, or more particularly, the existence of some hypothetical (we do not say “possible”) world in which everything was the case, would have drastic effects, forcing us to conclude that everything is indeed the case—and not just in the hypothesized world in question. The argument is inspired by a metaphysical (rather than modal-logical) argument of (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • Unity, truth and the liar: the modern relevance of medieval solutions to the liar paradox.Shahid Rahman, Tero Tulenheimo & Emmanuel Genot (eds.) - 2008 - New York: Springer.
    This volume includes a target paper, taking up the challenge to revive, within a modern (formal) framework, a medieval solution to the Liar Paradox which did ...
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  • Frege's Theory of Sense and Reference: Some Exegetical Notes.Saul A. Kripke - 2008 - Theoria 74 (3):181-218.
    Frege's theory of indirect contexts and the shift of sense and reference in these contexts has puzzled many. What can the hierarchy of indirect senses, doubly indirect senses, and so on, be? Donald Davidson gave a well-known 'unlearnability' argument against Frege's theory. The present paper argues that the key to Frege's theory lies in the fact that whenever a reference is specified (even though many senses determine a single reference), it is specified in a particular way, so that giving a (...)
    Download  
     
    Export citation  
     
    Bookmark   73 citations  
  • Some problems of perception in navya-nyāya.Pradyot Mandal - 1987 - Journal of Indian Philosophy 15 (2):125-148.
    Download  
     
    Export citation  
     
    Bookmark  
  • On 'analytic'.R. M. Martin - 1952 - Philosophical Studies 3 (3):42 - 47.
    Download  
     
    Export citation  
     
    Bookmark   14 citations  
  • Truth versus testability in quantum logic.Claudio Garola - 1992 - Erkenntnis 37 (2):197 - 222.
    We forward an epistemological perspective regarding non-classical logics which restores the universality of logic in accordance with the thesis of global pluralism. In this perspective every non-classical truth-theory is actually a theory of some metalinguistic concept which does not coincide with the concept of truth (described by Tarski's truth theory). We intend to apply this point of view to Quantum Logic (QL) in order to prove that its structure properties derive from properties of the metalinguistic concept of testability in Quantum (...)
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  • The importance of nonexistent objects and of intensionality in mathematics.Richard Sylvan - 2003 - Philosophia Mathematica 11 (1):20-52.
    In this article, extracted from his book Exploring Meinong's Jungle and Beyond, Sylvan argues that, contrary to widespread opinion, mathematics is not an extensional discipline and cannot be extensionalized without considerable damage. He argues that some of the insights of Meinong's theory of objects, and its modern development, item theory, should be applied to mathematics and that mathematical objects and structures should be treated as mind-independent, non-existent objects.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Do not claim too much: Second-order logic and first-order logic.Stewart Shapiro - 1999 - Philosophia Mathematica 7 (1):42-64.
    The purpose of this article is to delimit what can and cannot be claimed on behalf of second-order logic. The starting point is some of the discussions surrounding my Foundations without Foundationalism: A Case for Secondorder Logic.
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  • The origin of relation algebras in the development and axiomatization of the calculus of relations.Roger D. Maddux - 1991 - Studia Logica 50 (3-4):421 - 455.
    The calculus of relations was created and developed in the second half of the nineteenth century by Augustus De Morgan, Charles Sanders Peirce, and Ernst Schröder. In 1940 Alfred Tarski proposed an axiomatization for a large part of the calculus of relations. In the next decade Tarski's axiomatization led to the creation of the theory of relation algebras, and was shown to be incomplete by Roger Lyndon's discovery of nonrepresentable relation algebras. This paper introduces the calculus of relations and the (...)
    Download  
     
    Export citation  
     
    Bookmark   25 citations  
  • 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  
  • Moderate anti-exceptionalism and earthborn logic.Jaroslav Peregrin & Vladimír Svoboda - 2021 - Synthese 199 (3-4):8781-8806.
    In this paper we put forward and defend a view of the nature of logic that we call moderate anti-exceptionalism. In the first part of the paper we focus on the problem of genuine logical validity and consequence. We make use of examples from current debates to show that attempts to pinpoint the one and only authentic logic inevitably either yield irrefutable theories or lead to dead ends. We then outline a thoroughly naturalist account of logical consequence as grounded in (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Text and Its Structure.Andrzej Łachwa - 1990 - Studia Semiotyczne—English Supplement 19:118-137.
    Download  
     
    Export citation  
     
    Bookmark  
  • Elimination problems in logic: a brief history.William Craig - 2008 - Synthese 164 (3):321-332.
    A common aim of elimination problems for languages of logic is to express the entire content of a set of formulas of the language, or a certain part of it, in a way that is more elementary or more informative. We want to bring out that as the languages for logic grew in expressive power and, at the same time, our knowledge of their expressive limitations also grew, elimination problems in logic underwent some change. For languages other than that for (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Meaning Approached Via Proofs.Dag Prawitz - 2006 - Synthese 148 (3):507-524.
    According to a main idea of Gentzen the meanings of the logical constants are reflected by the introduction rules in his system of natural deduction. This idea is here understood as saying roughly that a closed argument ending with an introduction is valid provided that its immediate subarguments are valid and that other closed arguments are justified to the extent that they can be brought to introduction form. One main part of the paper is devoted to the exact development of (...)
    Download  
     
    Export citation  
     
    Bookmark   72 citations  
  • A Modest Logic of Plurals.Alex Oliver & Timothy Smiley - 2006 - Journal of Philosophical Logic 35 (3):317-348.
    We present a plural logic that is as expressively strong as it can be without sacrificing axiomatisability, axiomatise it, and use it to chart the expressive limits set by axiomatisability. To the standard apparatus of quantification using singular variables our object-language adds plural variables, a predicate expressing inclusion (is/are/is one of/are among), and a plural definite description operator. Axiomatisability demands that plural variables only occur free, but they have a surprisingly important role. Plural description is not eliminable in favour of (...)
    Download  
     
    Export citation  
     
    Bookmark   23 citations  
  • Reconstructing Arguments: Formalization and Reflective Equilibrium.Georg Brun - 2014 - History of Philosophy & Logical Analysis 17 (1):94-129.
    Traditional logical reconstruction of arguments aims at assessing the validity of ordinary language arguments. It involves several tasks: extracting argumentations from texts, breaking up complex argumentations into individual arguments, framing arguments in standard form, as well as formalizing arguments and showing their validity with the help of a logical formalism. These tasks are guided by a multitude of partly antagonistic goals, they interact in various feedback loops, and they are intertwined with the development of theories of valid inference and adequate (...)
    Download  
     
    Export citation  
     
    Bookmark   10 citations  
  • Phya pa Chos kyi seng ge on Argumentation by Consequence (thal ʼgyur): The Nature, Function, and Form of Consequence Statements.Pascale Hugon - 2013 - Journal of Indian Philosophy 41 (6):671-702.
    This paper presents the main aspects of the views of the Tibetan logician Phya pa Chos kyi seng ge (1109–1169) on argumentation “by consequence” (thal ʼgyur, Skt. prasaṅga) based on his exposition of the topic in the fifth chapter of his Tshad ma yid kyi mun sel and on a parallel excursus in his commentary on Dharmakīrti’s Pramānaviniścaya. It aims at circumscribing primarily the nature and function of consequences (thal ʼgyur/thal ba) for this author—in particular the distinction between “proving consequences” (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Hare and Others on the Proposition.John Corcoran - 2011 - Principia: An International Journal of Epistemology 15 (1):51-76.
    History witnesses alternative approaches to “the proposition”. The proposition has been referred to as the object of belief, disbelief, and doubt: generally as the object of propositional attitudes, that which can be said to be believed, disbelieved, understood, etc. It has also been taken to be the object of grasping, judging, assuming, affirming, denying, and inquiring: generally as the object of propositional actions, that which can be said to be grasped, judged true or false, assumed for reasoning purposes, etc. The (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Has the Correspondence Theory of Truth Been Refuted? From Gottlob Frege to Donald Davidson.Lorenz Krüger - 1995 - European Journal of Philosophy 3 (2):157-172.
    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  
  • 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  
  • What is categorical structuralism?Geoffrey Hellman - 2006 - In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics: Assessing Philosophy of Logic and Mathematics Today. Dordrecht, Netherland: Springer. pp. 151--161.
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • 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  
  • On rigorous definitions.Nuel Belnap - 1993 - Philosophical Studies 72 (2-3):115 - 146.
    Download  
     
    Export citation  
     
    Bookmark   57 citations  
  • Constructive empiricism and the problem of aboutness.Elliott Sober - 1985 - British Journal for the Philosophy of Science 36 (1):11-18.
    constructive empiricism asserts that it is not for science to reach a verdict on whether a theory is true or false, if the theory is about unobservable entities; science's only interest here, says Van Fraassen, is to discover whether the theory is ‘empirically adequate’. However, if a theory is soley about observables, empirical adequacy and truth are said to ‘coincide’, here discovering the theory's truth value is an appropriate scientific goal. Constructive empiricism thus rests an epistemological thesis on a semantical (...)
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  • Elementary categorial logic, predicates of variable degree, and theory of quantity.Brent Mundy - 1989 - Journal of Philosophical Logic 18 (2):115 - 140.
    Developing some suggestions of Ramsey (1925), elementary logic is formulated with respect to an arbitrary categorial system rather than the categorial system of Logical Atomism which is retained in standard elementary logic. Among the many types of non-standard categorial systems allowed by this formalism, it is argued that elementary logic with predicates of variable degree occupies a distinguished position, both for formal reasons and because of its potential value for application of formal logic to natural language and natural science. This (...)
    Download  
     
    Export citation  
     
    Bookmark   21 citations  
  • Being measured: truth and falsehood in Aristotle's Metaphysics.Mark Richard Wheeler - 2019 - Albany, New York: State University of New York Press.
    On the basis of careful textual exegesis and philosophical analysis, and contrary to the received view, Mark R. Wheeler demonstrates that Aristotle presents and systematically explicates his definition of the essence of the truth in the Metaphysics. Aristotle states the nominal definitions of the terms "truth" and "falsehood" as part of his arguments in defense of the logical axioms. These nominal definitions express conceptions of truth and falsehood his philosophical opponents would have recognized and accepted in the context of dialectical (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Peano’s structuralism and the birth of formal languages.Joan Bertran-San-Millán - 2022 - Synthese 200 (4):1-34.
    Recent historical studies have investigated the first proponents of methodological structuralism in late nineteenth-century mathematics. In this paper, I shall attempt to answer the question of whether Peano can be counted amongst the early structuralists. I shall focus on Peano’s understanding of the primitive notions and axioms of geometry and arithmetic. First, I shall argue that the undefinability of the primitive notions of geometry and arithmetic led Peano to the study of the relational features of the systems of objects that (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Making Sense of Non-Individuals in Quantum Mechanics.Jonas R. B. Arenhart, Otávio Bueno & Décio Krause - forthcoming - In Olimpia Lombardi, Sebastian Fortin, Cristian López & Frederico Holik (eds.), Quantum Worlds. Different Perspectives about the ontology of quantum mechanics. Cambridge University Press.
    In this work, we focus on a very specific case study: assuming that quantum theories deal with “particles” of some kind, what kind of entity can such particles be? One possible answer, the one we shall examine here, is that they are not the usual kind of object found in daily life: individuals. Rather, we follow a suggestion by Erwin Schrödinger, according to which quantum mechanics poses a revolutionary kind of entity: non-individuals. While physics, as a scientific field, is not (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • Wittgenstein and Gödel: An Attempt to Make ‘Wittgenstein’s Objection’ Reasonable†.Timm Lampert - 2018 - Philosophia Mathematica 26 (3):324-345.
    According to some scholars, such as Rodych and Steiner, Wittgenstein objects to Gödel’s undecidability proof of his formula $$G$$, arguing that given a proof of $$G$$, one could relinquish the meta-mathematical interpretation of $$G$$ instead of relinquishing the assumption that Principia Mathematica is correct. Most scholars agree that such an objection, be it Wittgenstein’s or not, rests on an inadequate understanding of Gödel’s proof. In this paper, I argue that there is a possible reading of such an objection that is, (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • 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  
  • Consistency, mechanicalness, and the logic of the mind.Qiuen Yu - 1992 - Synthese 90 (1):145-79.
    G. Priest's anti-consistency argument (Priest 1979, 1984, 1987) and J. R. Lucas's anti-mechanist argument (Lucas 1961, 1968, 1970, 1984) both appeal to Gödel incompleteness. By way of refuting them, this paper defends the thesis of quartet compatibility, viz., that the logic of the mind can simultaneously be Gödel incomplete, consistent, mechanical, and recursion complete (capable of all means of recursion). A representational approach is pursued, which owes its origin to works by, among others, J. Myhill (1964), P. Benacerraf (1967), J. (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • The Logic and Meaning of Plurals. Part I.Byeong-Uk Yi - 2005 - Journal of Philosophical Logic 34 (5-6):459-506.
    Contemporary accounts of logic and language cannot give proper treatments of plural constructions of natural languages. They assume that plural constructions are redundant devices used to abbreviate singular constructions. This paper and its sequel, "The logic and meaning of plurals, II", aim to develop an account of logic and language that acknowledges limitations of singular constructions and recognizes plural constructions as their peers. To do so, the papers present natural accounts of the logic and meaning of plural constructions that result (...)
    Download  
     
    Export citation  
     
    Bookmark   76 citations  
  • Partitions and conditionals.Peter W. Woodruff - 1999 - Journal of Philosophical Logic 28 (2):113-128.
    The literature on conditionals is rife with alternate formulations of the abstract semantics of conditional logic. Each formulation has its own advantages in terms of applications and generalizations; nevertheless, they are for the most part equivalent, in the sense that they underwrite the same range of logical systems. The purpose of the present note is to bring under this umbrella the partition semantics introduced by Brian Skyrms in (Skyrms, 1984).
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • The identity of strong indiscernibility.Horst Wessel - 1994 - Logic and Logical Philosophy 2 (5):117-134.
    The following considerations are to be seen in the framework of nontraditional theory of predication (NTP), which stems in its basic features from Sinowjew (cf. Sinowjew 1970, Sinowjew/Wessel 1975), and which is described in detail in Wessel 1989.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Aspekte der frege–hilbert-korrespondenz.Kai F. Wehmeier - 1997 - History and Philosophy of Logic 18 (4):201-209.
    In a letter to Frege of 29 December 1899, Hilbert advances his formalist doctrine, according to which consistency of an arbitrary set of mathematical sentences is a sufficient condition for its truth and for the existence of the concepts described by it. This paper discusses Frege's analysis, as carried out in the context of the Frege-Hilbert correspondence, of the formalist approach in particular and the axiomatic method in general. We close with a speculation about Frege's influence on Hilbert's later work (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Reading proofs with understanding.George Weaver - 1988 - Theoria 54 (1):31-47.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • A Strong Completeness Theorem for Pragmatics.Daniel Vanderveken - 1981 - Mathematical Logic Quarterly 27 (8-10):151-160.
    Download  
     
    Export citation  
     
    Bookmark  
  • Busting a Myth about Leśniewski and Definitions.Rafal Urbaniak & K. Severi Hämäri - 2012 - History and Philosophy of Logic 33 (2):159-189.
    A theory of definitions which places the eliminability and conservativeness requirements on definitions is usually called the standard theory. We examine a persistent myth which credits this theory to Leśniewski, a Polish logician. After a brief survey of its origins, we show that the myth is highly dubious. First, no place in Leśniewski's published or unpublished work is known where the standard conditions are discussed. Second, Leśniewski's own logical theories allow for creative definitions. Third, Leśniewski's celebrated ‘rules of definition’ lay (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • 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  
  • Objects and Modalities: A Study in the Semantics of Modal Logic.Tero Tulenheimo - 2017 - Cham, Switzerland: Springer Verlag.
    This book develops a novel generalization of possible world semantics, called ‘world line semantics’, which recognizes worlds and links between world-bound objects (world lines) as mutually independent aspects of modal semantics. Addressing a wide range of questions vital for contemporary debates in logic and philosophy of language and offering new tools for theoretical linguistics and knowledge representation, the book proposes a radically new paradigm in modal semantics. This framework is motivated philosophically, viewing a structure of world lines as a precondition (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • Denotation and reference.Pavel Materna - 2010 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 17 (1):3-20.
    The terms denotation and reference are commonly used as synonyms. A more fine-grained analysis of natural language as offered by TIL shows that we can distinguish these terms in the case of empirical expressions. The latter are shown to denote non-trivial intensions while their reference is the value of these intensions in the actual world.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Remarks on the development of computability.Stewart Shapiro - 1983 - History and Philosophy of Logic 4 (1-2):203-220.
    The purpose of this article is to examine aspects of the development of the concept and theory of computability through the theory of recursive functions. Following a brief introduction, Section 2 is devoted to the presuppositions of computability. It focuses on certain concepts, beliefs and theorems necessary for a general property of computability to be formulated and developed into a mathematical theory. The following two sections concern situations in which the presuppositions were realized and the theory of computability was developed. (...)
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  • On the notion of effectiveness.Stewart Shapiro - 1980 - History and Philosophy of Logic 1 (1-2):209-230.
    This paper focuses on two notions of effectiveness which are not treated in detail elsewhere. Unlike the standard computability notion, which is a property of functions themselves, both notions of effectiveness are properties of interpreted linguistic presentations of functions. It is shown that effectiveness is epistemically at least as basic as computability in the sense that decisions about computability normally involve judgments concerning effectiveness. There are many occurrences of the present notions in the writings of logicians; moreover, consideration of these (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • From Russell's Paradox to the Theory of Judgement: Wittgenstein and Russell on the Unity of the Proposition.Graham Stevens - 2004 - Theoria 70 (1):28-61.
    It is fairly well known that Wittgenstein's criticisms of Russell's multiple‐relation theory of judgement had a devastating effect on the latter's philosophical enterprise. The exact nature of those criticisms however, and the explanation for the severity of their consequences, has been a source of confusion and disagreement amongst both Russell and Wittgenstein scholars. In this paper, I offer an interpretation of those criticisms which shows them to be consonant with Wittgenstein's general critique of Russell's conception of logic and which serves (...)
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  • An Argument for Existentialism.Yannis Stephanou - 2020 - Acta Analytica 35 (4):507-520.
    Existentialism about propositions is the view that a proposition expressed in a sentence containing a nonempty name or indexical depends ontologically on the referent of the name or indexical: the proposition could not exist if the referent did not. The paper focuses on names. It discusses some arguments for existentialism and then presents a novel one. That argument does not presuppose that propositions have constituents, and it could be accepted by those who hold broadly Fregean views about names. It shows (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Non-classical operations hidden in classical logic.Vladimir Sotirov - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):309-324.
    Objects of consideration are various non-classical connectives “hidden” in the classical logic in the form of G˛s with ˛ —a classical connective, and s—a propositional variable. One of them is negation, which is defined as G ⇒ s; another is necessity, which is defined as G ∧ s. The new operations are axiomatized and it is shown that they belong to the 4-valued logic of Lukasiewicz. A 2-point Kripke semantics is built leading directly to the 4-valued logical tables.
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Russell And Frege On The Logic of Functions.Bernard Linsky - 2008 - The Baltic International Yearbook of Cognition, Logic and Communication 4:1-17.
    I compare Russell’s theory of mathematical functions, the “descriptive functions” from Principia Mathematica ∗30, with Frege’s well known account of functions as “unsaturated” entities. Russell analyses functional terms with propositional functions and the theory of definite descriptions. This is the primary technical role of the theory of descriptions in P M . In Principles of Mathematics and some unpublished writings from before 1905, Russell offered explicit criticisms of Frege’s account of functions. Consequenly, the theory of descriptions in “On Denoting” can (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • O comprometimento da identidade com a individuação nas teorias formais clássicas.Jaison Schinaider - 2015 - Filosofia Unisinos 16 (1).
    Download  
     
    Export citation  
     
    Bookmark