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  1. (2 other versions)Études sur les règles d'inférence dites règles de Gentzen.Hugues Leblanc - 1963 - Dialogue 1 (4):355-367.
    Je vais traiter ici des inférences dont la validité tient au rôle qu'y jouent les cinq connecteurs « ⊃ », « ∼ », « & », « V » et « ≡ », les deux quantificateurs « ∀ » et « ∃ », et le signe d'identité « = ». Qu'on me permette de rappeler que les deux conjectures présentéd dans ma première étude se sont avéré'es justes. En premier lieu, toute règle de structure et toute règie d'élimination ou d'introduction (...)
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  • (1 other version)A formal system of logic.Hao Wang - 1950 - Journal of Symbolic Logic 15 (1):25-32.
    The main purpose of this paper is to present a formal systemPin which we enjoy a smooth-running technique and which countenances a universe of classes which is symmetrical as between large and small. More exactly,Pis a system which differs from the inconsistent system of [1] only in the introduction of a rather natural new restrictive condition on the defining formulas of the elements. It will be proved that if the weaker system of [2] is consistent, thenPis also consistent.After the discovery (...)
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  • 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 (...)
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  • On Euclidean diagrams and geometrical knowledge.Tamires Dal Magro & Manuel J. García-Pérez - 2019 - Theoria. An International Journal for Theory, History and Foundations of Science 34 (2):255.
    We argue against the claim that the employment of diagrams in Euclidean geometry gives rise to gaps in the proofs. First, we argue that it is a mistake to evaluate its merits through the lenses of Hilbert’s formal reconstruction. Second, we elucidate the abilities employed in diagram-based inferences in the Elements and show that diagrams are mathematically reputable tools. Finally, we complement our analysis with a review of recent experimental results purporting to show that, not only is the Euclidean diagram-based (...)
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  • Two Syllogisms in the Mozi: Chinese Logic and Language.Byeong-uk Yi - 2019 - Review of Symbolic Logic 12 (3):589-606.
    This article examines two syllogistic arguments contrasted in an ancient Chinese book, theMozi, which expounds doctrines of the Mohist school of philosophers. While the arguments seem to have the same form, one of them (theone-horse argument) is valid but the other (thetwo-horse argument) is not. To explain this difference, the article uses English plural constructions to formulate the arguments. Then it shows that the one-horse argument is valid because it has a valid argument form, the plural cousin of a standard (...)
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  • Frege’s Unmanageable Thing.Michael Price - 2018 - Grazer Philosophische Studien 95 (3):368-413.
    _ Source: _Volume 95, Issue 3, pp 368 - 413 Frege famously maintained that concepts are not objects. A key argument of Frege’s for this view is, in outline, as follows: if we are to account for the unity of thought, concepts must be deemed _unsaturated_; since objects are, by contrast, saturated entities, concepts cannot be objects. The author investigates what can be made of this argument and, in particular, of the unsaturated/saturated distinction it invokes. Systematically exploring a range of (...)
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  • Enciclopédia de Termos Lógico-Filosóficos.João Miguel Biscaia Branquinho, Desidério Murcho & Nelson Gonçalves Gomes (eds.) - 2006 - São Paulo, SP, Brasil: Martins Fontes.
    Esta enciclopédia abrange, de uma forma introdutória mas desejavelmente rigorosa, uma diversidade de conceitos, temas, problemas, argumentos e teorias localizados numa área relativamente recente de estudos, os quais tem sido habitual qualificar como «estudos lógico-filosóficos». De uma forma apropriadamente genérica, e apesar de o território teórico abrangido ser extenso e de contornos por vezes difusos, podemos dizer que na área se investiga um conjunto de questões fundamentais acerca da natureza da linguagem, da mente, da cognição e do raciocínio humanos, bem (...)
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  • Modus Ponens and Derivation from Horn Formulas.William Craig - 1967 - Mathematical Logic Quarterly 13 (3-5):33-54.
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  • The logic of partitions: Introduction to the dual of the logic of subsets: The logic of partitions.David Ellerman - 2010 - Review of Symbolic Logic 3 (2):287-350.
    Modern categorical logic as well as the Kripke and topological models of intuitionistic logic suggest that the interpretation of ordinary “propositional” logic should in general be the logic of subsets of a given universe set. Partitions on a set are dual to subsets of a set in the sense of the category-theoretic duality of epimorphisms and monomorphisms—which is reflected in the duality between quotient objects and subobjects throughout algebra. If “propositional” logic is thus seen as the logic of subsets of (...)
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  • The prehistory of the subsystems of second-order arithmetic.Walter Dean & Sean Walsh - 2017 - Review of Symbolic Logic 10 (2):357-396.
    This paper presents a systematic study of the prehistory of the traditional subsystems of second-order arithmetic that feature prominently in the reverse mathematics program of Friedman and Simpson. We look in particular at: (i) the long arc from Poincar\'e to Feferman as concerns arithmetic definability and provability, (ii) the interplay between finitism and the formalization of analysis in the lecture notes and publications of Hilbert and Bernays, (iii) the uncertainty as to the constructive status of principles equivalent to Weak K\"onig's (...)
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  • 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.
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  • (1 other version)Aristotle's Prior Analytics and Boole's Laws of Thought.John Corcoran - 2003 - History and Philosophy of Logic 24 (4):261-288.
    Prior Analytics by the Greek philosopher Aristotle and Laws of Thought by the English mathematician George Boole are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle's system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does not discuss many other historically and philosophically important aspects (...)
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  • 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 (...)
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  • Four Ways from Universal to Particular: How Chomsky's Language-Acquisition Faculty is Not Selectionist.David Ellerman - 2016 - Journal of Applied Non-Classical Logics 3 (26):193-207.
    Following the development of the selectionist theory of the immune system, there was an attempt to characterize many biological mechanisms as being "selectionist" as juxtaposed to "instructionist." But this broad definition would group Darwinian evolution, the immune system, embryonic development, and Chomsky's language-acquisition mechanism as all being "selectionist." Yet Chomsky's mechanism (and embryonic development) are significantly different from the selectionist mechanisms of biological evolution or the immune system. Surprisingly, there is a very abstract way using two dual mathematical logics to (...)
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  • (1 other version)The Absence of Multiple Universes of Discourse in the 1936 Tarski Consequence-Definition Paper.John Corcoran & José Miguel Sagüillo - 2011 - History and Philosophy of Logic 32 (4):359-374.
    This paper discusses the history of the confusion and controversies over whether the definition of consequence presented in the 11-page 1936 Tarski consequence-definition paper is based on a monistic fixed-universe framework?like Begriffsschrift and Principia Mathematica. Monistic fixed-universe frameworks, common in pre-WWII logic, keep the range of the individual variables fixed as the class of all individuals. The contrary alternative is that the definition is predicated on a pluralistic multiple-universe framework?like the 1931 Gödel incompleteness paper. A pluralistic multiple-universe framework recognizes multiple (...)
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  • Evading the Slingshot.John Perry - 1996 - In J. Ezquerro A. Clark (ed.), Philosophy and Cognitive Science: Categories, Consciousness, and Reasoning. Kluwer Academic Publishers.
    The topic of this essay is “the slingshot,” a short argument that purports to show that sentences1 designate (stand for, refer to) truth values. Versions of this argument have been used by Frege 2, Church 3, Quine4 and Davidson5; thus it is historically important, even if it immediately strikes one as fishy. The argument turns on two principles, which I call substitution and redistribution. In “Semantic Innocence and Uncompromising Situations,”6 Jon Barwise and I rejected both principles, as part of our (...)
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  • An Introduction to Subjective Facts: Readings in From Brain to Cosmos.Mark F. Sharlow - manuscript
    This collection serves as an introduction to the concept of subjective fact, which plays a central role in some of the author's philosophical writings. The collection contains two book chapters and a paper. The first chapter (Chapter 2 of From Brain to Cosmos) begins with an informal characterization of the concept of subjective fact. Then it fleshes out this concept with examples, gives a more precise characterization, and addresses some potential weaknesses of the concept. This chapter shows how subjective fact (...)
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  • American Postulate Theorists and Alfred Tarski.Michael Scanlan - 2003 - History and Philosophy of Logic 24 (4):307-325.
    This article outlines the work of a group of US mathematicians called the American Postulate Theorists and their influence on Tarski's work in the 1930s that was to be foundational for model theory. The American Postulate Theorists were influenced by the European foundational work of the period around 1900, such as that of Peano and Hilbert. In the period roughly from 1900???1940, they developed an indigenous American approach to foundational investigations. This made use of interpretations of precisely formulated axiomatic theories (...)
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  • The gödel paradox and Wittgenstein's reasons.Francesco Berto - 2009 - Philosophia Mathematica 17 (2):208-219.
    An interpretation of Wittgenstein’s much criticized remarks on Gödel’s First Incompleteness Theorem is provided in the light of paraconsistent arithmetic: in taking Gödel’s proof as a paradoxical derivation, Wittgenstein was drawing the consequences of his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. It is shown that the features of paraconsistent arithmetics match (...)
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  • (1 other version)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 (...)
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  • (1 other version)Aristotle's Prior Analytics and Boole's Laws of thought.John Corcoran - 2003 - History and Philosophy of Logic. 24 (4):261-288.
    Prior Analytics by the Greek philosopher Aristotle (384 – 322 BCE) and Laws of Thought by the English mathematician George Boole (1815 – 1864) are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle’s system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does not discuss (...)
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  • 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 (...)
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  • Rejection.Timothy Smiley - 1996 - Analysis 56 (1):1–9.
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  • (1 other version)The separation theorem of intuitionist propositional calculus.Alfred Horn - 1962 - Journal of Symbolic Logic 27 (4):391-399.
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  • Finite axiomatizability using additional predicates.W. Craig & R. L. Vaught - 1958 - Journal of Symbolic Logic 23 (3):289-308.
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  • Completeness of an ancient logic.John Corcoran - 1972 - Journal of Symbolic Logic 37 (4):696-702.
    In previous articles, it has been shown that the deductive system developed by Aristotle in his "second logic" is a natural deduction system and not an axiomatic system as previously had been thought. It was also stated that Aristotle's logic is self-sufficient in two senses: First, that it presupposed no other logical concepts, not even those of propositional logic; second, that it is (strongly) complete in the sense that every valid argument expressible in the language of the system is deducible (...)
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  • Comparison of Russell's resolution of the semantical antinomies with that of Tarski.Alonzo Church - 1976 - Journal of Symbolic Logic 41 (4):747-760.
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  • An axiomatic version of positive semilattice relevance logic.G. Charlwood - 1981 - Journal of Symbolic Logic 46 (2):233-239.
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  • Existential graphs as an instrument of logical analysis: Part I. alpha.Francesco Bellucci & Ahti-Veikko Pietarinen - 2016 - Review of Symbolic Logic 9 (2):209-237.
    Peirce considered the principal business of logic to be the analysis of reasoning. He argued that the diagrammatic system of Existential Graphs, which he had invented in 1896, carries the logical analysis of reasoning to the furthest point possible. The present paper investigates the analytic virtues of the Alpha part of the system, which corresponds to the sentential calculus. We examine Peirce’s proposal that the relation of illation is the primitive relation of logic and defend the view that this idea (...)
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  • Aristotle: an ancient mathematical logician.George Boger - unknown
    We can now recognize Aristotle's many accomplishments in logical theory, not the least of which is treating the deduction process itself as a subject matter and thus establishing the science of logic. Aristotle took logic to be that part of epistemolo gy used to establish knowledge of logical consequence. Prior Analytics is a metalogical treatise on his syllogistic system in which Aristotle modelled his deduction system to demonstrate certain logical relationships among its rules. Aristotle's n otion of substitution distinguishes logical (...)
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  • (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 (...)
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  • 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.).
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  • Gödel on Concepts.Gabriella Crocco - 2006 - History and Philosophy of Logic 27 (2):171-191.
    This article is an attempt to present Gödel's discussion on concepts, from 1944 to the late 1970s, in particular relation to the thought of Frege and Russell. The discussion takes its point of departure from Gödel's claim in notes on Bernay's review of ?Russell's mathematical logic?. It then retraces the historical background of the notion of intension which both Russell and Gödel use, and offers some grounds for claiming that Gödel consistently considered logic as a free-type theory of concepts, called (...)
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  • Notes on the art of logic.Nuel Belnap - manuscript
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  • (1 other version)Sentences true in all constructive models.R. L. Vaught - 1960 - Journal of Symbolic Logic 25 (1):39-53.
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  • (1 other version)Non-standard models for formal logics.J. Barkley Rosser & Hao Wang - 1950 - Journal of Symbolic Logic 15 (2):113-129.
    In his doctor's thesis [1], Henkin has shown that if a formal logic is consistent, and sufficiently complex, then it must admit a non-standard model. In particular, he showed that there must be a model in which that portion of the model which is supposed to represent the positive integers of the formal logic is not in fact isomorphic to the positive integers; indeed it is not even well ordered by what is supposed to be the relation of ≦.For the (...)
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  • 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 (...)
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  • Disagreement and Conceptual Understanding.Gurpreet Rattan - 2018 - Theoria 84 (2):179-210.
    Does the epistemology of disagreement have significant consequences for theories of conceptual understanding? I argue that it does. I argue that the epistemology of disagreement manifests the existence of a special kind of concept, perspectival modes of metarepresentation, a kind of concept instances of which figure in the thinking about thoughts that occurs in deep disagreement. These perspectival modes of metarepresentation are de re modes of presentation of thoughts themselves – hence de re modes of metarepresentation – in which one (...)
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  • (1 other version)A Strong Completeness Theorem for Pragmatics.Daniel Vanderveken - 1981 - Mathematical Logic Quarterly 27 (8‐10):151-160.
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  • (1 other version)The philosophy of computer science.Raymond Turner - 2013 - Stanford Encyclopedia of Philosophy.
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  • (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 (...)
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  • A note on finite axiomatization of partial propositional calculi.W. E. Singletary - 1967 - Journal of Symbolic Logic 32 (3):352-354.
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  • Prefix classes of Krom formulas.Stål O. Aanderaa & Harry R. Lewis - 1973 - Journal of Symbolic Logic 38 (4):628-642.
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  • Mathematical Inference and Logical Inference.Yacin Hamami - 2018 - Review of Symbolic Logic 11 (4):665-704.
    The deviation of mathematical proof—proof in mathematical practice—from the ideal of formal proof—proof in formal logic—has led many philosophers of mathematics to reconsider the commonly accepted view according to which the notion of formal proof provides an accurate descriptive account of mathematical proof. This, in turn, has motivated a search for alternative accounts of mathematical proof purporting to be more faithful to the reality of mathematical practice. Yet, in order to develop and evaluate such alternative accounts, it appears as a (...)
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  • Files for Fiction.Eleonora Orlando - 2017 - Acta Analytica 32 (1):55-71.
    In this essay, I appeal to the mental file approach in order to give an anti-realist semantic analysis of statements containing fictional names. I claim that fictive and parafictive uses of them express conceptual, though not general, propositions constituted by mental files, anchored in the conceptual world of the corresponding fictional story. Moreover, by positing a referential shift determined by the presence of a simulative referential intention characteristic of those uses, it is possible to take them to be true with (...)
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  • Knowledge of How Things Seem to You: Readings in From Brain to Cosmos.Mark F. Sharlow - manuscript
    This document consists primarily of an excerpt (chapter 4) from the author’s book From Brain to Cosmos. That excerpt presents a study of a specific problem about knowledge: the logical justification of one’s knowledge of the immediate past. (This document depends heavily upon the concept of subjective fact that the author developed in chapters 2 and 3 of From Brain to Cosmos. Readers unfamiliar with that concept are strongly advised to read those chapters first. See the last page of this (...)
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  • Semantics for relevant logics.Alasdair Urquhart - 1972 - Journal of Symbolic Logic 37 (1):159-169.
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  • 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.
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  • On the Reality of Existence and Identity.Ian Hacking - 1978 - Canadian Journal of Philosophy 8 (4):613 - 632.
    “The confusion of a logical with a real predicate,” according to the Critique of Pure Reason, “is almost beyond correction”. Kant did not assert that existence is no predicate, but that it is only a “logical” one, and not a “real” one. Much the same thing has been said about identity, although Kant himself thought it is real and not logical. We have long lacked a rigorous criterion to distinguish real from logical predicates, and hence have not been able to (...)
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  • All or none; A novel choice of primitives for elementary logic.R. H. Thomason & H. Leblanc - 1967 - Journal of Symbolic Logic 32 (3):345-351.
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