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  1. The Truth and Nothing but the Truth, yet Never the Whole Truth: Frege, Russell and the Analysis of Unities.Graham Stevens - 2003 - History and Philosophy of Logic 24 (3):221-240.
    It is widely assumed that Russell's problems with the unity of the proposition were recurring and insoluble within the framework of the logical theory of his Principles of Mathematics. By contrast, Frege's functional analysis of thoughts (grounded in a type-theoretic distinction between concepts and objects) is commonly assumed to provide a solution to the problem or, at least, a means of avoiding the difficulty altogether. The Fregean solution is unavailable to Russell because of his commitment to the thesis that there (...)
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  • On the Development of the Notion of a Cardinal Number.Oliver Deiser - 2010 - History and Philosophy of Logic 31 (2):123-143.
    We discuss the concept of a cardinal number and its history, focussing on Cantor's work and its reception. J'ay fait icy peu pres comme Euclide, qui ne pouvant pas bien >faire< entendre absolument ce que c'est que raison prise dans le sens des Geometres, definit bien ce que c'est que memes raisons. (Leibniz) 1.
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  • Russell's Schema, Not Priest's Inclosure.Gregory Landini - 2009 - History and Philosophy of Logic 30 (2):105-139.
    On investigating a theorem that Russell used in discussing paradoxes of classes, Graham Priest distills a schema and then extends it to form an Inclosure Schema, which he argues is the common structure underlying both class-theoretical paradoxes (such as that of Russell, Cantor, Burali-Forti) and the paradoxes of ?definability? (offered by Richard, König-Dixon and Berry). This article shows that Russell's theorem is not Priest's schema and questions the application of Priest's Inclosure Schema to the paradoxes of ?definability?.1 1?Special thanks to (...)
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  • Circularity and Paradox.Stephen Yablo - 2006 - In Thomas Bolander, Vincent F. Hendricks & Stig Andur Pedersen (eds.), Self-Reference. CSLI Publications. pp. 139--157.
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  • Proceeding in Abstraction. From Concepts to Types and the Recent Perspective on Information.Giuseppe Primiero - 2009 - History and Philosophy of Logic 30 (3):257-282.
    This article presents an historical and conceptual overview on different approaches to logical abstraction. Two main trends concerning abstraction in the history of logic are highlighted, starting from the logical notions of concept and function. This analysis strictly relates to the philosophical discussion on the nature of abstract objects. I develop this issue further with respect to the procedure of abstraction involved by (typed) λ-systems, focusing on the crucial change about meaning and predicability. In particular, the analysis of the nature (...)
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  • Paradox, ZF, and the Axiom of Foundation.A. Rieger - 2011 - In P. Clark, M. Hallett & D. DeVidi (eds.), Logic, Mathematics, Philosophy, Vintage Enthusiasms: Essays in Honour of John L. Bell. Springer. pp. 171-187.
    This paper seeks to question the position of ZF as the dominant system of set theory, and in particular to examine whether there is any philosophical justification for the axiom of foundation. After some historical observations regarding Poincare and Russell, and the notions of circularity and hierarchy, the iterative conception of set is argued to be a semi-constructvist hybrid without philosophical coherence. ZF cannot be justified as necessary to avoid paradoxes, as axiomatizing a coherent notion of set, nor on pragmatic (...)
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  • What is Apophaticism? Ways of Talking About an Ineffable God.Scott Michael & Citron Gabriel - 2016 - European Journal for Philosophy of Religion 8 (4):23--49.
    Apophaticism -- the view that God is both indescribable and inconceivable -- is one of the great medieval traditions of philosophical thought about God, but it is largely overlooked by analytic philosophers of religion. This paper attempts to rehabilitate apophaticism as a serious philosophical option. We provide a clear formulation of the position, examine what could appropriately be said and thought about God if apophaticism is true, and consider ways to address the charge that apophaticism is self-defeating. In so doing (...)
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  • The Reception of Frege in Poland.Jan Woleński - 2004 - History and Philosophy of Logic 25 (1):37-51.
    This paper examines how the work of Frege was known and received in Poland in the period 1910?1935 (with one exception concerning the later work of Suszko). The main thesis is that Frege's reception in Poland was perhaps faster and deeper than in other countries, except England, due to works of Russell and Jourdain. The works of ?ukasiewicz, Le?niewski and Cze?owski are described.
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  • Russell's Early Theory of Denoting.David Bostock - 2009 - History and Philosophy of Logic 30 (1):49-67.
    The article concerns the treatment of the so-called denoting phrases, of the forms ?every A?, ?any A?, ?an A? and ?some A?, in Russell's Principles of Mathematics. An initially attractive interpretation of what Russell's theory was has been proposed by P.T. Geach, in his Reference and Generality (1962). A different interpretation has been proposed by P. Dau (Notre Dame Journal, 1986). The article argues that neither of these is correct, because both credit Russell with a more thought-out theory than he (...)
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  • Alonzo Church:His Life, His Work and Some of His Miracles.Maía Manzano - 1997 - History and Philosophy of Logic 18 (4):211-232.
    This paper is dedicated to Alonzo Church, who died in August 1995 after a long life devoted to logic. To Church we owe lambda calculus, the thesis bearing his name and the solution to the Entscheidungsproblem.His well-known book Introduction to Mathematical LogicI, defined the subject matter of mathematical logic, the approach to be taken and the basic topics addressed. Church was the creator of the Journal of Symbolic Logicthe best-known journal of the area, which he edited for several decades This (...)
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  • Mathematical Perspectives on Liar Paradoxes.José-Luis Usó-Doménech, Josué-Antonio Nescolarde-Selva, Lorena Segura-Abad, Kristian Alonso-Stenberg & Hugh Gash - 2021 - Logica Universalis 15 (3):251-269.
    The liar paradox is a famous and ancient paradox related to logic and philosophy. It shows it is perfectly possible to construct sentences that are correct grammatically and semantically but that cannot be true or false in the traditional sense. In this paper the authors show four approaches to interpreting paradoxes that illustrate the influence of: the levels of language, their belonging to indeterminate compatible propositions or indeterminate propositions, being based on universal antinomy and the theory of dialetheism.
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  • Logical Types in Quantum Mechanics.Andrew Soltau - manuscript
    Barbour shows that time does not exist in the physical world, and similar conclusions are reached by others such as Deutsch, Davies and Woodward. Every possible configuration of a physical environment simply exists in the universe. The system is objectively static. Observation, however, is an inherently transtemporal phenomenon, involving actual or effective change of the configuration, collapse. Since, in a static environment, all possible configurations exist, transtemporal reality is of the logical type of a movie. The frame of a movie (...)
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  • Times Two: The Tenses of Linear and Collapse Dynamics in Relational Quantum Mechanics.Andrew Soltau - manuscript
    The nature and topology of time remains an open question in philosophy, both tensed and tenseless concepts of time appear to have merit. A concept of time including both kinds of time evolution of physical systems in quantum mechanics subsumes the properties of both notions. The linear dynamics defines the universe probabilistically throughout space-time, and can be seen as the definition of a block universe. The collapse dynamics is the time evolution of the linear dynamics, and is thus of different (...)
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  • Interactive Destiny.Andrew Soltau - manuscript
    Mitra demonstrates that memory erasure can cause the observer to end up in a different sector of the multiverse with a different destiny, events in the future remote to any possible influence of the observer having radically different probabilities. The concept only applies to an observer defined by a structure of information, so cannot apply to the physical bodies of human observers. However, Everett defines the functional identity of the observer as the contents of the memory, a structure of information, (...)
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  • Times Two.Andrew Soltau - manuscript
    The nature and topology of time remain an open question in philosophy. Both tensed and tenseless concepts of time appear to have merit. Quantum mechanics demonstrates that both are instantiated, as complementary aspects of the time evolution of physical systems. The linear dynamics is tenseless. It defines the universe probabilistically throughout space-time, and can be seen as the definition of an unchanging block universe. All properties of the universe are defined for the whole extent of the linear time dimension of (...)
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  • When Curry Met Abel.Manuel Eduardo Tapia-Navarro & Luis Estrada-González - 2020 - Logic Journal of the IGPL 28 (6):1233-1242.
    Based on his Inclosure Schema and the Principle of Uniform Solution, Priest has argued that Curry’s paradox belongs to a different family of paradoxes than the Liar. Pleitz argued that Curry’s paradox shares the same structure as the other paradoxes and proposed a scheme of which the Inclosure Schema is a particular case and he criticizes Priest’s position by pointing out that applying the PUS implies the use of a paraconsistent logic that does not validate Contraction, but that this can (...)
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  • Themes in Plato, Aristotle, and Hellenistic Philosophy, Keeling Lectures 2011-2018, OPEN ACCESS.Fiona Leigh (ed.) - 2021 - University of Chicago Press.
  • Математизирането на историята: число и битие.Vasil Penchev - 2013 - Sofia: BAS: ISSk (IPR).
    The book is a philosophical refection on the possibility of mathematical history. Are poosible models of historical phenomena so exact as those of physical ones? Mathematical models borrowed from quantum mechanics by the meditation of its interpretations are accomodated to history. The conjecture of many-variant history, alternative history, or counterfactual history is necessary for mathematical history. Conclusions about philosophy of history are inferred.
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  • Отвъд машината на Тюринг: квантовият компютър.Vasil Penchev - 2014 - Sofia: BAS: ISSK (IPS).
    Quantum computer is considered as a generalization of Turing machine. The bits are substituted by qubits. In turn, a "qubit" is the generalization of "bit" referring to infinite sets or series. It extends the consept of calculation from finite processes and algorithms to infinite ones, impossible as to any Turing machines (such as our computers). However, the concept of quantum computer mets all paradoxes of infinity such as Gödel's incompletness theorems (1931), etc. A philosophical reflection on how quantum computer might (...)
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  • Esistenza e Persistenza.Damiano Costa - 2018 - Milan, IT: Mimesis.
    Nel nostro universo, qualunque cosa, dalla più piccola particella alla più smisurata galassia, esiste in un qualche tempo e in un qualche luogo. Ma cosa significa esistere in un qualche tempo? Il fenomeno dell’esistenza temporale gioca un ruolo fondamentale nella comprensione dell’universo e di noi stessi quali creature temporali. Eppure è un fenomeno profondamente misterioso. L’esistenza temporale è da intendersi come una relazione? Che legami ha con l’esistenza dell’ontologia? L’esistenza temporale e la localizzazione spaziale sono due fenomeni essenzialmente differenti o (...)
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  • Enciclopédia de Termos Lógico-Filosóficos.João 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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  • A Paradox for Some Theories of Welfare.Ben Bradley - 2007 - Philosophical Studies 133 (1):45 - 53.
    Sometimes people desire that their lives go badly, take pleasure in their lives going badly, or believe that their lives are going badly. As a result, some popular theories of welfare are paradoxical. I show that no attempt to defend those theories from the paradox fully succeeds.
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  • Disquotation, Conditionals, and the Liar.John Barker - 2009 - Polish Journal of Philosophy 3 (1):5-21.
    In this paper I respond to Jacquette’s criticisms, in (Jacquette, 2008), of my (Barker, 2008). In so doing, I argue that the Liar paradox is in fact a problem about the disquotational schema, and that nothing in Jacquette’s paper undermines this diagnosis.
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  • Truth, Paradox, and Ineffable Propositions.James R. Shaw - 2013 - Philosophy and Phenomenological Research 86 (1):64-104.
    I argue that on very weak assumptions about truth (in particular, that there are coherent norms governing the use of "true"), there is a proposition absolutely inexpressible with conventional language, or something very close. I argue for this claim "constructively": I use a variant of the Berry Paradox to reveal a particular thought for my readership to entertain that very strongly resists conventional expression. I gauge the severity of this expressive limitation within a taxonomy of expressive failures, and argue that (...)
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  • Putnam, Context, and Ontology.Steven Gross - 2004 - Canadian Journal of Philosophy 34 (4):507 - 553.
    When a debate seems intractable, with little agreement as to how one might proceed towards a resolution, it is understandable that philosophers should consider whether something might be amiss with the debate itself. Famously in the last century, philosophers of various stripes explored in various ways the possibility that at least certain philosophical debates are in some manner deficient in sense. Such moves are no longer so much in vogue. For one thing, the particular ways they have been made have (...)
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  • Ontological Pluralism and Notational Variance.Bruno Whittle - 2020 - Oxford Studies in Metaphysics 12:58-72.
    Ontological pluralism is the view that there are different ways to exist. It is a position with deep roots in the history of philosophy, and in which there has been a recent resurgence of interest. In contemporary presentations, it is stated in terms of fundamental languages: as the view that such languages contain more than one quantifier. For example, one ranging over abstract objects, and another over concrete ones. A natural worry, however, is that the languages proposed by the pluralist (...)
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  • Type-Logical Semantics.Reinhard Muskens - 2011 - Routledge Encyclopedia of Philosophy Online.
    Type-logical semantics studies linguistic meaning with the help of the theory of types. The latter originated with Russell as an answer to the paradoxes, but has the additional virtue that it is very close to ordinary language. In fact, type theory is so much more similar to language than predicate logic is, that adopting it as a vehicle of representation can overcome the mismatches between grammatical form and predicate logical form that were observed by Frege and Russell. The grammatical forms (...)
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  • The Limits of Computation.Andrew Powell - forthcoming - Axiomathes:1-21.
    This article provides a survey of key papers that characterise computable functions, but also provides some novel insights as follows. It is argued that the power of algorithms is at least as strong as functions that can be proved to be totally computable in type-theoretic translations of subsystems of second-order Zermelo Fraenkel set theory. Moreover, it is claimed that typed systems of the lambda calculus give rise naturally to a functional interpretation of rich systems of types and to a hierarchy (...)
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  • Foundations of applied mathematics I.Jeffrey Ketland - forthcoming - Synthese:1-43.
    This paper aims to study the foundations of applied mathematics, using a formalized base theory for applied mathematics: \ with atoms, where the subscript used refers to a signature specific to the application. Examples are given, illustrating the following five features of applied mathematics: comprehension principles, application conditionals, representation hypotheses, transfer principles and abstract equivalents.
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  • The Nature of Appearance in Kant’s Transcendentalism: A Seman- Tico-Cognitive Analysis.Sergey L. Katrechko - 2018 - Kantian Journal 37 (3):41-55.
  • The Liar, the Strengthened Liar, and Bivalence.Adam Rieger - 2001 - Erkenntnis 54 (2):195-203.
    A view often expressed is that to classify the liar sentence as neither true nor false is satisfactory for the simple liar but not for the strengthened liar. I argue that in fact it is equally unsatisfactory for both liars. I go on to discuss whether, nevertheless, Kripke''s theory of truth represents an advance on that of Tarski.
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  • The Number of Senses.Kevin C. Klement - 2003 - Erkenntnis 58 (3):303 - 323.
    Many philosophers still countenance senses or meanings in the broadly Fregean vein.However, it is difficult to posit the existence of senses without positing quite a lot ofthem, including at least one presenting every entity in existence. I discuss a number ofCantorian paradoxes that seem to result from an overly large metaphysics of senses, and various possible solutions. Certain more deflationary and non-traditional understandings of senses, and to what extent they fare better in solving the problems, are also discussed. In the (...)
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  • Platitudes Against Paradox.Sven Rosenkranz & Arash Sarkohi - 2006 - Erkenntnis 65 (3):319 - 341.
    We present a strategy to dissolve semantic paradoxes which proceeds from an explanation of why paradoxical sentences or their definitions are semantically defective. This explanation is compatible with the acceptability of impredicative definitions, self-referential sentences and semantically closed languages and leaves the status of the so-called truth-teller sentence unaffected. It is based on platitudes which encode innocuous constraints on successful definition and successful expression of propositional content. We show that the construction of liar paradoxes and of certain versions of Curry’s (...)
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  • A Correspondence Between Martin-Löf Type Theory, the Ramified Theory of Types and Pure Type Systems.Fairouz Kamareddine & Twan Laan - 2001 - Journal of Logic, Language and Information 10 (3):375-402.
    In Russell''s Ramified Theory of Types RTT, two hierarchical concepts dominate:orders and types. The use of orders has as a consequencethat the logic part of RTT is predicative.The concept of order however, is almost deadsince Ramsey eliminated it from RTT. This is whywe find Church''s simple theory of types (which uses the type concept without the order one) at the bottom of the Barendregt Cube rather than RTT. Despite the disappearance of orders which have a strong correlation with predicativity, predicative (...)
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  • Category Mistakes Are Meaningful.Ofra Magidor - 2009 - Linguistics and Philosophy 32 (6):553-581.
    Category mistakes are sentences such as ‘Colourless green ideas sleep furiously’ or ‘The theory of relativity is eating breakfast’. Such sentences are highly anomalous, and this has led a large number of linguists and philosophers to conclude that they are meaningless (call this ‘the meaninglessness view’). In this paper I argue that the meaninglessness view is incorrect and category mistakes are meaningful. I provide four arguments against the meaninglessness view: in Sect. 2, an argument concerning compositionality with respect to category (...)
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  • The Paradoxes and Russell’s Theory of Incomplete Symbols.Kevin C. Klement - 2014 - Philosophical Studies 169 (2):183-207.
    Russell claims in his autobiography and elsewhere that he discovered his 1905 theory of descriptions while attempting to solve the logical and semantic paradoxes plaguing his work on the foundations of mathematics. In this paper, I hope to make the connection between his work on the paradoxes and the theory of descriptions and his theory of incomplete symbols generally clearer. In particular, I argue that the theory of descriptions arose from the realization that not only can a class not be (...)
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  • Russell and the Vicious Circle Principle.Philippe De Rouilhan - 1992 - Philosophical Studies 65 (1/2):169.
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  • The (Metaphysical) Foundations of Arithmetic?Thomas Donaldson - 2017 - Noûs 51 (4):775-801.
    Gideon Rosen and Robert Schwartzkopff have independently suggested (variants of) the following claim, which is a varian of Hume's Principle: -/- When the number of Fs is identical to the number of Gs, this fact is grounded by the fact that there is a one-to-one correspondence between the Fs and Gs. -/- My paper is a detailed critique of the proposal. I don't find any decisive refutation of the proposal. At the same time, it has some consequences which many will (...)
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  • Anomaly and Quantification.James R. Shaw - 2015 - Noûs 49 (1):147-176.
    I argue for two theses about semantically anomalous utterances (more commonly called "category mistakes") like "sequestered slaps reel evergreen rights". First, semantic anomaly generates a unique form of semantically enforced quantifier domain restriction. Second, the best explanation for why anomaly interacts with quantifiers in this way is that anomalous utterances are truth-valueless. After arguing for these points, I trace out two consequences these theses have in semantics and logic. First, I argue they motivate a trivalent semantics on which truth-valueless material (...)
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  • Epistemically Possible Worlds and Propositions.Bruno Whittle - 2009 - Noûs 43 (2):265-285.
    Metaphysically possible worlds have many uses. Epistemically possible worlds promise to be similarly useful, especially in connection with propositions and propositional attitudes. However, I argue that there is a serious threat to the natural accounts of epistemically possible worlds, from a version of Russell’s paradox. I contrast this threat with David Kaplan’s problem for metaphysical possible world semantics: Kaplan’s problem can be straightforwardly rebutted, the problems I raise cannot. I argue that although there may be coherent accounts of epistemically possible (...)
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  • Bateson, Double Description, Todes, and Embodiment: Preparing Activities and Their Relation to Abduction.John Shotter - 2009 - Journal for the Theory of Social Behaviour 39 (2):219-245.
    Does all understanding consist in our using concepts to relate to the things around us, or do we also possess a more direct, spontaneous, bodily way of doing so? I explore this second possibility via Bateson's notion of “double description.” These phenomena are dynamic phenomena, in that they have their existence only in our embodied relations to the temporal unfolding of events in the two or more relevant sources. As such, as Bateson put it, they are of a different “logical (...)
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  • Epistemic Horizons and the Foundations of Quantum Mechanics.Jochen Szangolies - 2018 - Foundations of Physics 48 (12):1669-1697.
    In-principle restrictions on the amount of information that can be gathered about a system have been proposed as a foundational principle in several recent reconstructions of the formalism of quantum mechanics. However, it seems unclear precisely why one should be thus restricted. We investigate the notion of paradoxical self-reference as a possible origin of such epistemic horizons by means of a fixed-point theorem in Cartesian closed categories due to Lawvere that illuminates and unifies the different perspectives on self-reference.
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  • Why Believe Infinite Sets Exist?Andrei Mărăşoiu - 2018 - Axiomathes 28 (4):447-460.
    The axiom of infinity states that infinite sets exist. I will argue that this axiom lacks justification. I start by showing that the axiom is not self-evident, so it needs separate justification. Following Maddy’s :481–511, 1988) distinction, I argue that the axiom of infinity lacks both intrinsic and extrinsic justification. Crucial to my project is Skolem’s From Frege to Gödel: a source book in mathematical logic, 1879–1931, Cambridge, Harvard University Press, pp. 290–301, 1922) distinction between a theory of real sets, (...)
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  • Classes, Why and How.Thomas Schindler - 2019 - Philosophical Studies 176 (2):407-435.
    This paper presents a new approach to the class-theoretic paradoxes. In the first part of the paper, I will distinguish classes from sets, describe the function of class talk, and present several reasons for postulating type-free classes. This involves applications to the problem of unrestricted quantification, reduction of properties, natural language semantics, and the epistemology of mathematics. In the second part of the paper, I will present some axioms for type-free classes. My approach is loosely based on the Gödel–Russell idea (...)
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  • Anatomy of a Proposition.Bjørn Jespersen - 2019 - Synthese 196 (4):1285-1324.
    This paper addresses the mereological problem of the unity of structured propositions. The problem is how to make multiple parts interact such that they form a whole that is ultimately related to truth and falsity. The solution I propose is based on a Platonist variant of procedural semantics. I think of procedures as abstract entities that detail a logical path from input to output. Procedures are modeled on a function/argument logic, but are not functions. Instead they are higher-order, fine-grained structures. (...)
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  • The Forbidden Signs.Mogens Kilstrup - 2016 - Biosemiotics 9 (3):467-483.
    While the field of semiotics has been active since it was started by Peirce, it appears like the last decade has been especially productive with a number of important new concepts being developed within the biosemiotics community. The novel concept of the Semiotic scaffold by Hoffmeyer is an important addition that offers insight into the hardware requirements for bio-semiosis. As any type of semiosis must be dependent upon Semiotic scaffolds, I recently argued that the process of semiosis has to be (...)
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  • On the Number of Types.Miloš Kosterec - 2017 - Synthese 194 (12):5005-5021.
    In this paper, I investigate type theories from several perspectives. First, I present and elaborate the philosophical and technical motivations for these theories. I then offer a formal analysis of various TTs, focusing on the cardinality of the set of types contained in each. I argue that these TTs can be divided into four formal categories, which are derived from the cardinality of the set of their basic elementary types and the finiteness of the lengths of their molecular types. The (...)
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  • Cut-Elimination for Quantified Conditional Logic.Christoph Benzmüller - 2017 - Journal of Philosophical Logic 46 (3):333-353.
    A semantic embedding of quantified conditional logic in classical higher-order logic is utilized for reducing cut-elimination in the former logic to existing results for the latter logic. The presented embedding approach is adaptable to a wide range of other logics, for many of which cut-elimination is still open. However, special attention has to be payed to cut-simulation, which may render cut-elimination as a pointless criterion.
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  • On the Relationship Between Parts and Wholes in Husserl's Phenomenology.Ettore Casari - 2007 - In Luciano Boi, Pierre Kerszberg & Frédéric Patras (eds.), Rediscovering Phenomenology: Phenomenological Essays on Mathematical Beings, Physical Reality, Perception and Consciousness (Phaenomenologica) (English and French Edition). Springer. pp. 67-102.
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  • Hierarchical Propositions.Bruno Whittle - 2017 - Journal of Philosophical Logic 46 (2):215-231.
    The notion of a proposition is central to philosophy. But it is subject to paradoxes. A natural response is a hierarchical account and, ever since Russell proposed his theory of types in 1908, this has been the strategy of choice. But in this paper I raise a problem for such accounts. While this does not seem to have been recognized before, it would seem to render existing such accounts inadequate. The main purpose of the paper, however, is to provide a (...)
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