Results for '��Ystein Linnebo'

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  1.  16
    Øystein Linnebo.*Thin Objects.Thomas Donaldson - 2020 - Philosophia Mathematica 28 (2):258-263.
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  2.  14
    Øystein Linnebo, Philosophy of mathematics, Princeton University Press, 2017, pp. 216, € 29.00, ISBN 978-0691161402. [REVIEW]Filippo Mancini - 2019 - Universa. Recensioni di Filosofia 8.
    La matematica viene generalmente considerata uno degli ambiti più affidabili dell’intera impresa scientifica. Il suo successo e la sua solidità sono testimoniati, ad esempio, dall’uso imprescindibile che ne fanno le scienze empiriche e dall’accordo pressoché unanime con cui la comunità dei matematici delibera sulla validità di un nuovo risultato. Tuttavia, dal punto di vista filosofico la matematica rappresenta un puzzle tanto intrigante quanto intricato. Philosophy of Mathematics di Ø. Linnebo si propone di presentare e discutere le concezioni filosofiche della (...)
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  3.  84
    Review of Øystein Linnebo, Thin Objects.Thomas Donaldson - forthcoming - Philosophia Mathematica:6.
    A brief review of Øystein Linnebo's Thin Objects. The review ends with a brief discussion of cardinal number and metaphysical ground.
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  4.  37
    Reply to Øystein Linnebo and Stewart Shapiro.Ian Rumfitt - 2019 - Inquiry: An Interdisciplinary Journal of Philosophy 62 (7):842-858.
    ABSTRACTIn reply to Linnebo, I defend my analysis of Tait's argument against the use of classical logic in set theory, and make some preliminary comments on Linnebo's new argument for the same conclusion. I then turn to Shapiro's discussion of intuitionistic analysis and of Smooth Infinitesimal Analysis. I contend that we can make sense of intuitionistic analysis, but only by attaching deviant meanings to the connectives. Whether anyone can make sense of SIA is open to doubt: doing so (...)
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  5.  28
    Øystein Linnebo*. Philosophy of Mathematics. [REVIEW]Gregory Lavers - 2018 - Philosophia Mathematica 26 (3):413-417.
    Øystein Linnebo*. Philosophy of Mathematics. Princeton University Press, 2017. ISBN: 978-0-691-16140-2 ; 978-1-40088524-4. Pp. xviii + 203.
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  6. Bad Company Tamed.Øystein Linnebo - 2009 - Synthese 170 (3):371 - 391.
    The neo-Fregean project of basing mathematics on abstraction principles faces “the bad company problem,” namely that a great variety of unacceptable abstraction principles are mixed in among the acceptable ones. In this paper I propose a new solution to the problem, based on the idea that individuation must take the form of a well-founded process. A surprising aspect of this solution is that every form of abstraction on concepts is permissible and that paradox is instead avoided by restricting what concepts (...)
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  7.  46
    Thin Objects: An Abstractionist Account, by Øystein Linnebo.J. P. Studd - 2020 - Mind 129 (514):646-656.
    Thin Objects: Anionist Account, by LinneboØystein. Oxford: Oxford University Press, 2018. Pp. xviii + 238.
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  8.  77
    Cardinality and Acceptable Abstraction.Roy T. Cook & Øystein Linnebo - 2018 - Notre Dame Journal of Formal Logic 59 (1):61-74.
    It is widely thought that the acceptability of an abstraction principle is a feature of the cardinalities at which it is satisfiable. This view is called into question by a recent observation by Richard Heck. We show that a fix proposed by Heck fails but we analyze the interesting idea on which it is based, namely that an acceptable abstraction has to “generate” the objects that it requires. We also correct and complete the classification of proposed criteria for acceptable abstraction.
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  9.  76
    The Modal Logic of Set-Theoretic Potentialism and the Potentialist Maximality Principles.Joel David Hamkins & Øystein Linnebo - forthcoming - Review of Symbolic Logic:1-36.
  10.  15
    Modality and Tense: Philosophical Papers.Øystein Linnebo - 2007 - Philosophical Quarterly 57 (227):294-297.
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  11.  46
    Thin Objects.Øystein Linnebo - 2018 - Oxford: Oxford University Press.
    Are there objects that are “thin” in the sense that their existence does not make a substantial demand on the world? Frege famously thought so. He claimed that the equinumerosity of the knives and the forks suffices for there to be objects such as the number of knives and the number of forks, and for these objects to be identical. The idea of thin objects holds great philosophical promise but has proved hard to explicate. This book attempts to develop the (...)
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  12.  13
    New Waves in Philosophy of Mathematics.Otávio Bueno & Øystein Linnebo (eds.) - 2009 - Palgrave-Macmillan.
    Thirteen up-and-coming researchers in the philosophy of mathematics have been invited to write on what they take to be the right philosophical account of mathematics, examining along the way where they think the philosophy of mathematics is and ought to be going. A rich and diverse picture emerges. Some broader tendencies can nevertheless be detected: there is increasing attention to the practice, language and psychology of mathematics, a move to reassess the orthodoxy, as well as inspiration from philosophical logic.
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  13. The Potential Hierarchy of Sets.Øystein Linnebo - 2013 - Review of Symbolic Logic 6 (2):205-228.
    Some reasons to regard the cumulative hierarchy of sets as potential rather than actual are discussed. Motivated by this, a modal set theory is developed which encapsulates this potentialist conception. The resulting theory is equi-interpretable with Zermelo Fraenkel set theory but sheds new light on the set-theoretic paradoxes and the foundations of set theory.
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  14. Pluralities and Sets.Øystein Linnebo - 2010 - Journal of Philosophy 107 (3):144-164.
    Say that some things form a set just in case there is a set whose members are precisely the things in question. For instance, all the inhabitants of New York form a set. So do all the stars in the universe. And so do all the natural numbers. Under what conditions do some things form a set?
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  15.  19
    A Partisan Introduction to the Philosophy of Mathematics: Øystein Linnebo: Philosophy of Mathematics. Princeton: Princeton University Press, 2017, 216pp, $29.95 HB. [REVIEW]Michael Shaffer - 2019 - Metascience 28 (1):73-75.
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  16. Actual and Potential Infinity.Øystein Linnebo & Stewart Shapiro - 2019 - Noûs 53 (1):160-191.
    The notion of potential infinity dominated in mathematical thinking about infinity from Aristotle until Cantor. The coherence and philosophical importance of the notion are defended. Particular attention is paid to the question of whether potential infinity is compatible with classical logic or requires a weaker logic, perhaps intuitionistic.
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  17. Hierarchies Ontological and Ideological.Øystein Linnebo & Agustin Rayo - 2012 - Mind 121 (482):269 - 308.
    Gödel claimed that Zermelo-Fraenkel set theory is 'what becomes of the theory of types if certain superfluous restrictions are removed'. The aim of this paper is to develop a clearer understanding of Gödel's remark, and of the surrounding philosophical terrain. In connection with this, we discuss some technical issues concerning infinitary type theories and the programme of developing the semantics for higher-order languages in other higher-order languages.
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  18. Superplurals in English.Øystein Linnebo & David Nicolas - 2008 - Analysis 68 (3):186–197.
    where ‘aa’ is a plural term, and ‘F’ a plural predicate. Following George Boolos (1984) and others, many philosophers and logicians also think that plural expressions should be analysed as not introducing any new ontological commitments to some sort of ‘plural entities’, but rather as involving a new form of reference to objects to which we are already committed (for an overview and further details, see Linnebo 2004). For instance, the plural term ‘aa’ refers to Alice, Bob and Charlie (...)
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  19.  72
    Modality and Tense. Philosophical Papers. [REVIEW]Øystein Linnebo - 2006 - Tijdschrift Voor Filosofie 68 (2):408-409.
    Kit Fine has since the 1970s been one of the leading contributors to work at the intersection of logic and metaphysics. This is his eagerly-awaited first book in the area. It draws together a series of essays, three of them previously unpublished, on possibility, necessity, and tense. These puzzling aspects of the way the world is have been the focus of considerable philosophical attention in recent decades. A helpful introduction orients the reader and offers a way into some of the (...)
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  20. On the Innocence and Determinacy of Plural Quantification.Salvatore Florio & Øystein Linnebo - 2016 - Noûs 50 (3):565–583.
    Plural logic is widely assumed to have two important virtues: ontological innocence and determinacy. It is claimed to be innocent in the sense that it incurs no ontological commitments beyond those already incurred by the first-order quantifiers. It is claimed to be determinate in the sense that it is immune to the threat of non-standard interpretations that confronts higher-order logics on their more traditional, set-based semantics. We challenge both claims. Our challenge is based on a Henkin-style semantics for plural logic (...)
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  21. Structuralism and the Notion of Dependence.Øystein Linnebo - 2008 - Philosophical Quarterly 58 (230):59-79.
    This paper has two goals. The first goal is to show that the structuralists’ claims about dependence are more significant to their view than is generally recognized. I argue that these dependence claims play an essential role in the most interesting and plausible characterization of this brand of structuralism. The second goal is to defend a compromise view concerning the dependence relations that obtain between mathematical objects. Two extreme views have tended to dominate the debate, namely the view that all (...)
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  22.  2
    Philosophy of Mathematics.Øystein Linnebo - 2017 - Princeton, NJ: Princeton University Press.
    Mathematics is one of the most successful human endeavors—a paradigm of precision and objectivity. It is also one of our most puzzling endeavors, as it seems to deliver non-experiential knowledge of a non-physical reality consisting of numbers, sets, and functions. How can the success and objectivity of mathematics be reconciled with its puzzling features, which seem to set it apart from all the usual empirical sciences? This book offers a short but systematic introduction to the philosophy of mathematics. Readers are (...)
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  23. Epistemological Challenges to Mathematical Platonism.Øystein Linnebo - 2006 - Philosophical Studies 129 (3):545-574.
    Since Benacerraf’s “Mathematical Truth” a number of epistemological challenges have been launched against mathematical platonism. I first argue that these challenges fail because they unduely assimilate mathematics to empirical science. Then I develop an improved challenge which is immune to this criticism. Very roughly, what I demand is an account of how people’s mathematical beliefs are responsive to the truth of these beliefs. Finally I argue that if we employ a semantic truth-predicate rather than just a deflationary one, there surprisingly (...)
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  24.  41
    The Generous Ontology of Thin Objects: Øystein Linnebo: Thin Objects: An Abstractionist Account. New York: Oxford University Press, Xvii + 231 Pp, $50.00 HB. [REVIEW]Nathaniel Gan - 2019 - Metascience 28 (1):167-169.
  25. Plural Quantification Exposed.Øystein Linnebo - 2003 - Noûs 37 (1):71–92.
    This paper criticizes George Boolos's famous use of plural quantification to argue that monadic second-order logic is pure logic. I deny that plural quantification qualifies as pure logic and express serious misgivings about its alleged ontological innocence. My argument is based on an examination of what is involved in our understanding of the impredicative plural comprehension schema.
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  26. Two Types of Abstraction for Structuralism.Øystein Linnebo & Richard Pettigrew - 2014 - Philosophical Quarterly 64 (255):267-283.
    If numbers were identified with any of their standard set-theoretic realizations, then they would have various non-arithmetical properties that mathematicians are reluctant to ascribe to them. Dedekind and later structuralists conclude that we should refrain from ascribing to numbers such ‘foreign’ properties. We first rehearse why it is hard to provide an acceptable formulation of this conclusion. Then we investigate some forms of abstraction meant to purge mathematical objects of all ‘foreign’ properties. One form is inspired by Frege; the other (...)
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  27. Platonism in the Philosophy of Mathematics.Øystein Linnebo - 2009 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy.
    Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices. In this survey article, the view is clarified and distinguished from some related views, and arguments for and against the view are discussed.
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  28. Platonism in the Philosophy of Mathematics.Øystein Linnebo - forthcoming - Stanford Encyclopedia of Philosophy.
    Platonism about mathematics (or mathematical platonism) isthe metaphysical view that there are abstract mathematical objectswhose existence is independent of us and our language, thought, andpractices. Just as electrons and planets exist independently of us, sodo numbers and sets. And just as statements about electrons and planetsare made true or false by the objects with which they are concerned andthese objects' perfectly objective properties, so are statements aboutnumbers and sets. Mathematical truths are therefore discovered, notinvented., Existence. There are mathematical objects.
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  29. Plurals and Modals.Øystein Linnebo - 2016 - Canadian Journal of Philosophy 46 (4-5):654-676.
    Consider one of several things. Is the one thing necessarily one of the several? This key question in the modal logic of plurals is clarified. Some defenses of an affirmative answer are developed and compared. Various remarks are made about the broader philosophical significance of the question.
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  30. Category Theory as an Autonomous Foundation.Øystein Linnebo & Richard Pettigrew - 2011 - Philosophia Mathematica 19 (3):227-254.
    Does category theory provide a foundation for mathematics that is autonomous with respect to the orthodox foundation in a set theory such as ZFC? We distinguish three types of autonomy: logical, conceptual, and justificatory. Focusing on a categorical theory of sets, we argue that a strong case can be made for its logical and conceptual autonomy. Its justificatory autonomy turns on whether the objects of a foundation for mathematics should be specified only up to isomorphism, as is customary in other (...)
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  31. III-Reference by Abstraction.ØYstein Linnebo - 2012 - Proceedings of the Aristotelian Society 112 (1pt1):45-71.
    Frege suggests that criteria of identity should play a central role in the explanation of reference, especially to abstract objects. This paper develops a precise model of how we can come to refer to a particular kind of abstract object, namely, abstract letter types. It is argued that the resulting abstract referents are ‘metaphysically lightweight’.
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  32. Predicative Fragments of Frege Arithmetic.Øystein Linnebo - 2004 - Bulletin of Symbolic Logic 10 (2):153-174.
    Frege Arithmetic (FA) is the second-order theory whose sole non-logical axiom is Hume’s Principle, which says that the number of F s is identical to the number of Gs if and only if the F s and the Gs can be one-to-one correlated. According to Frege’s Theorem, FA and some natural definitions imply all of second-order Peano Arithmetic. This paper distinguishes two dimensions of impredicativity involved in FA—one having to do with Hume’s Principle, the other, with the underlying second-order logic—and (...)
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  33. Metaontological Minimalism.Øystein Linnebo - 2012 - Philosophy Compass 7 (2):139-151.
    Can there be objects that are ‘thin’ in the sense that very little is required for their existence? A number of philosophers have thought so. For instance, many Fregeans believe it suffices for the existence of directions that there be lines standing in the relation of parallelism; other philosophers believe it suffices for a mathematical theory to have a model that the theory be coherent. This article explains the appeal of thin objects, discusses the three most important strategies for articulating (...)
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  34. ‘Just is’-Statements as Generalized Identities.Øystein Linnebo - 2014 - Inquiry: An Interdisciplinary Journal of Philosophy 57 (4):466-482.
    Identity is ordinarily taken to be a relation defined on all and only objects. This consensus is challenged by Agustín Rayo, who seeks to develop an analogue of the identity sign that can be flanked by sentences. This paper is a critical exploration of the attempted generalization. First the desired generalization is clarified and analyzed. Then it is argued that there is no notion of content that does the desired philosophical job, namely ensure that necessarily equivalent sentences coincide in this (...)
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  35. Frege Meets Brouwer.Stewart Shapiro & Øystein Linnebo - 2015 - Review of Symbolic Logic 8 (3):540-552.
    We show that, by choosing definitions carefully, a version of Frege's theorem can be proved in intuitionistic logic.
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  36. Sets, Properties, and Unrestricted Quantification.Øystein Linnebo - 2006 - In Gabriel Uzquiano & Agustin Rayo (eds.), Absolute Generality. Oxford University Press.
    Call a quantifier unrestricted if it ranges over absolutely all things: not just over all physical things or all things relevant to some particular utterance or discourse but over absolutely everything there is. Prima facie, unrestricted quantification seems to be perfectly coherent. For such quantification appears to be involved in a variety of claims that all normal human beings are capable of understanding. For instance, some basic logical and mathematical truths appear to involve unrestricted quantification, such as the truth that (...)
     
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  37. Some Criteria for Acceptable Abstraction.Øystein Linnebo - 2011 - Notre Dame Journal of Formal Logic 52 (3):331-338.
    Which abstraction principles are acceptable? A variety of criteria have been proposed, in particular irenicity, stability, conservativeness, and unboundedness. This note charts their logical relations. This answers some open questions and corrects some old answers.
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  38. Aristotelian Continua.Øystein Linnebo, Stewart Shapiro & Geoffrey Hellman - 2016 - Philosophia Mathematica 24 (2):214-246.
    In previous work, Hellman and Shapiro present a regions-based account of a one-dimensional continuum. This paper produces a more Aristotelian theory, eschewing the existence of points and the use of infinite sets or pluralities. We first show how to modify the original theory. There are a number of theorems that have to be added as axioms. Building on some work by Linnebo, we then show how to take the ‘potential’ nature of the usual operations seriously, by using a modal (...)
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  39.  40
    Riemann’s Scale: A Puzzle About Infinity.Øystein Linnebo - forthcoming - Erkenntnis:1-3.
    Ordinarily, the order in which some objects are attached to a scale does not affect the total weight measured by the scale. This principle is shown to fail in certain cases involving infinitely many objects. In these cases, we can produce any desired reading of the scale merely by changing the order in which a fixed collection of objects are attached to the scale. This puzzling phenomenon brings out the metaphysical significance of a theorem about infinite series that is well (...)
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  40.  18
    Early Analytic Philosophy: Frege, Russell, Wittgenstein.Øystein Linnebo - 2000 - Philosophical Review 109 (1):98-101.
    Analytic philosophy has traditionally been little concerned with the history of philosophy, including that of analytic philosophy itself. But in recent years the study of the early period of the analytic tradition has become an active and lively branch of Anglo-American philosophy. Early Analytic Philosophy, a collection of papers presented in honor of professor Leonard Linsky at the University of Chicago in April 1992, is an example of this. The contributors, many of them leading scholars in the field of early (...)
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  41. Which Abstraction Principles Are Acceptable? Some Limitative Results.Øystein Linnebo & Gabriel Uzquiano - 2009 - British Journal for the Philosophy of Science 60 (2):239-252.
    Neo-Fregean logicism attempts to base mathematics on abstraction principles. Since not all abstraction principles are acceptable, the neo-Fregeans need an account of which ones are. One of the most promising accounts is in terms of the notion of stability; roughly, that an abstraction principle is acceptable just in case it is satisfiable in all domains of sufficiently large cardinality. We present two counterexamples to stability as a sufficient condition for acceptability and argue that these counterexamples can be avoided only by (...)
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  42. Thin Objects.Øystein Linnebo - 2009 - In Hieke Alexander & Leitgeb Hannes (eds.), Reduction, Abstraction, Analysis. Ontos Verlag. pp. 11--227.
  43. Øystein Vs Archimedes: A Note on Linnebo’s Infinite Balance.Daniel Hoek - forthcoming - Erkenntnis:1-6.
    Using Riemann’s Rearrangement Theorem, Øystein Linnebo (2020) argues that, if it were possible to apply an infinite positive weight and an infinite negative weight to a working scale, the resulting net weight could end up being any real number, depending on the procedure by which these weights are applied. Appealing to the First Postulate of Archimedes’ treatise on balance, I argue instead that the scale would always read 0 kg. Along the way, we stop to consider an infinitely jittery (...)
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  44. Term Models for Abstraction Principles.Leon Horsten & Øystein Linnebo - 2016 - Journal of Philosophical Logic 45 (1):1-23.
    Kripke’s notion of groundedness plays a central role in many responses to the semantic paradoxes. Can the notion of groundedness be brought to bear on the paradoxes that arise in connection with abstraction principles? We explore a version of grounded abstraction whereby term models are built up in a ‘grounded’ manner. The results are mixed. Our method solves a problem concerning circularity and yields a ‘grounded’ model for the predicative theory based on Frege’s Basic Law V. However, the method is (...)
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  45. Frege's Proof of Referentiality.Øystein Linnebo - 2004 - Notre Dame Journal of Formal Logic 45 (2):73-98.
    I present a novel interpretation of Frege’s attempt at Grundgesetze I §§29-31 to prove that every expression of his language has a unique reference. I argue that Frege’s proof is based on a contextual account of reference, similar to but more sophisticated than that enshrined in his famous Context Principle. Although Frege’s proof is incorrect, I argue that the account of reference on which it is based is of potential philosophical value, and I analyze the class of cases to which (...)
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  46. The Individuation of the Natural Numbers.Øystein Linnebo - 2009 - In Otavio Bueno & Øystein Linnebo (eds.), New Waves in Philosophy of Mathematics. Palgrave.
    It is sometimes suggested that criteria of identity should play a central role in an account of our most fundamental ways of referring to objects. The view is nicely illustrated by an example due to (Quine, 1950). Suppose you are standing at the bank of a river, watching the water that floats by. What is required for you to refer to the river, as opposed to a particular segment of it, or the totality of its water, or the current temporal (...)
     
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  47. Frege's Conception of Logic: From Kant to Grundgesetze.Øystein Linnebo - 2003 - Manuscrito 26 (2):235-252.
    I shall make two main claims. My first main claim is that Frege started out with a view of logic that is closer to Kant’s than is generally recognized, but that he gradually came to reject this Kantian view, or at least totally to transform it. My second main claim concerns Frege’s reasons for distancing himself from the Kantian conception of logic. It is natural to speculate that this change in Frege’s view of logic may have been spurred by a (...)
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  48. Frege's Context Principle and Reference to Natural Numbers.Øystein Linnebo - 2009 - In Sten Lindström (ed.), Logicism, Intuitionism, and Formalism: What Has Become of Them. Springer.
    Frege proposed that his Context Principle—which says that a word has meaning only in the context of a proposition—can be used to explain reference, both in general and to mathematical objects in particular. I develop a version of this proposal and outline answers to some important challenges that the resulting account of reference faces. Then I show how this account can be applied to arithmetic to yield an explanation of our reference to the natural numbers and of their metaphysical status.
     
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  49. Burgess on Plural Logic and Set Theory.Øystein Linnebo - 2007 - Philosophia Mathematica 15 (1):79-93.
    John Burgess in a 2004 paper combined plural logic and a new version of the idea of limitation of size to give an elegant motivation of the axioms of ZFC set theory. His proposal is meant to improve on earlier work by Paul Bernays in two ways. I argue that both attempted improvements fail. I am grateful to Philip Welch, two anonymous referees, and especially Ignacio Jané for written comments on earlier versions of this paper, which have led to substantial (...)
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  50. The Nature of Mathematical Objects.Øystein Linnebo - 2008 - In Bonnie Gold & Roger Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematical Association of America. pp. 205--219.
    On the face of it, platonism seems very far removed from the scientific world view that dominates our age. Nevertheless many philosophers and mathematicians believe that modern mathematics requires some form of platonism. The defense of mathematical platonism that is both most direct and has been most influential in the analytic tradition in philosophy derives from the German logician-philosopher Gottlob Frege (1848-1925).2 I will therefore refer to it as Frege’s argument. This argument is part of the background of any contemporary (...)
     
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