Search results for 'Oystein Linnebo' (try it on Scholar)

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  1. Oystein Linnebo, Ontology and the Concept of an Object.score: 240.0
    When people deny that there are objects of a certain kind, they normally take this to be a reason to stop speaking as if such objects existed. For instance, when atheists deny the existence of God, they take this to be a reason to stop speaking about God’s will or His mercy. Or, to take a more mundane example, when people deny that there are round squares or that there are unicorns, they take this to be a reason to stop (...)
     
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  2. Oystein Linnebo, To Be is to Be an F 1. Introduction.score: 240.0
    Is the natural number 3 identical with the Roman emperor Julius Caesar? In Grundlagen Frege raised some peculiar questions of this sort.1 There are two kinds of intuitions regarding such questions. On the one hand, these questions seem not only to be pointless but to be downright meaningless. Regardless of how much arithmetic one studies, no answer to the opening question will be forthcoming. Arithmetic tells us that 3 is the successor of 2 and that it is prime, but not (...)
     
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  3. Øystein Linnebo & David Nicolas (2008). Superplurals in English. Analysis 68 (299):186–197.score: 60.0
    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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  4. Øystein Linnebo (2006). Epistemological Challenges to Mathematical Platonism. Philosophical Studies 129 (3):545-574.score: 30.0
    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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  5. Øystein Linnebo (2010). Pluralities and Sets. Journal of Philosophy 107 (3):144-164.score: 30.0
    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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  6. James Ladyman, Øystein Linnebo & Richard Pettigrew (2012). Identity and Discernibility in Philosophy and Logic. Review of Symbolic Logic 5 (1):162-186.score: 30.0
    Questions about the relation between identity and discernibility are important both in philosophy and in model theory. We show how a philosophical question about identity and dis- cernibility can be ‘factorized’ into a philosophical question about the adequacy of a formal language to the description of the world, and a mathematical question about discernibility in this language. We provide formal definitions of various notions of discernibility and offer a complete classification of their logical relations. Some new and surprising facts are (...)
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  7. Øystein Linnebo & Richard Pettigrew (2011). Category Theory as an Autonomous Foundation. Philosophia Mathematica 19 (3):227-254.score: 30.0
    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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  8. Øystein Linnebo (2008). Structuralism and the Notion of Dependence. Philosophical Quarterly 58 (230):59-79.score: 30.0
    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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  9. Øystein Linnebo (2012). Review of P. Maddy, Defending the Axioms: On the Philosophical Foundations of Set Theory. [REVIEW] Philosophy 87 (01):133-137.score: 30.0
  10. Øystein Linnebo (2008). The Nature of Mathematical Objects. In Bonnie Gold & Roger Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematical Association of America. 205--219.score: 30.0
    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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  11. Øystein Linnebo (2012). Metaontological Minimalism. Philosophy Compass 7 (2):139-151.score: 30.0
    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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  12. Øystein Linnebo (2009). Platonism in the Philosophy of Mathematics. In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy.score: 30.0
    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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  13. Øystein Linnebo (2003). Plural Quantification Exposed. Noûs 37 (1):71–92.score: 30.0
  14. Øystein Linnebo (2009). Bad Company Tamed. Synthese 170 (3):371 - 391.score: 30.0
    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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  15. Øystein Linnebo, Plural Quantification. Stanford Encyclopedia of Philosophy.score: 30.0
    Ordinary English contains different forms of quantification over objects. In addition to the usual singular quantification, as in 'There is an apple on the table', there is plural quantification, as in 'There are some apples on the table'. Ever since Frege, formal logic has favored the two singular quantifiers ∀x and ∃x over their plural counterparts ∀xx and ∃xx (to be read as for any things xx and there are some things xx). But in recent decades it has been argued (...)
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  16. Øystein Linnebo (2003). Frege's Conception of Logic: From Kant to Grundgesetze. Manuscrito 26 (2):235-252.score: 30.0
    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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  17. Øystein Linnebo (2007). Burgess on Plural Logic and Set Theory. Philosophia Mathematica 15 (1):79-93.score: 30.0
    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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  18. Øystein Linnebo & Agustín Rayo (2012). Hierarchies Ontological and Ideological. Mind 121 (482):269 - 308.score: 30.0
    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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  19. Øystein Linnebo (2009). The Individuation of the Natural Numbers. In Otavio Bueno & Øystein Linnebo (eds.), New Waves in Philosophy of Mathematics. Palgrave.score: 30.0
    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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  20. Øystein Linnebo (2009). Introduction. Synthese 170 (3):321-329.score: 30.0
    Neo-Fregean logicism seeks to base mathematics on abstraction principles. But the acceptable abstraction principles are surrounded by unacceptable (indeed often paradoxical) ones. This is the “bad company problem.” In this introduction I first provide a brief historical overview of the problem. Then I outline the main responses that are currently being debated. In the course of doing so I provide summaries of the contributions to this special issue.
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  21. Øystein Linnebo (2009). Frege's Context Principle and Reference to Natural Numbers. In Sten Lindström (ed.), Logicism, Intuitionism, and Formalism: What Has Become of Them. Springer.score: 30.0
    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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  22. Øystein Linnebo (2004). Predicative Fragments of Frege Arithmetic. Bulletin of Symbolic Logic 10 (2):153-174.score: 30.0
    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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  23. Øystein Linnebo & Gabriel Uzquiano (2009). Which Abstraction Principles Are Acceptable? Some Limitative Results. British Journal for the Philosophy of Science 60 (2):239-252.score: 30.0
    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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  24. Øystein Linnebo (2013). What is the Infinite? The Philosophers' Magazine 61 (61):42-47.score: 30.0
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  25. Øystein Linnebo & F. A. Muller (2013). On Witness-Discernibility of Elementary Particles. Erkenntnis 78 (5):1133-1142.score: 30.0
    In the context of discussions about the nature of ‘identical particles’ and the status of Leibniz’s Principle of the Identity of Indiscernibles in Quantum Mechanics, a novel kind of physical discernibility has recently been proposed, which we call witness-discernibility. We inquire into how witness-discernibility relates to known kinds of discernibility. Our conclusion will be that for a wide variety of cases, including the intended quantum-mechanical ones, witness-discernibility collapses extensionally to absolute discernibility, that is, to discernibility by properties.
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  26. Øystein Linnebo (2012). Reference by Abstraction. Proceedings of the Aristotelian Society 112 (1pt1):45-71.score: 30.0
    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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  27. Øystein Linnebo (2005). To Be is to Be an F. Dialectica 59 (2):201–222.score: 30.0
  28. Øystein Linnebo (2007). Modality and Tense: Philosophical Papers – Kit Fine. Philosophical Quarterly 57 (227):294–297.score: 30.0
  29. Øystein Linnebo (2006). Sets, Properties, and Unrestricted Quantification. In Gabriel Uzquiano & Agustin Rayo (eds.), Absolute Generality. Oxford University Press.score: 30.0
    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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  30. Øystein Linnebo (2004). Frege's Proof of Referentiality. Notre Dame Journal of Formal Logic 45 (2):73-98.score: 30.0
    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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  31. Øystein Linnebo (2001). Reason's Nearest Kin. Michael Potter. Mind 110 (439):810-813.score: 30.0
  32. Øystein Linnebo (2010). Some Criteria for Acceptable Abstraction. Notre Dame Journal of Formal Logic 52 (3):331-338.score: 30.0
    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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  33. Øystein Linnebo (2004). The Limits of Abstraction. Australasian Journal of Philosophy 82 (4):653 – 656.score: 30.0
    Book Information The Limits of Abstraction. The Limits of Abstraction Kit Fine , Oxford : Clarendon Press , 2002 , x + 203 , £18.99 (cloth). By Kit Fine. Clarendon Press. Oxford. Pp. x + 203. £18.99 (cloth).
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  34. Øystein Linnebo & Agustín Rayo (2014). Reply to Florio and Shapiro. Mind 123 (489):175-181.score: 30.0
    Florio and Shapiro take issue with an argument in ‘Hierarchies Ontological and Ideological’ for the conclusion that the set-theoretic hierarchy is open-ended. Here we clarify and reinforce the argument in light of their concerns.
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  35. Øystein Linnebo (forthcoming). Platonism in the Philosophy of Mathematics. Stanford Encyclopedia of Philosophy.score: 30.0
    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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  36. O. Linnebo (2003). Stewart Shapiro. Philosophy of Mathematics: Structure and Ontology. Philosophia Mathematica 11 (1):92-103.score: 30.0
  37. Øystein Linnebo (2014). 'Just Is'-Statements as Generalized Identities. 57 (4):466-482.score: 30.0
    (2014). ‘Just is’-Statements as Generalized Identities. Inquiry: Vol. 57, The Construction of Logical Space, pp. 466-482. doi: 10.1080/0020174X.2014.905037.
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  38. Øystein Linnebo (2006). Mending the Master: John P. Burgess, Fixing Frege. Princeton, N. J.: Princeton University Press, 2005. ISBN 0-691-12231-8. Pp. XII + 257. [REVIEW] Philosophia Mathematica 14 (3):338-400.score: 30.0
  39. Øystein Linnebo (2000). Early Analytic Philosophy. Philosophical Review 109 (1):98-101.score: 30.0
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  40. O. Linnebo (2000). Early Analytic Philosophy: Frege, Russell, Wittgenstein. Philosophical Review 109 (1):98-101.score: 30.0
  41. Øystein Linnebo (2006). Mending the Master (Critical Notice of John Burgess's Fixing Frege). Philosophia Mathematica 14 (3):338-351.score: 30.0
    Fixing Frege is one of the most important investigations to date of Fregean approaches to the foundations of mathematics. In addition to providing an unrivalled survey of the technical program to which Frege’s writings have given rise, the book makes a large number of improvements and clarifications. Anyone with an interest in the philosophy of mathematics will enjoy and benefit from the careful and well informed overview provided by the first of its three chapters. Specialists will find the book an (...)
     
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  42. James Ladyman, Øystein Linnebo & Tomasz Bigaj (2013). Entanglement and Non-Factorizability. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44 (3):215-221.score: 30.0
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  43. Øystein Linnebo (2003). Critical Studies/Book Reviews. Philosophia Mathematica 11 (1):92-104.score: 30.0
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  44. Øystein Linnebo (2009). Thin Objects. In. In Hieke Alexander & Leitgeb Hannes (eds.), Reduction, Abstraction, Analysis. Ontos Verlag. 11--227.score: 30.0
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  45. Øystein Linnebo (2009). New Model Naturalism. Metascience 18 (3):433-436.score: 30.0
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  46. O. Linnebo & R. Pettigrew (forthcoming). Two Types of Abstraction for Structuralism. Philosophical Quarterly.score: 30.0
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  47. Øystein Linnebo (2008). Review: Fraser MacBride (Ed.): Identity and Modality. [REVIEW] Mind 117 (467):705-708.score: 30.0
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  48. O. Linnebo (2008). Review: Fraser MacBride (Ed.): Identity and Modality. [REVIEW] Mind 117 (467):705-708.score: 30.0
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  49. Otávio Bueno & Øystein Linnebo (eds.) (2009). New Waves in Philosophy of Mathematics. Palgrave Macmillan.score: 30.0
    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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  50. J. C. C. McKinsey (1943). Review: Oystein Ore, Theory of Equivalence Relations. [REVIEW] Journal of Symbolic Logic 8 (1):55-56.score: 15.0
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