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Abstract Objects

Edited by Sam Cowling (Denison University)
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  1. David J. Anderson & Edward N. Zalta (2004). Frege, Boolos, and Logical Objects. Journal of Philosophical Logic 33 (1):1-26.
    In this paper, the authors discuss Frege's theory of "logical objects" and the recent attempts to rehabilitate it. We show that the 'eta' relation George Boolos deployed on Frege's behalf is similar, if not identical, to the encoding mode of predication that underlies the theory of abstract objects. Whereas Boolos accepted unrestricted Comprehension for Properties and used the 'eta' relation to assert the existence of logical objects under certain highly restricted conditions, the theory of abstract objects uses unrestricted Comprehension for (...)
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  2. Dimitri Z. Andriopoulos (1972). Is Michelis a ‘Platonist’? British Journal of Aesthetics 12 (4):395-402.
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  3. István Aranyosi (2011). The Solo Numero Paradox. American Philosophical Quarterly 48 (4):347.
    Leibniz notoriously insisted that no two individuals differ solo numero, that is, by being primitively distinct, without differing in some property. The details of Leibniz’s own way of understanding and defending the principle –known as the principle of identity of indiscernibles (henceforth ‘the Principle’)—is a matter of much debate. However, in contemporary metaphysics an equally notorious and discussed issue relates to a case put forward by Max Black (1952) as a counter-example to any necessary and non-trivial version of the principle. (...)
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  4. David M. Armstrong (2003). Resemblance Nominalism: A Solution to the Problem of Universals. Australasian Journal of Philosophy 81 (2):285-286.
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  5. Keith Augustine (2001). A Defense of Naturalism. Dissertation, University of Maryland, College Park
    The first part of this essay discusses what naturalism in the philosophy of religion should entail for one's ontology, considers various proposed criteria for categorizing something as natural, uses an analysis of these proposed criteria to develop theoretical criteria for both the natural and nonnatural, and develops a set of criteria for identifying a potentially supernatural event in practice. The second part of the essay presents a persuasive empirical case for naturalism based on the lack of uncontroversial evidence for any (...)
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  6. Bruce Aune (1973). On Postulating Universals. Canadian Journal of Philosophy 3 (2):285 - 294.
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  7. D. M. Azraf (1958). The Nature of Universals. Pakistan Philosophical Journal 2 (1):60.
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  8. Jody Azzouni (2015). Why Deflationary Nominalists Shouldn’T Be Agnostics. Philosophical Studies 172 (5):1143-1161.
    A feature of agnostic views—views that officially express ignorance about the existence of something —is that they are widely perceived to be epistemically more cautious than views that are committed to the entities in question. This is often seen as giving agnostics a debating advantage: all things being equal, fence-sitters have smaller argumentative burdens. Otávio Bueno argues in this way for what he calls “agnostic nominalism,” the view that we don’t know whether ontologically-independent Platonic objects exist. I show that agnostic (...)
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  9. John Bacon (1986). Abstract Objects: An Introduction to Axiomatic Metaphysics by Edward N. Zalta. Critical Philosophy 3 (3):218.
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  10. Bogdan Bakies (1982). Between the Concretist and Abstract Concepts of Being. Roczniki Filozoficzne 30 (1):91.
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  11. Mark Balaguer (2008). Fictionalism in the Philosophy of Mathematics. Stanford Encyclopedia of Philosophy.
    Mathematical fictionalism (or as I'll call it, fictionalism) is best thought of as a reaction to mathematical platonism. Platonism is the view that (a) there exist abstract mathematical objects (i.e., nonspatiotemporal mathematical objects), and (b) our mathematical sentences and theories provide true descriptions of such objects. So, for instance, on the platonist view, the sentence ‘3 is prime’ provides a straightforward description of a certain object—namely, the number 3—in much the same way that the sentence ‘Mars is red’ provides a (...)
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  12. Mark Balaguer (2008). Platonism in Metaphysics. Stanford Encyclopedia of Philosophy.
    Platonism is the view that there exist such things as abstract objects — where an abstract object is an object that does not exist in space or time and which is therefore entirely non-physical and nonmental. Platonism in this sense is a contemporary view. It is obviously related to the views of Plato in important ways, but it is not entirely clear that Plato endorsed this view, as it is defined here. In order to remain neutral on this question, the (...)
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  13. Mark Balaguer (2001). A Theory of Mathematical Correctness and Mathematical Truth. Pacific Philosophical Quarterly 82 (2):87–114.
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  14. J. D. Bastable (1955). Realism and Nominalism Revisited. Philosophical Studies 5:164-165.
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  15. Paul Benacerraf (1984). Comments on Maddy and Tymoczko. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1984:476 - 485.
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  16. Ermanno Bencivenga (2006). Mathematics and Poetry. Inquiry 49 (2):158 – 169.
    Since Descartes, mathematics has been dominated by a reductionist tendency, whose success would seem to promise greater certainty: the fewer basic objects mathematics can be understood as dealing with, and the fewer principles one is forced to assume about these objects, the easier it will be to establish a secure foundation for it. But this tendency has had the effect of sharply limiting the expressive power of mathematics, in a way that is made especially apparent by its disappointing applications to (...)
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  17. David Wells Bennett (1961). The Natural Numbers From Frege to Hilbert. Dissertation, Columbia University
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  18. Hugh H. Benson (1988). Universals as Sortals in the Categories. Pacific Philosophical Quarterly 69 (4):282-306.
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  19. Gustav Bergmann (1958). Frege's Hidden Nominalism. Philosophical Review 67 (4):437-459.
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  20. S. Bernard Lonergan (1996). The Notion of Structure. Method 14 (2):117-132.
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  21. J. M. Bernstein (2004). Readymades, Monochromes, Etc.: Nominalism and the Paradox of Modernism. Diacritics 32 (1):83-100.
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  22. Alexander U. Bertland (1996). Abstract. New Vico Studies 14:96-99.
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  23. Peter Bieri (1982). Nominalism and Inner Experience. The Monist 65 (January):68-87.
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  24. John Bigelow (1991). The Reality of Numbers. Mind 100 (2):283-287.
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  25. John Bigelow (1981). Semantic Nominalism. Australasian Journal of Philosophy 59 (4):403 – 421.
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  26. Alexander Bird (2006). Potency and Modality. Synthese 149 (3):447-52.
    Let us call a property that is essentially dispositional a potency.1 David Armstrong thinks that potencies do not exist. All sparse properties are essentially categorical, where sparse properties are the explanatory properties of the type science seeks to discover. An alternative view, but not the only one, is that all sparse properties are potencies or supervene upon them. In this paper I shall consider the differences between these views, in particular the objections Armstrong raises against potencies.
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  27. Katharina Biske (1930). Otto Heyn Als Nominalist Dissertation. Druckerei-Genossenschaft.
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  28. Patricia Blanchette (2007). 3 Mathematical Objects and Identity. In Michael O'Rourke Corey Washington (ed.), Situating Semantics: Essays on the Philosophy of John Perry. 73.
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  29. C. D. Blanton (2010). Medieval Currencies : Nominalism and Art. In Andrew Cole & D. Vance Smith (eds.), The Legitimacy of the Middle Ages: On the Unwritten History of Theory. Duke University Press
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  30. Daniel Bonevac (1984). Mathematics and Metalogic. The Monist 67 (1):56-71.
    In this paper I shall attempt to outline a nominalistic theory of mathematical truth. I call my theory nominalistic because it avoids a real (see [4]) ontological commitment to abstract entities. Traditionally, nominalists have found it difficult to justify any reference to infinite collections in mathematics. Even those who have tried to do so have typically restricted themselves to predicative and, thus, denumerable realms. I Indeed, many have linked impredicative definitions to platonism; nominalists have tended to agree with Weyl that (...)
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  31. George Boolos (1995). Frege's Theorem and the Peano Postulates. Bulletin of Symbolic Logic 1 (3):317-326.
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  32. George Boolos (1993). Whence the Contradiction? Aristotelian Society Supplementary Volume 67:211--233.
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  33. Reprinted Boolos (1998). P. 54-72.(1985)'Nominalist Platonism'. Philosophical Review 94:327-44.
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  34. Gerd A. Bornheim (1998). O Conceito de Descobrimento. Monograph Collection (Matt - Pseudo).
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  35. Andrew Boucher, Against Angles and the Fregean-Cantorian Theory of Number.
    How-many numbers, such as 2 and 1000, relate or are capable of expressing the size of a group or set. Both Cantor and Frege analyzed how-many number in terms of one-to-one correspondence between two sets. That is to say, one arrived at numbers by either abstracting from the concept of correspondence, in the case of Cantor, or by using it to provide an out-and-out definition, in the case of Frege.
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  36. Sacha Bourgeois-Gironde (2004). On Zalta's Notion of Encoding in Conceivability Contexts. Metaphysica.
    Zalta's notion of encoding which lies at the core of his theory of abstract objects is refined so that it can capture cognitive dynamic phenomena such as multiple object-tracking in particular intentional contexts; namely hypothetical stipulation concerning abstract objects and counter-essential conceivability about ordinary ones. Zalta's Modal Axiom of Encoding is weakened and the notion of 'quasi-encoding' is spelt out.
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  37. George Mcmillan Bowles (1970). Did Plato Believe in Immanent Universals? Dissertation, Stanford University
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  38. Hag Braakhuis (1993). Wessel Gansfort Between Albertism and Nominalism. In Fokke Akkerman, Gerda C. Huisman & Arie Johan Vanderjagt (eds.), Wessel Gansfort (1419-1489) and Northern Humanism. E.J. Brill 40--30.
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  39. Richard B. Brandt (1957). The Languages of Realism and Nominalism. Philosophy and Phenomenological Research 17 (4):516-535.
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  40. Ada Bronowski (2007). The Stoic View on Universals. Documenti E Studi Sulla Tradizione Filosofica Medievale 18:71-87.
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  41. James Robert Brown (1988). Abstract Objects Bob Hale Oxford: Blackwell, 1987. Pp. 282. $75.00. [REVIEW] Dialogue 27 (04):729-.
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  42. James Robert Brown (1988). Bob Hale, "Abstract Objects". [REVIEW] Dialogue 27 (4):729.
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  43. Tyler Burge (1998). Frege on Knowing the Foundation. Mind 107 (426):305-347.
    The paper scrutinizes Frege's Euclideanism - his view of arithmetic and geometry as resting on a small number of self-evident axioms from which non-self-evident theorems can be proved. Frege's notions of self-evidence and axiom are discussed in some detail. Elements in Frege's position that are in apparent tension with his Euclideanism are considered - his introduction of axioms in The Basic Laws of Arithmetic through argument, his fallibilism about mathematical understanding, and his view that understanding is closely associated with inferential (...)
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  44. Edmund C. Burke (1929). Attaining to the Abstract. Modern Schoolman 6 (1):8-9.
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  45. Panayot Butchvarov (1968). Resemblance and Identity: An Examination of the Problem of Universals. Philosophical Review 77 (3):386-389.
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  46. Andrea Cantini (1988). Two Impredicative Theories of Properties and Sets. Mathematical Logic Quarterly 34 (5):403-420.
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  47. Emily Carson (1996). On Realism in Set Theory. Philosophia Mathematica 4 (1):3-17.
    In her recent book, Realism in mathematics, Penelope Maddy attempts to reconcile a naturalistic epistemology with realism about set theory. The key to this reconciliation is an analogy between mathematics and the physical sciences based on the claim that we perceive the objects of set theory. In this paper I try to show that neither this claim nor the analogy can be sustained. But even if the claim that we perceive some sets is granted, I argue that Maddy's account fails (...)
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  48. Dasiea Yvonne Cavers-Huff (1997). Cognitive Science and Metaphysics Revisited: Toward a Theory of Properties. Dissertation, University of California, Riverside
    This dissertation explores the implications of recent developments in cognitive science for the metaphysical problem of property attribution. The structure of this dissertation is as follows: first, I critique a number of received accounts of the basis of property attribution, and secondly, I survey some recent literature in cognitive psychology, and discuss its relevance to the ontological basis of the attribution of properties to objects. Finally, I draw a distinction between the ontological basis of our attribution of properties to objects, (...)
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  49. O. Chateaubriand (2008). Agnostic Nominalism: Response to Otávio Bueno. Manuscrito 31 (1):441-444.
    Otávio Bueno gives a positive and accurate summary of my defense of Platonism, with special emphasis on the epistemological issues. He criticizes “skeptical nominalism”, and proposes instead an “agnostic nominalism”, which treats mathematical objects as “objects of thought”, and neither rejects nor accepts abstract entities. In my response I argue that the main problem for nominalism is to account for abstract properties and relations, and that treating mathematical objects as objects of thought does not provide a satisfactory solution to that (...)
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  50. R. M. Chisholm (1991). The Bearers of Psychological Properties. Daimon: Revista de Filosofia 3:7.
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