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The Proceedings of the Twentieth World Congress of Philosophy:
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W. V. Quine
Three Networks:
Similarity, Implication, and Membership
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This essay addresses the problem of how to account for our meeting of minds, for our being able to linguistically express agreement regarding external events despite wild dissimilarity of our nerve nets. An explanation is provided based on the instinct of induction, the instinct of similarity, and natural selection. There are three networks at play in the meeting of minds: perceptual similarity, the intersubjective harmony of similarity standards and thus the relation structuring the intake of perceptions; implication, the relation expressed by the universally quantified conditional and structuring our system of the world; and class membership, the relation structuring the domain of pure mathematics.
... for quantifying over abstract objects as values of variables? One thinks of
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, which are abstract objects. So I see no hope of nominalism.
Just as perceptual
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taxa.
A domain that does seem inescapably to call for quantification over abstract
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The Proceedings of the Twentieth World Congress of Philosophy:
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2
Roger Wertheimer
Identity Syntax
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Like ‘&’, ‘=’ is no term; it represents no extrasentential property. It marks an atomic, nonpredicative, declarative structure, sentences true solely by codesignation. Identity (its necessity and total reflexivity, its substitution rule, its metaphysical vacuity) is the objectual face of codesignation. The syntax demands pure reference, without predicative import for the asserted fact. ‘Twain is Clemens’ is about Twain, but nothing is predicated of him. Its informational value is in its ‘metailed’ semantic content: the fact of codesignation (that ‘Twain’ names Clemens) that explains what fact it asserts and why it is necessary. Critques of concepts of rigidity and elimination of singular terms result.
... correlates of names of abstract objects. Predicating a property is describing the objects
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synonymy of sentences considered as abstract objects of a common language.The semantic
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The Proceedings of the Twentieth World Congress of Philosophy:
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3
Katalin G. Havas
Learning to Think:
Logic for Children
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Thinking should be taught in every class, but only children’s philosophy workshops allow learning and the practice of correct thinking without linking them to the acquisition of some other mandatory learning. The reading of stories with veiled philosophical content is one way to conduct philosophical workshops for children. We may give children stories that contain some laws of correct logical reasoning. However, in order to achieve this aim, we must extract the content from the symbolic logic and translate it into everyday language. We must choose areas where the thought process is of interest for children, such as that found in logical games. This method was used by Lewis Carroll in his book The Game of Logic. We attempt to develop further his idea by suggesting games which are used by children in their everyday life.
... special kinds of abstract objects. But at the same time the philosophical spirit of
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The Proceedings of the Twentieth World Congress of Philosophy:
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4
Keith E. Yandell
God, Freedom, and Creation in Cross-Cultural Perspective:
Ramanuja, Madhva, Augustine, Aquinas
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Crossculturally, monotheistic traditions view God as occupying the apex of power, knowledge and goodness, and as enjoying independent existence. This conceptual context provides room for maneuvering concerning God’s nature (e.g., does God have logically necessary existence?) and God’s creatures (e.g., do created persons have libertarian freedom?). Logical consistency is always a constraint on such maneuvering. With that constraint in mind, our purpose here is to consider different conceptual maneuvers concerning God, created persons, and freedom (both human and divine) within Christian and Hindu Vedantic monotheism.
... for only so long.
Or besides God and abstract objects.
Abstract objects aside.
One
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The Proceedings of the Twentieth World Congress of Philosophy:
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Sharon Kaye
Russell, Strawson, and William of Ockham
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Realism and conventionalism generally establish the parameters of debate over universals. Do abstract terms in language refer to abstract things in the world? The realist answers yes, leaving us with an inflated ontology; the conventionalist answers no, leaving us with subjective categories. I want to defend nominalism in its original medieval sense, as one possibility that aims to preserve objectivity while positing nothing more than concrete individuals in the world. First, I will present paradigmatic statements of realism and conventionalism as developed by Russell and Strawson. Then, I will present the nominalist alternative as developed by William of Ockham.
... abstract objects, but they are acts of abstracting triggered by objects; and thus, they
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The Proceedings of the Twentieth World Congress of Philosophy:
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E. Jonathan Lowe
Abstraction, Properties, and Immanent Realism
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Objects which philosophers have traditionally categorized as abstract are standardly referred to by complex noun phrases of certain canonical forms, such as ‘the set of Fs’, ‘the number of Fs’, ‘the proposition that P’, and ‘the property of being F’. It is no accident that such noun phrases are well-suited to appear in ‘Fregean’ identity-criteria, or ‘abstraction’ principles, for which Frege’s criterion of identity for cardinal numbers provides the paradigm. Notoriously, such principlesare apt to create paradoxes, and the most intuitively plausible ‘Fregean’ identity-criterion for properties is afflicted by this problem. In this case, it may be possible to overcome the difficulty by modifying the criterion in a way which requires an independent account of the existence-conditions of properties, but it appears that such a strategy demands acceptance of the doctrine of immanent realism—the view that a property exists only if it is exemplified by some object.
..., Durham, UK DH1 3HN; [email protected] E. J. Lowe, “The Metaphysics of Abstract
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Objects,” Journal of Philosophy 92 (1995): 509–24.
G. Frege, The Foundations of
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The Proceedings of the Twentieth World Congress of Philosophy:
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Brian Leftow
Aquinas on the Infinite
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Both Copleston and Duhem—I believe—claim that for Thomas Aquinas, there cannot be an infinity of anything. In this essay I argue that Thomas allows that there can be an infinity of some sorts of item and, more, that there actually are infinities of some items.
... separately-existing abstract objects. Rather, in his eyes, “the species of numbers” are
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The Proceedings of the Twentieth World Congress of Philosophy:
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Bob Hale
Reals by Abstraction
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While Frege’s own attempt to provide a purely logical foundation for arithmetic failed, Hume’s principle suffices as a foundation for elementary arithmetic. It is known that the resulting system is consistent—or at least if second-order arithmetic is. Some philosophers deny that HP can be regarded as either a truth of logic or as analytic in any reasonable sense. Others—like Crispin Wright and I—take the opposed view. Rather than defend our claim that HP is a conceptual truth about numbers, I explain one way it may be possible to extend our view beyond elementary arithmetic to encompass the theory of real numbers. My approach has affinities to the leading ideas of Frege’s own treatment of the reals, although differing in one fundamental way. I attempt, like the HP approach to elementary arithmetic, to obtain the reals very directly by means of abstraction principles without any essential reliance on a theory of sets. This is the most natural way of extending the neo-Fregean position to the reals.
... abstract objects introduced by abstraction on quantitative equivalence relations (the
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The Proceedings of the Twentieth World Congress of Philosophy:
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Akihiro Kanamori
Volume Introduction
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The Proceedings of the Twentieth World Congress of Philosophy:
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Manuel García-Carpintero
Token-Reflexivity and Indirect Discourse
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According to a Reichenbachian treatment, indexicals are token-reflexive. That is, a truth-conditional contribution is assigned to tokens relative to relational properties which they instantiate. By thinking of the relevant expressions occurring in “ordinary contexts” along these lines, I argue that we can give a more accurate account of their semantic behavior when they occur in indirect contexts. The argument involves the following: (1) A defense of theories of indirect discourse which allows that a reference to modes of presentation associated with expressions occurring in indirect contexts can be made depending on contextual aspects. (2) A defense of the “doubleindexing” theories proposed by Stalnaker and others in order to account for the difference between metaphysical and epistemological modalities. (3) The claim that a Reichenbachian view improves upon the theories defended in (1) and (2).
... relations to abstract objects, propositions, which determine non-relativized truth
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