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41. Studia Neoaristotelica: Volume > 8 > Issue: 1
James Franklin Aristotelianism in the Philosophy of Mathematics: A Journal of Analytic Scholasticism
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Modern philosophy of mathematics has been dominated by Platonism and nominalism, to the neglect of the Aristotelian realist option. Aristotelianism holds that mathematics studies certain real properties of the world – mathematics is neither about a disembodied world of “abstract objects”, as Platonism holds, nor it is merely a language of science, as nominalism holds. Aristotle’s theory that mathematics is the “science of quantity” is a good account of at least elementarymathematics: the ratio of two heights, for example, is a perceivable and measurable real relation between properties of physical things, a relation that can be shared by the ratio of two weights or two time intervals. Ratios are an example of continuous quantity; discrete quantities, such as whole numbers, are also realised as relations between a heap and a unit-making universal. For example, the relation between foliage and being-a-leaf is the number of leaves on a tree,a relation that may equal the relation between a heap of shoes and being-a-shoe. Modern higher mathematics, however, deals with some real properties that are not naturally seen as quantity, so that the “science of quantity” theory of mathematics needs supplementation. Symmetry, topology and similar structural properties are studied by mathematics, but are about pattern, structure or arrangement rather than quantity.
... disembodied world of “abstract objects”, as Platonism holds, nor it is merely a language ... defended a Platonist view of the reality of the “abstract objects” of ... world – mathematics is neither about a disembodied world of “abstract objects ...
42. The Modern Schoolman: Volume > 53 > Issue: 1
Beth J. Singer Substitutes for Substances
... be equally unities. But (abstract) eternal objects are ... principle of universality: eternal objects are abstract, unchanging ... " as the antonym of "abstract," it does not always have this ...
43. Philosophia Christi: Volume > 17 > Issue: 2
William Lane Craig God and Abstract Objects
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Central to classical theism is the conception of God as the sole ultimate reality, the creator of all things apart from Himself. Such a doctrine is rooted in Hebrew-Christian scripture and unfolded by the ante-Nicene church fathers. Platonism, which postulates the existence of uncreated abstract objects, is therefore theologically objectionable. In order to overcome the presumption which anti-Platonism enjoys theologically, the Platonist would have to show that all other positions, both realist and nonrealist, are rationally untenable. No one has even attempted so audacious a project, nor is there any reasonable expectation that it could be carried out.
...God and Abstract Objects ... , which postulates the existence of uncreated abstract objects, is therefore ... God and Abstract Objects William Lane Craig ...
44. Philosophia Christi: Volume > 13 > Issue: 2
William Lane Craig A Nominalist Perspective on God and Abstract Objects
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A metaphysically robust, as opposed to lightweight, Platonism with respect to uncreatable abstract objects is theologically unacceptable because it fatally compromises creatio ex nihilo and divine aseity. The principal argument for Platonism is the so-called Indispensability Argument based on the ontological commitments required by singular terms and existential quantifiers in true sentences. Different varieties of Nominalism challenge each of the argument’s premises. Fictionalism accepts the assumed criterion of ontological commitment but rejects the truth of the relevant sentences. Neutralism accepts the truth of the relevant sentences but denies the assumed criterion of ontological commitment. Both of these perspectives, but especially the last, are plausible routes available for the Christian theist.
... indispensability of quantification over putatively abstract objects. 22 ... A Nominalist Perspective on God and Abstract Objects ... uncreatable abstract objects is theologically unacceptable because it fatally compromises ...
45. Environmental Ethics: Volume > 22 > Issue: 2
Rick O’Neil Animal Liberation versus Environmentalism
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Animal liberationism and environmentalism generally are considered incompatible positions. But, properly conceived, they simply provide answers to different questions, concerning moral standing and intrinsic value, respectively. The two views together constitute an environmental ethic that combines environmental justice and environmental care. I show that this approach is not only consistent but defensible.
...22 ... be objects of aesthetic appreciation, they cannot properly be foci of moral ... collections and systems of natural objects, such as species and ecosystems ...
46. Grazer Philosophische Studien: Volume > 53
Rolf George Bolzano's Programme and Abstract Objects
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Most of the Bolzano literature is exegetical, neglecting, unfortunately, the great potential of his logic as the beginning of a PROGRAMME. Specifically, his unorthodox construai of the consequence relation as triadic, and his account of logical form are promising beginnings which even as they stand shed light on question of relevance, the ancient problems of enthymemes and others. Instead of developing these suggestions, Bolzano scholars have been occupied with elucidating the ontology of sentences in themselves, and related topics. I argue, and believe to be in agreement with Bolzano, that the nature of sentences is fully explained by the relations that hold between them, just as money has no nature or essence beyond the transactions it makes possible. It follows that the development of his logic would contribute at least as much to the understanding of sentences than any exegesis.
...Bolzano's Programme and Abstract Objects ... BOLZANO'S PROGRAMME AND ABSTRACT OBJECTS Rolf GEORGE ... , it will turn out, are abstract objects of an odd sort: they ...
47. Southwest Philosophy Review: Volume > 19 > Issue: 1
James Page ARE NUMBERS UNIVERSALS AND SETS THEIR INSTANCES?
.... They are, more over, abstract objects. For Lowe, an object is abstract just in ... -independent objects. But we cannot causally interact with abstract, mind-independent objects. So ... ,1,2,3, ...could not be objects because there is no principled way to identify them with any ...
48. Dialogue and Universalism: Volume > 28 > Issue: 1
Alicja Kuczyńska Katarzyna Kobro. A Vision of the Open Sculpture
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The paper is on Katarzyna Kobro’s artistic achievements and theoretical writings which present the foreshadowing of a new understanding of the space, articulated later by philosophers. Her and her husband conception of avant-garde sculpture postulates new mechanisms of seeing reality. By eliminating borders between sculpture and space, Kobro initiated a true breakthrough in art. Her achievement should be recognized for its truly pioneering and visionary status. Kobro was one of the first artists who revealed the intimate relation between art and its environment.
... SCULPTURE ABSTRACT The paper is on Katarzyna Kobro ... .” Diacritics, 16, 22–27. 116 Alicja Kuczyńska long been ... objects as separated from their surroundings. The borders of ...
49. Proceedings of the XIth International Congress of Philosophy: Volume > 13
Ian Thomas Ramsey Notions and Ideas in Berkeley’s Philosophy
... are reasonably abstract21), and involve an act of the mind 22 ... “particular objects” of sensation and reflection, and that with this ... assumption he criticised Locke’s doctrine of abstract ideas as a meaningless ...
50. The Modern Schoolman: Volume > 67 > Issue: 1
Winston A. Wilkinson George Berkeley: Essays and Replies: Edited by David Berman
... Academic Press, 1985. Pp. 171. £ 22.50. The 300th anniversary of ... Trinity on May 6, 1985 and on August 19-22, 1985. The papers were previously ... , in the case of God's creation of objects, to an infinite regress, and that ...
51. The Philosophical Review: Volume > 119 > Issue: 3
Thomas Sattig Compatibilism about Coincidence
... seems to be a platitude of common sense that distinct ordinary objects ... ordinary objects, the paradoxes threaten this conception with inconsistency ... sustains the folk conception of ordinary objects in its entirety. According ...
52. International Philosophical Quarterly: Volume > 59 > Issue: 4
James Orr No God, No Powers: Classical Theism and Pandispositionalist Laws
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One common feature of debates about the best metaphysical analysis of putatively lawful phenomena is the suspicion that nomic realists who locate the modal force of such phenomena in quasi-causal necessitation relations between universals are working with a model of law that cannot convincingly erase its theological pedigree. Nancy Cartwright distills this criticism into slogan form: no God, no laws. Some have argued that a more plausible alternative for nomic realists who reject theism is to ground laws of nature in the fundamental dispositional properties or “pure powers” of physical objects. This article argues that for all its advantages over deflationary and rival realist accounts, a pandispositionalist account of law cuts against the commitment to metaphysical naturalism that its supporters almost always presuppose. It then examines and rejects a Platonic version of this account before elaborating and advancing a theistic alternative that is more theoretically powerful and more metatheoretically parsimonious. In slogan form: no God, no powers.
...- 22 Alexius Meinong, “The Theory of Objects” in Realism and the ... Thus Michael J. Loux, “Towards an Aristotelian Theory of Abstract Objects,” Midwest ... “pure powers” of physical objects. This article argues that for all its advantages ...
53. Proceedings of the XXIII World Congress of Philosophy: Volume > 50
Valery Meskov Philosophy of Education: Models and Methodology
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Since the mid-20th century philosophy of education has taken a well-deserved place in science and teaching. University faculties and departments have appeared; there are research teams collaborating and creating open content material. Nowadays as usual during the time of critical fundamental changing, mankind tries to find out the answers to eternal questions: about the relationships between I as a Subject of Education, an Education, and relationship between them. We need modern solutions of these eternal questions. A “modern solution” is provided by the information society, the new post-non-classical approach. It has been crucial to modify the method of passing from the abstract to something concrete; to define the terms of subject philosophy and also of education as cognitive activity and pedagogy. A cognitive and competency-based educational model has been developed and a relevant post-non-classical pattern of educational processes has been established. The information model of Philosophy of Science is applied to Philosophy of Education which is considered in three senses: as a discipline, scope for interdisciplinary studies and cognitive activity. The “road map” of education is rational basis and methods for innovative practices in education.
... of passing from the abstract to something concrete; to define the terms of ... and Methodology ABSTRACT: Since the mid-20th century philosophy ... the method of passing from the abstract to something concrete; to define the ...
54. The Modern Schoolman: Volume > 86 > Issue: 1/2
Rega Wood Appellation, Signification, & Universal Names According to Richard Rufus (d. circa 1250)
... equally well stand for objects in the past; it just depends on the tense of the verb ... , quam significat homo. Et haec |22| forma dupliciter ... , quam significat homo. Et haec |22| forma dupliciter ...
55. Idealistic Studies: Volume > 34 > Issue: 3
Douglas McDermid Keeping the World In Mind: Schopenhauer’s Misunderstood Reductio of Realism
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In this essay, I focus exclusively on an ill-understood Schopenhauerian objection to realism, which I call the Inconceivability Argument (since its conclusion is that realism is inconceivable or unintelligible). The received scholarly view of Schopenhauer’s supposedly conclusive disproof of realism is that it is nothing but a simple and familiar fallacy. I disagree; and in this paper I develop three ways of understanding the Inconceivability Argument, according to which Schopenhauer’s reductio is not an insubstantial and worthless sophism but a solid construction in which some valuable philosophical insights are embedded.
...Abstract: In this essay, I focus exclusively on an ill ... which it exists” (WWR I: §1, 3; WWR II: I, 3). All objects known via sense ... ways: materially (insofar as such objects are nothing more than mind ...
56. Balkan Journal of Philosophy: Volume > 5 > Issue: 1
Iris Merkač The Structuralist Ontology of Mathematics: a Brief Introduction
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The paper offers an overview of the motivation for structuralist ontology of mathematics and of the main structuralist position. It discusses the shortcomings ofeliminativist structuralism, and then presents the more promising options: ante rem structuralism, Platonic structuralism, and Parsons’ particular version of structuralism. Our discussion does not cover all of the issues that have relevance for the choice of the particular version of mathematical structuralism, but we do focus on the problem of indeterminacy and on the solution to it. So the positions of some versions of structuralism and the solutions to the problem of indeterminacy are briefly presented and compared, and a clear picture of structuralist ontologies is drawn.
... be abstract objects (Balaguer, 1998, 184). 2. If there exist ... any abstract mathematical objects, then they exist outside of ... of abstract objects that are necessary for mathematical ...
57. Stance: An International Undergraduate Philosophy Journal: Volume > 14
Megan Wu In Defense of Platonic Essentialism about Numbers
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In defense of anti-essentialism, pragmatist Richard Rorty holds that we may think of all objects as if they were numbers. I find that Rorty’s metaphysics hinges on two rather weak arguments against the essences of numbers. In contrast, Plato’s metaphysics offers a plausible definition of essentiality by which numbers do have essential properties. Further, I argue that Rorty’s argumentative mistake is mischaracterizing Plato’s definition. I conclude that Plato’s definition of “essential” is a robust one which implies that many properties, beyond those we might intuitively think of, can count as essential properties of objects.
... whether numbers are particular objects or are themselves abstract ... , despite being more abstract than physical objects like cups. Fortunately ... think of all objects as if they were numbers. I find that Rorty’s metaphysics hinges ...
58. Res Philosophica: Volume > 93 > Issue: 2
Zsófia Zvolenszky Fictional Characters, Mythical Objects, and the Phenomenon of Inadvertent Creation
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My goal is to reflect on the phenomenon of inadvertent creation and argue that—various objections to the contrary—it doesn’t undermine the view that fictional characters are abstract artifacts. My starting point is a recent challenge by Jeffrey Goodman that is originally posed for those who hold that fictional characters and mythical objects alike are abstract artifacts. The challenge: if we think that astronomers like Le Verrier, in mistakenly hypothesizing the planet Vulcan, inadvertently created an abstract artifact, then the “inadvertent creation” element turns out to be inescapable yet theoretically unattractive. Based on considerations about actually existing concrete objects featured in fictional works (as Napoleon is in Tolstoy’s War and Peace), I argue that independently of one’s stand on mythical objects, admitting fictional characters as abstract artifacts is enough to give rise to the challenge at hand; yet this very point serves to undermine the challenge, indicating that inadvertent creation is not nearly as worrisome as Goodman suggests. Indeed, the inadvertent creation phenomenon’s generality extends far beyond objects of fiction and myth, and I will use this observation to counter a further objection. Taking fictional characters (and mythical objects) to be abstract artifacts therefore remains a viable option.
... fictional characters (and mythical objects) to be abstract artifacts therefore remains a ... characters and mythical objects alike are abstract artifacts. The ... . Taking fictional characters (and mythical objects) to be abstract ...
59. Studia Phaenomenologica: Volume > 21
Alexis Delamare The Power of Husserl’s Third Logical Investigation: Formal and Applied Mereology in Zur Lehre von den Ganzen und Teilen
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The peculiar legacy of Husserl’s mereology, chiefly studied by analytic philosophers interested in ontology, has led to a partial understanding of the III. LU, which is too often reduced to a chapter of “formal ontology”. Yet, the power of this Investigation goes far beyond: it enabled Husserl to deal, in the framework of a unified theory, with a vast range of particular problems. The paper focuses on one of these issues, namely abstraction, so as to expose how Husserl instrumentalizes his formal tools in order to tackle material issues. The existence of an up and down pattern is uncovered: Husserl first reinterprets the psychological problem of abstraction in ontological terms (“bottom-up”), before coming back to the original problem with new insights (“top-down”). The second, correlative aim of the paper is to emphasize the key role played by Friedrich Schumann, a forgotten yet crucial character for Husserl’s conception of abstraction.
... objects (Husserl 1979: 99) 22 , and are thus not limited to the material sphere of ... Abstract: The peculiar legacy of Husserl’s mereology, chiefly studied by analytic ... objects. Husserl’s extension of the concept of part was influenced by Brentano ...
60. Studia Phaenomenologica: Volume > 15
George Heffernan The Paradox of Objectless Presentations in Early Phenomenology: A Brief History of the Intentional Object from Bolzano to Husserl With Concise Analyses of the Positions of Brentano, Frege, Twardowski and Meinong
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This paper explores the close connection in early phenomenology between the problem of objectless presentations and the concept of intentional objects. It clarifies how this basic concept of Husserl’s early phenomenology emerged within the horizons of Bolzano’s logical objectivism, Brentano’s descriptive psychology, Frege’s mathematical logicism, Twardowski’s psychological representationalism, and Meinong’s object theory. It shows how in collaboration with these thinkers Husserl argued that a theory of intentionality is incomplete without a concept of the intentional object. It provides a brief history of the concept of intentional objects in the philosophical logic of the nineteenth century that demonstrates its relevance to the problem of objectless presentations in the early phenomenology of the twentieth century. It suggests that Husserl accepts Bolzano’s objectivism and Frege’s logicism, rejects Brentano’s conception of immanent objects and Twardowski’s notion of representational pictures, and ignores Meinong’s theory of objects. Thus the paper employs the formation of Husserl’s concept of the intentional object to enhance the understanding of the historical and philosophical relationships between early phenomenology and contemporaneous philosophical movements.
...-propositional mental acts to be abstract logical objects, Twardowski holds them ... “actual” (wirkliche) objects. 22 On the other hand, in “Intentional Objects ... recognizes abstract logical objects, Meinong deviates from the ...