Search results for 'Infinity' (try it on Scholar)

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  1. Anne Newstead (2007). Review of Oppy's Philosophical Perspectives on Infinity. [REVIEW] Australasian Journal of Philosophy 85 (4):679-695.score: 18.0
    This is a book review of Oppy's "Philosophical Perspectives on Infinity", which is of interest to those in metaphysics, epistemology, philosophy of science, mathematics, and philosophy of religion.
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  2. John Bowin (2007). Aristotelian Infinity. Oxford Studies in Ancient Philosophy 32:233-250.score: 18.0
    Bowin begins with an apparent paradox about Aristotelian infinity: Aristotle clearly says that infinity exists only potentially and not actually. However, Aristotle appears to say two different things about the nature of that potential existence. On the one hand, he seems to say that the potentiality is like that of a process that might occur but isn't right now. Aristotle uses the Olympics as an example: they might be occurring, but they aren't just now. On the other hand, (...)
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  3. Nino B. Cocchiarella (2008). Infinity in Ontology and Mind. Axiomathes 18 (1):1-24.score: 18.0
    Two fundamental categories of any ontology are the category of objects and the category of universals. We discuss the question whether either of these categories can be infinite or not. In the category of objects, the subcategory of physical objects is examined within the context of different cosmological theories regarding the different kinds of fundamental objects in the universe. Abstract objects are discussed in terms of sets and the intensional objects of conceptual realism. The category of universals is discussed in (...)
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  4. Gilbert B. Côté (2013). Mathematical Platonism and the Nature of Infinity. Open Journal of Philosophy 3 (3):372-375.score: 18.0
    An analysis of the counter-intuitive properties of infinity as understood differently in mathematics, classical physics and quantum physics allows the consideration of various paradoxes under a new light (e.g. Zeno’s dichotomy, Torricelli’s trumpet, and the weirdness of quantum physics). It provides strong support for the reality of abstractness and mathematical Platonism, and a plausible reason why there is something rather than nothing in the concrete universe. The conclusions are far reaching for science and philosophy.
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  5. Eduardo Castro (2013). Defending the Indispensability Argument: Atoms, Infinity and the Continuum. Journal for General Philosophy of Science 44 (1):41-61.score: 18.0
    This paper defends the Quine-Putnam mathematical indispensability argument against two objections raised by Penelope Maddy. The objections concern scientific practices regarding the development of the atomic theory and the role of applied mathematics in the continuum and infinity. I present two alternative accounts by Stephen Brush and Alan Chalmers on the atomic theory. I argue that these two theories are consistent with Quine’s theory of scientific confirmation. I advance some novel versions of the indispensability argument. I argue that these (...)
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  6. Paul Corazza (2010). The Axiom of Infinity and Transformations J: V→V. Bulletin of Symbolic Logic 16 (1):37-84.score: 18.0
    We suggest a new approach for addressing the problem of establishing an axiomatic foundation for large cardinals. An axiom asserting the existence of a large cardinal can naturally be viewed as a strong Axiom of Infinity. However, it has not been clear on the basis of our knowledge of ω itself, or of generally agreed upon intuitions about the true nature of the mathematical universe, what the right strengthening of the Axiom of Infinity is—which large cardinals ought to (...)
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  7. Yitzhak Melamed (forthcoming). Hasdai Crescas and Spinoza on Actual Infinity and the Infinity of God’s Attributes. In Steven Nadler (ed.), Spinoza and Jewish Philosophy. Cambridge University Press.score: 18.0
    The seventeenth century was an important period in the conceptual development of the notion of the infinite. In 1643, Evangelista Torricelli (1608-1647)—Galileo’s successor in the chair of mathematics in Florence—communicated his proof of a solid of infinite length but finite volume. Many of the leading metaphysicians of the time, notably Spinoza and Leibniz, came out in defense of actual infinity, rejecting the Aristotelian ban on it, which had been almost universally accepted for two millennia. Though it would be another (...)
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  8. Massimo Leone (2012). Motility, Potentiality, and Infinity—A Semiotic Hypothesis on Nature and Religion. Biosemiotics 5 (3):369-389.score: 18.0
    Against any obscurantist stand, denying the interest of natural sciences for the comprehension of human meaning and language, but also against any reductionist hypothesis, frustrating the specificity of the semiotic point of view on nature, the paper argues that the deepest dynamic at the basis of meaning consists in its being a mechanism of ‘potentiality navigation’ within a universe generally characterized by motility. On the one hand, such a hypothesis widens the sphere of meaning to all beings somehow endowed with (...)
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  9. Anne Newstead (1997). Actual Versus Potential Infinity (BPhil Manuscript.). Dissertation, University of Oxfordscore: 18.0
    Does mathematical practice require the existence of actual infinities, or are potential infinities enough? Contrasting points of view are examined in depth, concentrating on Aristotle’s arguments against actual infinities, Cantor’s attempts to refute Aristotle, and concluding with Zermelo’s assertion of the primacy of potential infinity in mathematics.
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  10. Steffen Borge (2003). Actualised Infinity: Before-Effect and Nullify-Effect. Disputatio 14 (14):1 - 17.score: 15.0
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  11. Charles McCarty (2013). Paradox and Potential Infinity. Journal of Philosophical Logic 42 (1):195-219.score: 15.0
    We describe a variety of sets internal to models of intuitionistic set theory that (1) manifest some of the crucial behaviors of potentially infinite sets as described in the foundational literature going back to Aristotle, and (2) provide models for systems of predicative arithmetic. We close with a brief discussion of Church’s Thesis for predicative arithmetic.
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  12. Chunghyoung Lee (2011). Infinity and Newton's Three Laws of Motion. Foundations of Physics 41 (12):1810-1828.score: 15.0
    It is shown that the following three common understandings of Newton’s laws of motion do not hold for systems of infinitely many components. First, Newton’s third law, or the law of action and reaction, is universally believed to imply that the total sum of internal forces in a system is always zero. Several examples are presented to show that this belief fails to hold for infinite systems. Second, two of these examples are of an infinitely divisible continuous body with finite (...)
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  13. Stefano Baratella & Ruggero Ferro (1993). A Theory of Sets with the Negation of the Axiom of Infinity. Mathematical Logic Quarterly 39 (1):338-352.score: 15.0
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  14. Ferrante Formato & Giangiacomo Gerla (1998). Grasping Infinity by Finite Sets. Mathematical Logic Quarterly 44 (3):383-393.score: 15.0
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  15. Marnie Luce (1969). Infinity, What is It? Minneapolis, Lerner Publications Co..score: 15.0
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  16. David J. Chalmers, Pick a Number Between Zero and Infinity.score: 12.0
    In article <18311.25b44848@merrimack.edu> ain14924@merrimack.edu writes: Reminds me of a friend of mine who claims that the number 17 is "the most random" number. His proof ran as follows: pick a number. It's not really as good a random number as 17, is it? (Invariable Answer: "Umm, well, no...") This reminds me of a little experiment I did a couple of years ago. I stood on a busy street corner in Oxford, and asked passers by to "name a random number between (...)
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  17. Massimiliano Badino, The Concept of Infinity in Modern Cosmology.score: 12.0
    The aim of this paper is not only to deal with the concept of infinity, but also to develop some considerations about the epistemological status of cosmology. These problems are connected because from an epistemological point of view, cosmology, meant as the study of the universe as a whole, is not merely a physical (or empirical) science. On the contrary it has an unavoidable metaphysical character which can be found in questions like “why is there this universe (or a (...)
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  18. Josh Dever, Worlds Apart: On the Possibility of an Actual Infinity.score: 12.0
    Cosmological arguments attempt to prove the existence of God by appeal to the necessity of a first cause. Schematically, a cosmological argument will thus appear as: (1) All contingent beings have a cause of existence. (2) There can be no infinite causal chains. (3) Therefore, there must be some non-contingent First Cause. Cosmological arguments come in two species, depending on their justification of the second premiss. Non-temporal cosmological arguments, such as those of Aristotle and Aquinas, view causation as requiring explanatory (...)
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  19. Graham Robert Oppy (2006). Philosophical Perspectives on Infinity. Cambridge University Press.score: 12.0
    Exploring philosophical questions about infinity, Graham Oppy examines how the infinite lurks everywhere, both in science and in our ordinary thoughts about the world. He also analyzes the many puzzles and paradoxes that follow in the train of the infinite, addressing such simple notions as counting, adding, and maximizing present serious difficulties. Other topics examined include the nature of space and time, infinities in physical science, infinities in theories of probability and decision, the nature of part/whole relations, mathematical theories (...)
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  20. Tullia D' Aragona (1997). Dialogue on the Infinity of Love. University of Chicago Press.score: 12.0
    Celebrated as a courtesan and poet, and as a woman of great intelligence and wit, Tullia d'Aragona (1510–56) entered the debate about the morality of love that engaged the best and most famous male intellects of sixteenth-century Italy. First published in Venice in 1547, but never before published in English, Dialogue on the Infinity of Love casts a woman rather than a man as the main disputant on the ethics of love. Sexually liberated and financially independent, Tullia d'Aragona dared (...)
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  21. Wolfgang Achtner (2005). Infinity in Science and Religion. The Creative Role of Thinking About Infinity. Neue Zeitschrift Für Systematische Theologie Und Religionsphilosophie 47 (4):392-411.score: 12.0
    This article discusses the history of the concepts of potential infinity and actual infinity in the context of Christian theology, mathematical thinking and metaphysical reasoning. It shows that the structure of Ancient Greek rationality could not go beyond the concept of potential infinity, which is highlighted in Aristotle's metaphysics. The limitations of the metaphysical mind of ancient Greece were overcome through Christian theology and its concept of the infinite God, as formulated in Gregory of Nyssa's theology. That (...)
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  22. G. Landini (2011). Logicism and the Problem of Infinity: The Number of Numbers. Philosophia Mathematica 19 (2):167-212.score: 12.0
    Simple-type theory is widely regarded as inadequate to capture the metaphysics of mathematics. The problem, however, is not that some kinds of structure cannot be studied within simple-type theory. Even structures that violate simple-types are isomorphic to structures that can be studied in simple-type theory. In disputes over the logicist foundations of mathematics, the central issue concerns the problem that simple-type theory fails to assure an infinity of natural numbers as objects . This paper argues that the problem of (...)
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  23. Michał Heller & W. H. Woodin (eds.) (2011). Infinity: New Research Frontiers. Cambridge University Press.score: 12.0
    Machine generated contents note: Introduction Rudy Rucker; Part I. Perspectives on Infinity from History: 1. Infinity as a transformative concept in science and theology Wolfgang Achtner; Part II. Perspectives on Infinity from Mathematics: 2. The mathematical infinity Enrico Bombieri; 3. Warning signs of a possible collapse of contemporary mathematics Edward Nelson; Part III. Technical Perspectives on Infinity from Advanced Mathematics: 4. The realm of the infinite W. Hugh Woodin; 5. A potential subtlety concerning the distinction (...)
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  24. Carl Posy (2008). Intuition and Infinity: A Kantian Theme with Echoes in the Foundations of Mathematics. Royal Institute of Philosophy Supplement 83 (63):165-193.score: 12.0
    Kant says patently conflicting things about infinity and our grasp of it. Infinite space is a good case in point. In his solution to the First Antinomy, he denies that we can grasp the spatial universe as infinite, and therefore that this universe can be infinite; while in the Aesthetic he says just the opposite: ‘Space is represented as a given infinite magnitude’ (A25/B39). And he rests these upon consistently opposite grounds. In the Antinomy we are told that we (...)
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  25. Theokritos Kouremenos (1995). Aristotle on Mathematical Infinity. F. Steiner.score: 12.0
    Aristotle was the first not only to distinguish between potential and actual infinity but also to insist that potential infinity alone is enough for mathematics ...
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  26. Ohad Nachtomy (2011). A Tale of Two Thinkers, One Meeting, and Three Degrees of Infinity: Leibniz and Spinoza (1675–8). British Journal for the History of Philosophy 19 (5):935-961.score: 12.0
    The article presents Leibniz's preoccupation (in 1675?6) with the difference between the notion of infinite number, which he regards as impossible, and that of the infinite being, which he regards as possible. I call this issue ?Leibniz's Problem? and examine Spinoza's solution to a similar problem that arises in the context of his philosophy. ?Spinoza's solution? is expounded in his letter on the infinite (Ep.12), which Leibniz read and annotated in April 1676. The gist of Spinoza's solution is to distinguish (...)
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  27. Michał Heller (2008). Infinity in Cosmology. Dialogue and Universalism 18 (9-10):77-87.score: 12.0
    The issue of infinity appeared in cosmology in the form of a question on spatial and time finiteness or infinity of the universe. Recently, more and more talking is going on about “other universes” (different ones from “our”), the number of which may be infinite. Speculations on this topic emerged in effect of the discussions on the issue of the anthropic principle, and the so-called inflation scenario. In truth, this kind of speculations are hardly recognized as scientific theories, (...)
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  28. Timm Lampert (2008). Wittgenstein on the Infinity of Primes. History and Philosophy of Logic 29 (1):63-81.score: 12.0
    It is controversial whether Wittgenstein's philosophy of mathematics is of critical importance for mathematical proofs, or is only concerned with the adequate philosophical interpretation of mathematics. Wittgenstein's remarks on the infinity of prime numbers provide a helpful example which will be used to clarify this question. His antiplatonistic view of mathematics contradicts the widespread understanding of proofs as logical derivations from a set of axioms or assumptions. Wittgenstein's critique of traditional proofs of the infinity of prime numbers, specifically (...)
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  29. Daniel A. Dombrowski (2007). Oppy, Infinity, and the Neoclassical Concept of God. International Journal for Philosophy of Religion 61 (1):25 - 37.score: 12.0
    In this article I concentrate on three issues. First, Graham Oppy’s treatment of the relationship between the concept of infinity and Zeno’s paradoxes lay bare several porblems that must be dealt with if the concept of infinity is to do any intellectual work in philosophy of religion. Here I will expand on some insightful remarks by Oppy in an effort ot adequately respond to these problems. Second, I will do the same regarding Oppy’s treatment of Kant’s first antinomy (...)
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  30. April Capili (2011). The Created Ego in Levinas' Totality and Infinity. Sophia 50 (4):677-692.score: 12.0
    There are two seemingly opposed descriptions of the subject in Totality and Infinity : the separate and autonomous I and the self that is ready to respond to the Other’s suffering and need. This paper points out that there is in fact another way Levinas speaks of the subject, which reinforces and reconciles the other two accounts. Throughout his first major work, Levinas explains how the ego is allowed to emerge as such by the Other who constantly confronts it. (...)
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  31. Jon Perez Laraudogoitia (1998). Infinity Machines and Creation Ex Nihilo. Synthese 115 (2):259-265.score: 12.0
    In this paper a simple model in particle dynamics of a well-known supertask is constructed (the supertask was introduced by Max Black some years ago). As a consequence, a new and simple result about creation ex nihilo of particles can be proved compatible with classical dynamics. This result cannot be avoided by imposing boundary conditions at spatial infinity, and therefore is really new in the literature. It follows that there is no reason why even a world of rigid spheres (...)
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  32. Eli Maor (1987/1991). To Infinity and Beyond: A Cultural History of the Infinite. Princeton University Press.score: 12.0
    Eli Maor examines the role of infinity in mathematics and geometry and its cultural impact on the arts and sciences. He evokes the profound intellectual impact the infinite has exercised on the human mind--from the "horror infiniti" of the Greeks to the works of M. C. Escher from the ornamental designs of the Moslems, to the sage Giordano Bruno, whose belief in an infinite universe led to his death at the hands of the Inquisition. But above all, the book (...)
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  33. Eric Steinhart (2009). A Modern Analysis of Divine Infinity. Theology and Science 7 (3):261-274.score: 12.0
    Mathematics is obviously important in the sciences. And so it is likely to be equally important in any effort that aims to understand God in a scientifically significant way or that aims to clarify the relations between science and theology. The degree to which God has any perfection is absolutely infinite. We use contemporary mathematics to precisely define that absolute infinity. For any perfection, we use transfinite recursion to define an endlessly ascending series of degrees of that perfection. That (...)
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  34. Jon Perez Laraudogoitia (2010). A Flawed Argument Against Actual Infinity in Physics. Foundations of Physics 40 (12):1902-1910.score: 12.0
    In “Nonconservation of Energy and loss of Determinism II. Colliding with an Open Set” (2010) Atkinson and Johnson argue in favour of the idea that an actual infinity should be excluded from physics, at least in the sense that physical systems involving an actual infinity of component elements should not be admitted. In this paper I show that the argument Atkinson and Johnson use is erroneous and that an analysis of the situation considered by them is possible without (...)
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  35. P. Cariani (2012). Infinity and the Observer: Radical Constructivism and the Foundations of Mathematics. Constructivist Foundations 7 (2):116-125.score: 12.0
    Problem: There is currently a great deal of mysticism, uncritical hype, and blind adulation of imaginary mathematical and physical entities in popular culture. We seek to explore what a radical constructivist perspective on mathematical entities might entail, and to draw out the implications of this perspective for how we think about the nature of mathematical entities. Method: Conceptual analysis. Results: If we want to avoid the introduction of entities that are ill-defined and inaccessible to verification, then formal systems need to (...)
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  36. Dale Jacquette (2001). David Hume's Critique of Infinity. Brill.score: 12.0
    The present work considers Hume's critique of infinity in historical context as a product of Enlightenment theory of knowledge, and assesses the prospects of ...
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  37. Franco Parlamento & Alberto Policriti (1991). Expressing Infinity Without Foundation. Journal of Symbolic Logic 56 (4):1230-1235.score: 12.0
    The axiom of infinity can be expressed by stating the existence of sets satisfying a formula which involves restricted universal quantifiers only, even if the axiom of foundation is not assumed.
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  38. Peter Vallentyne, Infinity in Ethics. Routledge Encyclopedia of Philosophy.score: 12.0
    Puzzles can arise in ethical theory (as well as decision theory) when infinity is involved. The puzzles arise primarily in theories—such as consequentialist theories—that appeal to the value of actions or states of affairs. Section 1 addresses the question of whether one source of value (such as major aesthetic pleasures) can be infinitely more valuable than another (such as minor gustatory pleasures). An affirmative answer is given by appealing to the notion of lexicographic priority. Section 2 address the question (...)
     
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  39. Philip Clayton (1996). The Theistic Argument From Infinity in Early Modern Philosophy. International Philosophical Quarterly 36 (1):5-17.score: 12.0
    The article traces the links between theism and the concept of infinity in modern philosophy. Descartes appealed to "infinite perfection" as intuitive and immediately knowable, basing his theism upon it. Leibniz's quantitative understanding of infinity, as in the infinitesimals, made the break between finite and infinite less central without erasing it. Both are challenged by the infinite set theory of Georg Cantor, which finally provides a mechanism for speaking of greater and lesser infinite quantities--and yet he still posits (...)
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  40. Richard A. Cohen (2006). Some Notes on the Title of Levinas's Totality and Infinity and its First Sentence. Studia Phaenomenologica 6:117-137.score: 12.0
    Alternative oppositions to “infinity” and “totality” are suggested, examined and shown to be inadequate by comparison to the sense of the opposition contained in title Totality and Infinity chosen by Levinas. Special attention is given to this opposition and the priority given to ethics in relation Kant’s distinction between understanding and reason and the priority given by Kant to ethics. The book’s title is further illuminated by means of its first sentence, and the first sentence is illuminated by (...)
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  41. Abhay Ashtekar (1985). Logarithmic Ambiguities in the Description of Spatial Infinity. Foundations of Physics 15 (4):419-431.score: 12.0
    Logarithmic ambiguities in the choice of asymptotically Cartesian coordinates at spatial infinity are discussed. It is shown that they do not affect the definitions of energy-momentum and angular momentum at i°. Thus, from a physical viewpoint, the ambiguities are “pure gauge.” A prescription is given for fixed this gauge freedom for the class of space-times in which the leading-order part of the Weyl tensor satisfies a certain reflection symmetry. This class admits, in all (relatively boosted) rest frames at (...), a one-parameter family of asymptotically distinct 3-surfaces (generalized 3-planes) on which the trace of the extrinsic curvature falls off faster than usual. (shrink)
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  42. David Deutsch (2011). The Beginning of Infinity: Explanations That Transform the World. Viking Adult.score: 12.0
    The reach of explanations -- Closer to reality -- The spark -- Creation -- The reality of abstractions -- The jump to universality -- Artificial creativity -- A window on infinity -- Optimism -- A dream of Socrates -- The multiverse -- A physicist's history of bad philosophy -- Choices -- Why are flowers beautiful? -- The evolution of culture -- The evolution of creativity -- Unsustainable -- The beginning.
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  43. Matthew Alexander & Peter G. Bergmann (1984). Electrodynamics at Spatial Infinity. Foundations of Physics 14 (10):925-951.score: 12.0
    In preparation for the treatment of the gravitational field at spatial infinity, this paper deals with the electromagnetic field at spatial infinity. The field equations on this three-dimensional(1+2) manifold can be obtained from an action principle, which in turn lends itself to a Hamiltonian formulation. Quantization is formally straightforward, but some thought is given to the physical interpretation of the results.
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  44. Matthew Alexander & Peter G. Bergmann (1986). The Gravitational Field at Spatial Infinity. Foundations of Physics 16 (5):445-454.score: 12.0
    This paper treats the formulation of the gravitational field variables and the equations obeyed by them at spatial infinity. The variables consist of a three-dimensional tensor and a scalar, which satisfy separate field equations, which in turn can be obtained from two distinct Lagrangians. Aside from Lorentz rotations, the symmetry operations include an Abelian gauge group and an Abelian Lie group, leading to a number of conservation laws and to differential identities between the field equations.
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  45. Hansen Casper Storm (2011). New Zeno and Actual Infinity. Open Journal of Philosophy 1 (2):57.score: 12.0
    In 1964 José Benardete invented the “New Zeno Paradox” about an infinity of gods trying to prevent a traveller from reaching his destination. In this paper it is argued, contra Priest and Yablo, that the paradox must be resolved by rejecting the possibility of actual infinity. Further, it is shown that this paradox has the same logical form as Yablo’s Paradox. It is suggested that constructivism can serve as the basis of a common solution to New Zeno and (...)
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  46. Sampie Terreblanche (2005). Subjek En Etiese Verantwoordelikheidsbesef: Die Idee van Die Oneindige in Levinas Se Totality and Infinity. South African Journal of Philosophy 19 (2).score: 12.0
    Subject and the realisation of ethical responsibility – The Idea of the In finite in Levinas' Totality and Infinity. In Totality and Infinity Emmanuel Levinas writes about the categorical character of the ethical responsibility that the subject owes to the other. The confrontation with the suffering other puts the subject's natural self-interest into question, and brings him/her to realise an ethical responsibility of which s/he cannot unburden himself/herself. The question arises as to what in the constitution of the (...)
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  47. Rovelli Carlo (2011). Some Considerations on Infinity in Physics. In Michał Heller & W. H. Woodin (eds.), Infinity: New Research Frontiers. Cambridge University Press. 167--175.score: 12.0
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  48. Angelos Mouzakitis (2007). Radical Finitude Meets Infinity: Levinas's Gestures To Heidegger's Fundamental Ontology. Thesis Eleven 90 (1):61-78.score: 12.0
    This article explores the consecutive modifications that phenomenology underwent in the works of Heidegger and Levinas. In particular, it discusses their importance for contemporary attempts to expand — and transcend — phenomenology in philosophy and the social sciences. Heidegger and Levinas responded to the problem of subjectivity — and intersubjectivity — in diametrically opposed ways and consequently the exposition of their thoughts involves focusing on conceptual dichotomies like finitude and infinity, time and eternity. Ultimately, it is argued that the (...)
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  49. Carlo Rovelli (2011). Some Considerations on Infinity in Physics. In Michał Heller & W. H. Woodin (eds.), Infinity: New Research Frontiers. Cambridge University Press. 167.score: 12.0
    I am a theoretical physicist, and, following Aristotles' injunction (Aristotle, Physics III, 202b 34), I do consider it my responsibility to discuss the problem of the notion of infinity in the world--in particular, to "inquire whether there is such a thing or not." I will do so here by illustrating some aspects of the notion of infinity in the natural sciences.
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  50. Henry Simoni-Wastila (2002). Inclusive Infinity and Radical Particularity: Hegel, Hartshorne and Nishida. [REVIEW] Sophia 41 (1):33-54.score: 12.0
    Three writers who utilize a similar metaphysics to understand the relationship between Ultimate Reality and conventional reality are compared. The metaphysics of what I call an inclusive Infinity is the common thread employed in comparing the thought of Hegel, Hartshorne and Nishida. I contrast the concept of inclusive Infinity with that of radical particularity and argue that people are private centers of conscious awareness who cannot be encompassed within an infinity or totality. Because of the individuality and (...)
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