Results for 'Infinity'

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  1.  73
    Approaching Infinity.Michael Huemer - 2016 - New York: Palgrave Macmillan.
    Approaching Infinity addresses seventeen paradoxes of the infinite, most of which have no generally accepted solutions. The book addresses these paradoxes using a new theory of infinity, which entails that an infinite series is uncompletable when it requires something to possess an infinite intensive magnitude. Along the way, the author addresses the nature of numbers, sets, geometric points, and related matters. The book addresses the need for a theory of infinity, and reviews both old and new theories (...)
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  2.  30
    Infinity and the Mind: The Science and Philosophy of the Infinite.Rudy von Bitter Rucker - 1982 - Boston, MA, USA: Princeton University Press.
    In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Here Rucker acquaints us with Gödel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpretation of quantum mechanics in which billions of parallel worlds are produced every microsecond. It is in the realm of (...)
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  3. Actual and Potential Infinity.Øystein Linnebo & Stewart Shapiro - 2019 - Noûs 53 (1):160-191.
    The notion of potential infinity dominated in mathematical thinking about infinity from Aristotle until Cantor. The coherence and philosophical importance of the notion are defended. Particular attention is paid to the question of whether potential infinity is compatible with classical logic or requires a weaker logic, perhaps intuitionistic.
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  4. Abstraction and Infinity.Paolo Mancosu - 2016 - Oxford, England: Oxford University Press.
    Paolo Mancosu provides an original investigation of historical and systematic aspects of the notions of abstraction and infinity and their interaction. A familiar way of introducing concepts in mathematics rests on so-called definitions by abstraction. An example of this is Hume's Principle, which introduces the concept of number by stating that two concepts have the same number if and only if the objects falling under each one of them can be put in one-one correspondence. This principle is at the (...)
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  5.  14
    Infinity, Causation, and Paradox.Alexander R. Pruss - 2018 - Oxford, England: Oxford University Press.
    Alexander R. Pruss examines a large family of paradoxes to do with infinity - ranging from deterministic supertasks to infinite lotteries and decision theory. Having identified their common structure, Pruss considers at length how these paradoxes can be resolved by embracing causal finitism.
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  6. Three Infinities in Early Modern Philosophy.Anat Schechtman - 2019 - Mind 128 (512):1117-1147.
    Many historical and philosophical studies treat infinity as an exclusively quantitative notion, whose proper domain of application is mathematics and physics. The main aim of this paper is to disentangle, by critically examining, three notions of infinity in the early modern period, and to argue that one—but only one—of them is quantitative. One of these non-quantitative notions concerns being or reality, while the other concerns a particular iterative property of an aggregate. These three notions will emerge through examination (...)
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  7. Philosophical Perspectives on Infinity.Graham Oppy - 2006 - Cambridge University Press.
    This book is an exploration of 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 analyses the many puzzles and paradoxes that follow in the train of the infinite. Even simple notions, such as counting, adding and maximising 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 (...)
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  8.  1
    Infinity: A Very Short Introduction.Ian Stewart - 2017 - Oxford University Press UK.
    Infinity is an intriguing topic, with connections to religion, philosophy, metaphysics, logic, and physics as well as mathematics. Its history goes back to ancient times, with especially important contributions from Euclid, Aristotle, Eudoxus, and Archimedes. The infinitely large is intimately related to the infinitely small. Cosmologists consider sweeping questions about whether space and time are infinite. Philosophers and mathematicians ranging from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals. Many vital areas of mathematics rest upon (...)
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  9. Totality and Infinity: An Essay on Exteriority.Emmanuel Levinas - 1961 - Distribution for the U.S. And Canada, Kluwer Boston.
    INTRODUCTION Ever since the beginning of the modern phenomenological movement disciplined attention has been paid to various patterns of human experience as ...
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  10. Infinity in Early Modern Philosophy.Nachtomy Ohad & Winegar Reed (eds.) - 2018 - Dordrecht, Netherlands: Springer.
    This volume contains essays that examine infinity in early modern philosophy. The essays not only consider the ways that key figures viewed the concept. They also detail how these different beliefs about infinity influenced major philosophical systems throughout the era. These domains include mathematics, metaphysics, epistemology, ethics, science, and theology. Coverage begins with an introduction that outlines the overall importance of infinity to early modern philosophy. It then moves from a general background of infinity up through (...)
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  11.  81
    Infinity and the Foundations of Linguistics.Ryan Nefdt - 2019 - Synthese 196 (5):1671-1711.
    The concept of linguistic infinity has had a central role to play in foundational debates within theoretical linguistics since its more formal inception in the mid-twentieth century. The conceptualist tradition, marshalled in by Chomsky and others, holds that infinity is a core explanandum and a link to the formal sciences. Realism/Platonism takes this further to argue that linguistics is in fact a formal science with an abstract ontology. In this paper, I argue that a central misconstrual of formal (...)
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  12. The Infinity From Nothing Paradox and the Immovable Object Meets the Irresistible Force.Nicholas Shackel - 2018 - European Journal for Philosophy of Science 8 (3):417-433.
    In this paper I present a novel supertask in a Newtonian universe that destroys and creates infinite masses and energies, showing thereby that we can have infinite indeterminism. Previous supertasks have managed only to destroy or create finite masses and energies, thereby giving cases of only finite indeterminism. In the Nothing from Infinity paradox we will see an infinitude of finite masses and an infinitude of energy disappear entirely, and do so despite the conservation of energy in all collisions. (...)
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  13.  58
    Infinity: An Essay in Metaphysics.Jose Benardete - 1964 - Clarendon Press.
  14.  64
    Infinity and Continuity in Ancient and Medieval Thought.Norman Kretzmann (ed.) - 1982 - Cornell University Press.
  15.  39
    To Infinity and Beyond: A Cultural History of the Infinite.Eli Maor - 1987 - Princeton University Press.
    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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  16. Totality and Infinity.Emmanuel Levinas - 1961/1969 - Pittsburgh: Duquesne University Press.
  17.  10
    Infinity, Infinite Processes and Limit Concepts: Recovering a Neglected Background of Social and Critical Theory.Piet Strydom - 2017 - Philosophy and Social Criticism 43 (8):793-811.
    This article seeks to recover a neglected chapter in the historical and theoretical background of social theory in general and critical theory in particular with a view to refining the understanding of the presuppositions of a cognitively enhanced critical social science appropriate to our troubled times. For this purpose, it offers a brief reconstruction of the mathematical-philosophical tradition from ancient to modern times by extrapolating that part of it that is marked by the ideas of infinity, infinite processes and (...)
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  18. Infinity Goes Up on Trial: Must Immortality Be Meaningless?Timothy Chappell - 2009 - European Journal of Philosophy 17 (1):30-44.
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  19. Aristotle's Actual Infinities.Jacob Rosen - 2021 - Oxford Studies in Ancient Philosophy 59.
    Aristotle is said to have held that any kind of actual infinity is impossible. I argue that he was a finitist (or "potentialist") about _magnitude_, but not about _plurality_. He did not deny that there are, or can be, infinitely many things in actuality. If this is right, then it has implications for Aristotle's views about the metaphysics of parts and points.
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  20.  1
    Infinity and the Brain: A Unified Theory of Mind, Matter and God.Glenn Dudley - 2002 - Paragon House.
    Infinity and the Brain proposes a logical and scientific way to resolve the paradox of mind and matter -- by explaining how the perception of a finite image is dependent upon the contrasting infinitude of God. The theory holds that awareness is equal to a tension between existence and nonexistence, such that the self is illuminated to itself (becomes conscious) to the exact measure that it anticipates the infinitude of its own nonexistence. This "anticipation" is actually a "tendency toward" (...)
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  21. Aristotelian Infinity.John Bowin - 2007 - Oxford Studies in Ancient Philosophy 32:233-250.
    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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  22.  26
    An Infinity of Super-Belnap Logics.Umberto Rivieccio - 2012 - Journal of Applied Non-Classical Logics 22 (4):319 - 335.
    We look at extensions (i.e., stronger logics in the same language) of the Belnap?Dunn four-valued logic. We prove the existence of a countable chain of logics that extend the Belnap?Dunn and do not coincide with any of the known extensions (Kleene?s logics, Priest?s logic of paradox). We characterise the reduced algebraic models of these new logics and prove a completeness result for the first and last element of the chain stating that both logics are determined by a single finite logical (...)
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  23. Finitude, Infinity and Time: A Study in Hegel's Idea of System.Mitchell S. Aboulafia - 1978 - Dissertation, Boston College
     
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  24.  11
    Infinity. Edited by Daniel O. Dahlstrom, David T. Ozar, Leo Sweeney.Fernand Van Steenberghen - 1986 - Revue Philosophique De Louvain 84 (61):122-122.
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  25.  13
    Infinity in the Presocratics: A Bibliographical and Philosophical Study.Leo Sweeney - 1972 - The Hague: M. Nijhoff.
    Throughout the long centuries of western metaphysics the problem of the infinite has kept surfacing in different but important ways. It had confronted Greek philosophical speculation from earliest times. It appeared in the definition of the divine attributed to Thales in Diogenes Laertius (I, 36) under the description "that which has neither beginning nor end. " It was presented on the scroll of Anaximander with enough precision to allow doxographers to transmit it in the technical terminology of the unlimited (apeiron) (...)
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  26. Infinity and Givenness: Kant on the Intuitive Origin of Spatial Representation.Daniel Smyth - 2014 - Canadian Journal of Philosophy 44 (5-6):551-579.
    I advance a novel interpretation of Kant's argument that our original representation of space must be intuitive, according to which the intuitive status of spatial representation is secured by its infinitary structure. I defend a conception of intuitive representation as what must be given to the mind in order to be thought at all. Discursive representation, as modelled on the specific division of a highest genus into species, cannot account for infinite complexity. Because we represent space as infinitely complex, the (...)
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  27. Ethics and Infinity.Emmanuel Lévinas & Philippe Nemo - 1985
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  28.  3
    Infinity: The Quest to Think the Unthinkable.Brian Clegg - 2003 - Publishers Group West.
    It amazes children, as they try to count themselves out of numbers, only to discover one day that the hundreds, thousands, and zillions go on forever—to something like infinity. And anyone who has advanced beyond the bounds of basic mathematics has soon marveled at that drunken number eight lying on its side in the pages of their work. Infinity fascinates; it takes the mind beyond its everyday concerns—indeed, beyond everything—to something always more. Infinity makes even the infinite (...)
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  29.  27
    The Beginning of Infinity: Explanations That Transform the World.David Deutsch - 2011 - Viking Adult.
    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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  30. Infinity, an essay in metaphysics. [REVIEW]R. Blanché - 1964 - Revue Philosophique de la France Et de l'Etranger 156:502-503.
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  31.  12
    Infinity: Beyond the Beyond the Beyond.Lillian R. Lieber - 1953 - Paul Dry Books.
    This elegant, accessible artfully illuminates the concept of infinity with its striking drawings.
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  32.  39
    Infinity Goes Up On Trial: Must Immortality Be Meaningless?Timothy Chappell - 2009 - European Journal of Philosophy 17 (1):30-44.
    Critically debates the distinction of different types of boredom and its impact on Williams’s argument, as well as the question of why personal identity should be threatened by eternally having new ground projects.
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  33.  74
    Infinity and Vagueness.David H. Sanford - 1975 - Philosophical Review 84 (4):520-535.
    Many philosophic arguments concerned with infinite series depend on the mutual inconsistency of statements of the following five forms: (1) something exists which has R to something; (2) R is asymmetric; (3) R is transitive; (4) for any x which has R to something, there is something which has R to x; (5) only finitely many things are related by R. Such arguments are suspect if the two-place relation R in question involves any conceptual vagueness or inexactness. Traditional sorites arguments (...)
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  34. Infinity Machines and Creation Ex Nihilo.Jon Perez Laraudogoitia - 1998 - Synthese 115 (2):259-265.
    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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  35.  2
    Medieval Cosmology: Theories of Infinity, Place, Time, Void, and the Plurality of Worlds.Pierre Duhem - 1985 - University of Chicago Press.
    These selections from Le système du monde, the classic ten-volume history of the physical sciences written by the great French physicist Pierre Duhem (1861-1916), focus on cosmology, Duhem's greatest interest. By reconsidering the work of such Arab and Christian scholars as Averroes, Avicenna, Gregory of Rimini, Albert of Saxony, Nicole Oresme, Duns Scotus, and William of Occam, Duhem demonstrated the sophistication of medieval science and cosmology.
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  36.  88
    Infinity in Mathematics: Is Cantor Necessary?Solomon Feferman - 1989 - Philosophical Topics 17 (2):23-45.
  37.  34
    Grasping Infinity by Finite Sets.Ferrante Formato & Giangiacomo Gerla - 1998 - Mathematical Logic Quarterly 44 (3):383-393.
    We show that the existence of an infinite set can be reduced to the existence of finite sets “as big as we will”, provided that a multivalued extension of the relation of equipotence is admitted. In accordance, we modelize the notion of infinite set by a fuzzy subset representing the class of wide sets.
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  38. Avicennan Infinity: A Select History of the Infinite Through Avicenna.Jon Mcginnis - 2010 - Documenti E Studi Sulla Tradizione Filosofica Medievale 21:199-222.
     
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  39.  59
    Aristotelian Infinity.Jaakko Hintikka - 1966 - Philosophical Review 75 (2):197-218.
  40. Infinity and Perspective.Howard H. Newman Professor of Philosophy Karsten Harries & Karsten Harries - 2001 - Mit Press.
    A philosophical exploration of the origin and limits of the modern world.
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  41. Infinity and Continuity.John E. Murdoch - 1982 - In Norman Kretzmann, Anthony Kenny & Jan Pinborg (eds.), Cambridge History of Later Medieval Philosophy. Cambridge: Cambridge University Press. pp. 564--91.
     
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  42.  14
    Infinities as Natural Places.Juliano Neves - 2019 - Foundations of Science 24 (1):39-49.
    It is shown that a notion of natural place is possible within modern physics. For Aristotle, the elements—the primary components of the world—follow to their natural places in the absence of forces. On the other hand, in general relativity, the so-called Carter–Penrose diagrams offer a notion of end for objects along the geodesics. Then, the notion of natural place in Aristotelian physics has an analog in the notion of conformal infinities in general relativity.
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  43. Oppy, Infinity, and the Neoclassical Concept of God.Daniel A. Dombrowski - 2007 - International Journal for Philosophy of Religion 61 (1):25 - 37.
    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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  44. Reflecting on Absolute Infinity.Philip Welch & Leon Horsten - 2016 - Journal of Philosophy 113 (2):89-111.
    This article is concerned with reflection principles in the context of Cantor’s conception of the set-theoretic universe. We argue that within such a conception reflection principles can be formulated that confer intrinsic plausibility to strong axioms of infinity.
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  45.  12
    Infinity in Early Modern Philosophy.Igor Agostini, Richard T. W. Arthur, Geoffrey Gorham, Paul Guyer, Mogens Lærke, Yitzhak Y. Melamed, Ohad Nachtomy, Sanja Särman, Anat Schechtman, Noa Shein & Reed Winegar (eds.) - 2018 - Springer Verlag.
    This volume contains essays that examine infinity in early modern philosophy. The essays not only consider the ways that key figures viewed the concept. They also detail how these different beliefs about infinity influenced major philosophical systems throughout the era. These domains include mathematics, metaphysics, epistemology, ethics, science, and theology. Coverage begins with an introduction that outlines the overall importance of infinity to early modern philosophy. It then moves from a general background of infinity up through (...)
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  46. Infinity and Kant's Conception of the "Possibility of Experience".Charles Parsons - 1964 - Philosophical Review 73 (2):182-197.
  47. Infinity and the Past.Quentin Smith - 1987 - Philosophy of Science 54 (1):63-75.
    infinite, and offer several arguments in sup port of this thesis. I believe their arguments are unsuccessful and aim to refute six of them in the six sections of the paper. One of my main criticisms concerns their supposition that an infinite series of past events must contain some events separated from the present event by an infinite number of intermediate events, and consequently that from one of these infinitely distant past events the present could never have been reached. I (...)
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  48. Infinity in Science and Religion. The Creative Role of Thinking About Infinity.Wolfgang Achtner - 2005 - Neue Zeitschrift für Systematicsche Theologie Und Religionsphilosophie 47 (4):392-411.
    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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  49.  13
    Truth, Objects, Infinity: New Perspectives on the Philosophy of Paul Benacerraf.Fabrice Pataut (ed.) - 2016 - Springer Verlag.
    This volume features essays about and by Paul Benacerraf, whose ideas have circulated in the philosophical community since the early nineteen sixties, shaping key areas in the philosophy of mathematics, the philosophy of language, the philosophy of logic, and epistemology. The book started as a worskhop held in Paris at the Collège de France in May 2012 with the participation of Paul Benacerraf. The introduction addresses the methodological point of the legitimate use of so-called “Princess Margaret Premises” in drawing philosophical (...)
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  50.  67
    Rails to Infinity: Essays on Themes From Wittgenstein's Philosophical Investigations.Crispin Wright (ed.) - 2001 - Harvard University Press.
    This volume, published on the fiftieth anniversary of Wittgenstein's death, brings together thirteen of Crispin Wright's most influential essays on Wittgenstein ...
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