Results for 'Infinity'

1000+ found
Order:
See also
  1.  31
    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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   53 citations  
  2.  78
    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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  3. 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. (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  4. 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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  5.  82
    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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  6.  16
    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.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  7. 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.
    Direct download  
     
    Export citation  
     
    Bookmark   15 citations  
  8.  61
    Infinity: An Essay in Metaphysics.Jose Benardete - 1964 - Clarendon Press.
  9. 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 (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  10. 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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  11. 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 (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   16 citations  
  12. Totality and Infinity.Emmanuel Levinas - 1961/1969 - Pittsburgh: Duquesne University Press.
  13. Infinity Goes Up on Trial: Must Immortality Be Meaningless?Timothy Chappell - 2009 - European Journal of Philosophy 17 (1):30-44.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   23 citations  
  14.  28
    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.
    Direct download  
     
    Export citation  
     
    Bookmark   29 citations  
  15. 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 ...
    Direct download  
     
    Export citation  
     
    Bookmark   398 citations  
  16. 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.
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  17.  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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   15 citations  
  18. 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 (...)
    Direct download  
     
    Export citation  
     
    Bookmark   34 citations  
  19. 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, (...)
    Direct download  
     
    Export citation  
     
    Bookmark   2 citations  
  20.  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 (...)
    Direct download  
     
    Export citation  
     
    Bookmark   2 citations  
  21. Strong Axioms of Infinity and the Debate About Realism.Kai Hauser & W. Hugh Woodin - 2014 - Journal of Philosophy 111 (8):397-419.
    One of the most distinctive and intriguing developments of modern set theory has been the realization that, despite widely divergent incentives for strengthening the standard axioms, there is essentially only one way of ascending the higher reaches of infinity. To the mathematical realist the unexpected convergence suggests that all these axiomatic extensions describe different aspects of the same underlying reality.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  22. 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 (...)
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  23. Infinity, an essay in metaphysics. [REVIEW]R. Blanché - 1964 - Revue Philosophique de la France Et de l'Etranger 156:502-503.
    Translate
     
     
    Export citation  
     
    Bookmark   29 citations  
  24. Ethics and Infinity.Emmanuel Lévinas & Philippe Nemo - 1985
    No categories
     
    Export citation  
     
    Bookmark   169 citations  
  25.  41
    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.
    Direct download  
     
    Export citation  
     
    Bookmark   10 citations  
  26.  8
    Infinity, Time, and Successive Addition.Wes Morriston - 2022 - Australasian Journal of Philosophy 100 (1):70-85.
    ABSTRACT According to an influential line of argument, the past must be finite because no infinite series can be formed by successive addition. The present paper pinpoints the non sequitur at the heart of this argument, disentangles the ambiguities that disguise it, and dismantles the misleading picture of ‘traversing the infinite’ that gives the argument so much of its allure. Finally, the paper critically explores the related argument that a beginningless series of past events is impossible because there could be (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  27.  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 (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  28. 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 (...)
    No categories
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  29.  34
    Strong Axioms of Infinity and Elementary Embeddings.Robert M. Solovay - 1978 - Annals of Mathematical Logic 13 (1):73.
  30.  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.
    Direct download  
     
    Export citation  
     
    Bookmark   4 citations  
  31.  88
    Infinity in Mathematics: Is Cantor Necessary?Solomon Feferman - 1989 - Philosophical Topics 17 (2):23-45.
  32.  40
    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 (...)
    Direct download  
     
    Export citation  
     
    Bookmark   4 citations  
  33. Avicennan Infinity: A Select History of the Infinite Through Avicenna.Jon Mcginnis - 2010 - Documenti E Studi Sulla Tradizione Filosofica Medievale 21:199-222.
     
    Export citation  
     
    Bookmark   8 citations  
  34.  39
    The Nothing From Infinity Paradox Versus Plenitudinous Indeterminism.Nicholas Shackel - 2022 - European Journal for Philosophy of Science 12 (online early):1-14.
    The Nothing from Infinity paradox arises when the combination of two infinitudes of point particles meet in a supertask and disappear. Corral-Villate claims that my arguments for disappearance fail and concedes that this failure also produces an extreme kind of indeterminism, which I have called plenitudinous. So my supertask at least poses a dilemma of extreme indeterminism within Newtonian point particle mechanics. Plenitudinous indeterminism might be trivial, although easy attempts to prove it so seem to fail in the face (...)
    Direct download (4 more)  
    Translate
     
     
    Export citation  
     
    Bookmark  
  35.  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 (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   13 citations  
  36.  1
    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.
    Direct download  
     
    Export citation  
     
    Bookmark   10 citations  
  37. 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.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  38.  51
    Infinity and the Observer: Radical Constructivism and the Foundations of Mathematics.P. Cariani - 2012 - Constructivist Foundations 7 (2):116-125.
    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 (...)
    Direct download  
     
    Export citation  
     
    Bookmark   2 citations  
  39. 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 (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  40. 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.
     
    Export citation  
     
    Bookmark   17 citations  
  41.  59
    Aristotelian Infinity.Jaakko Hintikka - 1966 - Philosophical Review 75 (2):197-218.
  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.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  43. Infinity and Kant's Conception of the "Possibility of Experience".Charles Parsons - 1964 - Philosophical Review 73 (2):182-197.
  44.  64
    Infinity and Continuity in Ancient and Medieval Thought.Norman Kretzmann (ed.) - 1982 - Cornell University Press.
  45. Cantorian Infinity and Philosophical Concepts of God.Joanna Van der Veen & Leon Horsten - 2013 - European Journal for Philosophy of Religion 5 (3):117--138.
    It is often alleged that Cantor’s views about how the set theoretic universe as a whole should be considered are fundamentally unclear. In this article we argue that Cantor’s views on this subject, at least up until around 1896, are relatively clear, coherent, and interesting. We then go on to argue that Cantor’s views about the set theoretic universe as a whole have implications for theology that have hitherto not been sufficiently recognised. However, the theological implications in question, at least (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  46.  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 ...
    Direct download  
     
    Export citation  
     
    Bookmark   43 citations  
  47.  43
    Infinity and Newton’s Three Laws of Motion.Chunghyoung Lee - 2011 - Foundations of Physics 41 (12):1810-1828.
    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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  48. 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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  49. Finitude, Infinity and Time: A Study in Hegel's Idea of System.Mitchell S. Aboulafia - 1978 - Dissertation, Boston College
     
    Export citation  
     
    Bookmark  
  50.  33
    Infinity in Science and Religion. The Creative Role of Thinking About Infinity.Pd Wolfgang Achtner - 2005 - Neue Zeitschrift für Systematicsche Theologie Und Religionsphilosophie 47 (4).
    Direct download  
     
    Export citation  
     
    Bookmark  
1 — 50 / 1000