This category needs an editor. We encourage you to help if you are qualified.
Volunteer, or read more about what this involves.
Related categories
Siblings:
85 found
Search inside:
(import / add options)   Sort by:
1 — 50 / 85
  1. Wolfgang Achtner (2011). Part I. Perspectives on Infinity From History : 1. Infinity as a Transformative Concept in Science and Theology. In Michał Heller & W. H. Woodin (eds.), Infinity: New Research Frontiers. Cambridge University Press.
    Remove from this list |
     
    My bibliography  
     
    Export citation  
  2. Victor Allis & Teun Koetsier (1995). On Some Paradoxes of the Infinite II. British Journal for the Philosophy of Science 46 (2):235-247.
    In an earlier paper the authors discussed some super-tasks by means of a kinematical interpretation. In the present paper we show a semi-formal way that a more abstract treatment is possible. The core idea of our approach is simple: if a super-task can be considered as a union of (finite) tasks, it is natural to define the effect of the super-task as the union of the effects of the finite tasks it consists of. We show that this approach enables us (...)
    Remove from this list | Direct download (10 more)  
     
    My bibliography  
     
    Export citation  
  3. L. Anckaert (2006). A Critique of Infinity: Rosenzweig and Levinas. Peeters.
    As such, this book is both a critique and a tribute to Rosenzweig and Levinas. The book contains an exhaustive bibliography of the comparative studies.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  4. Vieri Benci, Leon Horsten & Sylvia Wenmackers (2012). Axioms for Non-Archimedean Probability (NAP). In De Vuyst J. & Demey L. (eds.), Future Directions for Logic; Proceedings of PhDs in Logic III - Vol. 2 of IfColog Proceedings. College Publications.
    In this contribution, we focus on probabilistic problems with a denumerably or non-denumerably infinite number of possible outcomes. Kolmogorov (1933) provided an axiomatic basis for probability theory, presented as a part of measure theory, which is a branch of standard analysis or calculus. Since standard analysis does not allow for non-Archimedean quantities (i.e. infinitesimals), we may call Kolmogorov's approach "Archimedean probability theory". We show that allowing non-Archimedean probability values may have considerable epistemological advantages in the infinite case. The current paper (...)
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  5. J. Biard & J. Celeyrette (eds.) (2005). De la Théologie aux Mathématiques: L'Infini au Xive Siècle. Belles Lettres.
    Remove from this list |
    Translate to English
    |
     
    My bibliography  
     
    Export citation  
  6. Johannes Brachtendorf (ed.) (2008). Unendlichkeit: Interdisziplinäre Perspektiven. Mohr Siebeck.
    Remove from this list |
    Translate to English
    |
     
    My bibliography  
     
    Export citation  
  7. Manuel Bremer, Frege's Basic Law V and Cantor's Theorem.
    The following essay reconsiders the ontological and logical issues around Frege’s Basic Law (V). If focuses less on Russell’s Paradox, as most treatments of Frege’s Grundgesetze der Arithmetik (GGA)1 do, but rather on the relation between Frege’s Basic Law (V) and Cantor’s Theorem (CT). So for the most part the inconsistency of Naïve Comprehension (in the context of standard Second Order Logic) will not concern us, but rather the ontological issues central to the conflict between (BLV) and (CT). These ontological (...)
    Remove from this list |
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  8. Douglas S. Bridges (1995). Constructive Mathematics and Unbounded Operators — a Reply to Hellman. Journal of Philosophical Logic 24 (5):549 - 561.
    It is argued that Hellman's arguments purporting to demonstrate that constructive mathematics cannot cope with unbounded operators on a Hilbert space are seriously flawed, and that there is no evidence that his thesis is correct.
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  9. Manuel Cabada Castro (2008). Recuperar la Infinitud: En Torno Al Debate Histórico-Filosófico Sobre la Limitación o Ilimitación de la Realidad. Universidad Pontificia Comillas.
    Remove from this list |
    Translate to English
    |
     
    My bibliography  
     
    Export citation  
  10. Adelino Cardoso (ed.) (2006). O Envolvimento Do Infinito No Finito. Centro de Filosofia da Universidade de Lisboa.
    Remove from this list |
    Translate to English
    |
     
    My bibliography  
     
    Export citation  
  11. P. Cariani (2012). Infinity and the Observer: Radical Constructivism and the Foundations of Mathematics. 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 (...)
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  12. Massimiliano Carrara & Enrico Martino (2011). On the Infinite in Mereology with Plural Quantification. Review of Symbolic Logic 4 (1):54-62.
    In Lewis reconstructs set theory using mereology and plural quantification (MPQ). In his recontruction he assumes from the beginning that there is an infinite plurality of atoms, whose size is equivalent to that of the set theoretical universe. Since this assumption is far beyond the basic axioms of mereology, it might seem that MPQ do not play any role in order to guarantee the existence of a large infinity of objects. However, we intend to demonstrate that mereology and plural quantification (...)
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  13. Joseph S. Catalano (1969). Aristotle and Cantor: On the Mathematical Infinite. The Modern Schoolman 46 (3):264-267.
  14. Mark Cauchi (2003). Infinite Spaces Walter Benjamin and the Spurious Creations of Capitalism. Angelaki 8 (3):23 – 39.
  15. Michael Clark (1992). An Introduction to Infinity. Cogito 6 (1):18-23.
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  16. Brian Clegg (2003). Infinity: The Quest to Think the Unthinkable. Distributed by 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 universe seem (...)
    Remove from this list |
     
    My bibliography  
     
    Export citation  
  17. Daniel O. Dahlstrom, David T. Ozar & Leo Sweeney (eds.) (1981). Infinity. National Office of the American Catholic Philosophical Association, Catholic University of America.
    Remove from this list |
     
    My bibliography  
     
    Export citation  
  18. Joseph W. Dauben (1977). Georg Cantor and Pope Leo XIII: Mathematics, Theology, and the Infinite. Journal of the History of Ideas 38 (1):85-108.
    Remove from this list |
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  19. Anne Ashley Davenport (1999). Measure of a Different Greatness: The Intensive Infinite, 1250-1650. Brill.
    This volume examines a selection of late medieval works devoted to the intensive infinite in order to draw a comprehensive picture of the context, character and ...
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  20. Donatella Di Cesare (2004). Ermeneutica Della Finitezza. Guerini Studio.
    Remove from this list |
    Translate to English
    |
     
    My bibliography  
     
    Export citation  
  21. Adam Drozdek (2008). In the Beginning Was the Apeiron: Infinity in Greek Philosophy. Steiner.
    Remove from this list |
     
    My bibliography  
     
    Export citation  
  22. Philip Ehrlich (1982). Negative, Infinite, and Hotter Than Infinite Temperatures. Synthese 50 (2):233 - 277.
    We examine the notions of negative, infinite and hotter than infinite temperatures and show how these unusual concepts gain legitimacy in quantum statistical mechanics. We ask if the existence of an infinite temperature implies the existence of an actual infinity and argue that it does not. Since one can sensibly talk about hotter than infinite temperatures, we ask if one could legitimately speak of other physical quantities, such as length and duration, in analogous terms. That is, could there be longer (...)
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  23. Austin Marsden Farrer (1979). Finite and Infinite: A Philosophical Essay. Seabury Press.
    Remove from this list |
     
    My bibliography  
     
    Export citation  
  24. Joseph S. Fulda (1992). Reply to an Objection to Animal Rights. Journal of Value Inquiry 26 (1):87-88.
    Notwithstanding the numerous errors in this piece, the core teaching remains unscathed: Arithmetic (or any other branch of mathematics) cannot do moral work. If it appears otherwise, that simply means some nonstandard version of the relevant area of mathematics will work. -/- Negative results can indeed sometimes be shown using mathematics, but not on such fundamental normative questions as whether something/someone has rights. Also, mathematics can put into relief, sometimes, a fundamental normative question, even though it cannot resolve it.
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  25. D. A. Gillies (1980). Phenomenology and the Infinite in Mathematics. [REVIEW] British Journal for the Philosophy of Science 31 (3):289-298.
    Remove from this list | Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  26. Philip Goodchild (ed.) (2003). Difference in Philosophy of Religion. Ashgate Pub Ltd.
    This book challenges the dominant agenda in the discipline of philosophy of religion by exploring issues of difference that have hitherto been obscured.
    Remove from this list |
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  27. André Gravil (2007). Philosophie Et Finitude. Cerf.
    Remove from this list |
    Translate to English
    |
     
    My bibliography  
     
    Export citation  
  28. Jeremy Gwiazda (2013). Two Concepts of Completing an Infinite Number of Tasks. The Reasoner 7 (6):69-70.
    Remove from this list |
     
    My bibliography  
     
    Export citation  
  29. Jeremy Gwiazda, Infinite Numbers Are Large Finite Numbers.
    In this paper, I suggest that infinite numbers are large finite numbers, and that infinite numbers, properly understood, are 1) of the structure omega + (omega* + omega)Ө + omega*, and 2) the part is smaller than the whole. I present an explanation of these claims in terms of epistemic limitations. I then consider the importance, part of which is demonstrating the contradiction that lies at the heart of Cantorian set theory: the natural numbers are too large to be counted (...)
    Remove from this list |
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  30. Jan-Olav Henriksen (2011). Finitude and Theological Anthropology: An Interdisciplinary Exploration Into Theological Dimensions of Finitude. Peeters.
    The finite body -- Experiencing finitude n the body and its world -- Finitude, language, and the alterity of the world -- The appearance of the other : and the disruption of finitude by infinity -- Transcending and affirming finitude in desire -- Finitude and authenticity : a discussion of some elements in Heidegger -- Finitude and concrete experience -- Hans Jonas : a limited life is a better life than one that goes on forever -- Coming to terms with (...)
    Remove from this list |
     
    My bibliography  
     
    Export citation  
  31. Philip Hugly & Charles Sayward (1984). Do We Need Quantification? Notre Dame Journal of Formal Logic 25 (4):289-302.
    The standard response is illustrated by E, J. Lemmon's claim that if all objects in a given universe had names and there were only finitely many of them, then we could always replace a universal proposition about that universe by a complex proposition. It is because these two requirements are not always met that we need universal quantification. This paper is partly in agreement with Lemmon and partly in disagreement. From the point of view of syntax and semantics we can (...)
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  32. Carlo Ierna (2003). Husserl and the Infinite. Studia Phaenomenologica 3 (1-2):179-194.
    In the article Husserl’s view of the infinite around 1890 is analysed. I give a survey of his mathematical background and other important influences (especially Bolzano). The article contains a short exposition on Husserl's distinction between proper and symbolic presentations in the "Philosophie der Arithmetik" and between finite and infinite symbolic collections. Subsequently Husserl’s conception of surrogate presentations in his treatise "Zur Logik der Zeichen (Semiotik)" is discussed. In this text Husserl gives a detailed account of infinity, using surrogate presentations. (...)
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  33. Ignasi Jané (2010). Idealist and Realist Elements in Cantor's Approach to Set Theory. Philosophia Mathematica 18 (2):193-226.
    There is an apparent tension between the open-ended aspect of the ordinal sequence and the assumption that the set-theoretical universe is fully determinate. This tension is already present in Cantor, who stressed the incompletable character of the transfinite number sequence in Grundlagen and avowed the definiteness of the totality of sets and numbers in subsequent philosophical publications and in correspondence. The tension is particularly discernible in his late distinction between sets and inconsistent multiplicities. I discuss Cantor’s contrasting views, and I (...)
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  34. Juliette Kennedy (ed.) (forthcoming). Interpreting Gödel. Cambridge.
  35. Theokritos Kouremenos (1995). Aristotle on Mathematical Infinity. F. Steiner.
    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 ...
    Remove from this list | Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  36. Norman Kretzmann (ed.) (1982). Infinity and Continuity in Ancient and Medieval Thought. Cornell University Press.
    Remove from this list |
     
    My bibliography  
     
    Export citation  
  37. G. Landini (2011). Logicism and the Problem of Infinity: The Number of Numbers. Philosophia Mathematica 19 (2):167-212.
    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 infinity (...)
    Remove from this list | Direct download (11 more)  
     
    My bibliography  
     
    Export citation  
  38. Shaughan Lavine (1995). Finite Mathematics. Synthese 103 (3):389 - 420.
    A system of finite mathematics is proposed that has all of the power of classical mathematics. I believe that finite mathematics is not committed to any form of infinity, actual or potential, either within its theories or in the metalanguage employed to specify them. I show in detail that its commitments to the infinite are no stronger than those of primitive recursive arithmetic. The finite mathematics of sets is comprehensible and usable on its own terms, without appeal to any form (...)
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  39. Shaughan Lavine (1994). Understanding the Infinite. Harvard University Press.
    An engaging account of the origins of the modern mathematical theory of the infinite, his book is also a spirited defense against the attacks and misconceptions ...
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  40. Hugh Lehman (1983). Intuitionism and Platonism on Infinite Totalities. Idealistic Studies 13 (3):190-198.
  41. Lillian R. Lieber (1953/2007). Infinity: Beyond the Beyond the Beyond. Paul Dry Books.
    This elegant, accessible artfully illuminates the concept of infinity with its striking drawings.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  42. Laureano Luna (2012). Grim's Arguments Against Omniscience and Indefinite Extensibility. International Journal for Philosophy of Religion 72 (2):89-101.
    Patrick Grim has put forward a set theoretical argument purporting to prove that omniscience is an inconsistent concept and a model theoretical argument for the claim that we cannot even consistently define omniscience. The former relies on the fact that the class of all truths seems to be an inconsistent multiplicity (or a proper class, a class that is not a set); the latter is based on the difficulty of quantifying over classes that are not sets. We first address the (...)
    Remove from this list | Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  43. Laureano Luna & William Taylor (2010). Cantor's Proof in the Full Definable Universe. Australasian Journal of Logic 9:11-25.
    Cantor’s proof that the powerset of the set of all natural numbers is uncountable yields a version of Richard’s paradox when restricted to the full definable universe, that is, to the universe containing all objects that can be defined not just in one formal language but by means of the full expressive power of natural language: this universe seems to be countable on one account and uncountable on another. We argue that the claim that definitional contexts impose restrictions on the (...)
    Remove from this list |
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  44. Ofra Magidor (2008). Another Note on Zeno's Arrow. Phronesis 53 (s 4-5):359-372.
    In Physics VI.9 Aristotle addresses Zeno's four paradoxes of motion and amongst them the arrow paradox. In his brief remarks on the paradox, Aristotle suggests what he takes to be a solution to the paradox.In two famous papers, both called 'A note on Zeno's arrow', Gregory Vlastos and Jonathan Lear each suggest an interpretation of Aristotle's proposed solution to the arrow paradox. In this paper, I argue that these two interpretations are unsatisfactory, and suggest an alternative interpretation. In particular, I (...)
    Remove from this list | Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  45. Ofra Magidor (2007). Strict Finitism Refuted? Proceedings of the Aristotelian Society 107 (1pt3):403-411.
    In his paper ‘Wang’s Paradox’, Michael Dummett provides an argument for why strict finitism in mathematics is internally inconsistent and therefore an untenable position. Dummett’s argument proceeds by making two claims: (1) Strict finitism is committed to the claim that there are sets of natural numbers which are closed under the successor operation but nonetheless have an upper bound; (2) Such a commitment is inconsistent, even by finitistic standards. -/- In this paper I claim that Dummett’s argument fails. I question (...)
    Remove from this list | Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  46. Eli Maor (1987/1991). To Infinity and Beyond: A Cultural History of the Infinite. 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 describes (...)
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  47. Mathieu Marion (1998). Wittgenstein, Finitism, and the Foundations of Mathematics. Oxford University Press.
    This pioneering book demonstrates the crucial importance of Wittgenstein's philosophy of mathematics to his philosophy as a whole. Marion traces the development of Wittgenstein's thinking in the context of the mathematical and philosophical work of the times, to make coherent sense of ideas that have too often been misunderstood because they have been presented in a disjointed and incomplete way. In particular, he illuminates the work of the neglected 'transitional period' between the Tractatus and the Investigations.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  48. John Mayberry (1977). The Consistency Problem for Set Theory: An Essay on the Cantorian Foundations of Mathematics (II). British Journal for the Philosophy of Science 28 (2):137-170.
    Remove from this list | Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  49. Yitzhak Y. Melamed (2010). The Metaphysics of Spinoza's Theological Political Treatise. In Yitzhak Melamed (ed.), Spinoza's Theological Political Treatise: A Critical Guide. Cambridge.
  50. Elliott Mendelson (2007). Graham Oppy. Philosophical Perspectives on Infinity. Philosophia Mathematica 15 (3):397-399.
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
1 — 50 / 85