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  1. Infinity: An Essay in Metaphysics. [REVIEW]B. D. A. - 1965 - Review of Metaphysics 18 (4):772-772.
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  2. Part I. Perspectives on Infinity From History : 1. Infinity as a Transformative Concept in Science and Theology.Wolfgang Achtner - 2011 - In Michał Heller & W. H. Woodin (eds.), Infinity: New Research Frontiers. Cambridge University Press.
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  3. Unity and Infinity: Parmenides 142b-145a.R. E. Allen - 1974 - Review of Metaphysics 27 (4):697 - 725.
  4. Infinity and Perspective.B. Allen - 2004 - Common Knowledge 10 (2):366-366.
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  5. On Some Paradoxes of the Infinite II.Victor Allis & Teun Koetsier - 1995 - 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 (...)
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  6. Nothing, Something, Infinity.Joseph Almog - 1999 - Journal of Philosophy 96 (9):462-478.
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  7. Nothing, Something, Infinity.Joseph Almog - 1999 - Journal of Philosophy 96 (9):462.
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  8. Some Attempts at a Direct Reduction of the Infinite to the (Large) Finite Luca Bellotti.Logique A. Analyse - 2008 - Logique Et Analyse 51:3.
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  9. A Critique of Infinity: Rosenzweig and Levinas.L. Anckaert - 2006 - 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.
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  10. The Philosophy of Mathematics the Invisible Art.W. S. Anglin - 1997
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  11. Aristotle's Philosophy of Mathematics.Hippocrates George Apostle - 1952 - University of Chicago Press.
  12. The Ethics of the Infinite.Leslie Armour & Suzie Johnston - 1999 - Maritain Studies/Etudes Maritainiennes 15.
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  13. Keys To Infinity.Morton F. Arnsdorf - 1997 - Perspectives in Biology and Medicine 40 (3):455.
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  14. Keys to Infinity by Clifford A. Pickover.Morton F. Arnsdorf - 1997 - Perspectives in Biology and Medicine 40 (3):459-463.
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  15. Comment on His "Infinity of the Universe." By Paul Carus.Svante Arrhenius - 1911 - The Monist 21:285.
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  16. Infinity of the Universe.Svante Arrhenius - 1911 - The Monist 21 (2):161-173.
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  17. An Analysis of Finitism and the Justification of Set Theory.Sidney C. Bailin - 1985
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  18. Scotus: Adumbrations of a New Concept of Infinity.S. Barbone - 1996 - Wissenschaft Und Weisheit 59 (1):35-43.
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  19. Infinity in Descartes.Steven Barbone - 1995 - Philosophical Inquiry 17 (3-4):23-38.
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  20. The Infinite Zero.Arabinda Basu - 1974 - In Aurobindo Ghose, Srinivasa Iyengar & R. K. (eds.), Sri Aurobindo: A Centenary Tribute. Sri Aurobindo Ashram Press. pp. 310.
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  21. Logica Yearbook 2003.Libor Behounek (ed.) - 2004
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  22. The Infinite in Mathematics.J. Benardete - 1979 - Review of Metaphysics 32 (4):761-762.
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  23. Infinity: An Essay in Metaphysics.José A. Benardete - 1964 - Clarendon Press.
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  24. Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity.Peter K. Benbow - 2011 - Annals of Science 70 (3):1-3.
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  25. An Aristotelian Notion of Size.Vieri Benci, Mauro Di Nasso & Marco Forti - 2006 - Annals of Pure and Applied Logic 143 (1):43-53.
    The naïve idea of “size” for collections seems to obey both Aristotle’s Principle: “the whole is greater than its parts” and Cantor’s Principle: “1-to-1 correspondences preserve size”. Notoriously, Aristotle’s and Cantor’s principles are incompatible for infinite collections. Cantor’s theory of cardinalities weakens the former principle to “the part is not greater than the whole”, but the outcoming cardinal arithmetic is very unusual. It does not allow for inverse operations, and so there is no direct way of introducing infinitesimal numbers. Here (...)
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  26. Axioms for Non-Archimedean Probability (NAP).Vieri Benci, Leon Horsten & Sylvia Wenmackers - 2012 - 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 (...)
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  27. Infinity in Descartes.Sophie Berman - 1993 - Dissertation, Fordham University
    In Descartes's Cogito the mind discovers itself as an infinite power of self-assertion, a subjectivity, positing itself from within. But the mind also knows that it is finite, and receives its being from an "Other"--the infinite substance, or God, of which it finds within itself the idea, as one which cannot be derived from its idea of itself. The Cartesian conception of subjectivity is openness to the infinite. ;Descartes's ontological argument shows the infinite as radically "essence". But more fundamentally than (...)
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  28. Infinity: An Essay in Metaphysics.Jose Bernadete - 1964 - Clarendon Press.
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  29. De la Théologie aux Mathématiques: L'Infini au XIVe Siècle.Joël Biard & J. Celeyrette (eds.) - 2005 - Belles Lettres.
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  30. Reasoning with the Infinite: From the Closed World to the Mathematical Universe.Michel Blay - 1999 - University of Chicago Press.
    "One of Michael Blay's many fine achievements in Reasoning with the Infinite is to make us realize how velocity, and later instantaneous velocity, came to play a vital part in the development of a rigorous mathematical science of motion. ...
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  31. On The Infinite / Sur L’Infini.Marcel Bodea - 2001 - Studia Philosophica 1.
    The conception of intuition in mathematics is prominent in early twentieth-century work on foundations of mathematics. The conception of mathematical intuition is partly based on Hilbert’s ideas about the methods of proof theory, a conception of intuitive evidence closer to the finitary method of Hilbert. Hilbert claimed some kind of evidence for finitist mathematics. Hilbert claimed intuitive evidence for individual instances of induction where the predicates involved are of the right kind, in practice primitive recursive. The objects of such intuition (...)
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  32. Les Paradoxes de L'Infini.Bernard Bolanzo, Hourya Sinaceur, Bernard Bolzano & Centre National des Lettres - 1993
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  33. Paradoxes of the Infinite. Translated From the German of the Posthumous Ed. By Fr. Prihonský and Furnished with a Historical Introd. By Donald A. Steele. --. [REVIEW]Bernard Bolzano - 1950 - Routledge and Kegan Paul.
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  34. Les Paradoxes de L'Infini.Emile Borel - 1946 - Gallimard.
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  35. A Secret Ethics of Infinity.Janet Borgerson - forthcoming - Levinas, Business Ethics.
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  36. Unendlichkeit: Interdisziplinäre Perspektiven.Johannes Brachtendorf (ed.) - 2008 - Mohr Siebeck.
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  37. ''While Being as Infinite is Formless, Being as Infinite is Not Concrete: A Reply to Georges Hélal's' Pure Existence, Formless Infinite Being as Ultimate Reality and Meaning'(URAM 17: 70-83). [REVIEW]J. A. Bracken - 1996 - Ultimate Reality and Meaning 19 (2):156-157.
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  38. Frege's Basic Law V and Cantor's Theorem.Manuel Bremer - manuscript
    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 (...)
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  39. Varieties of Finitism.Manuel Bremer - 2007 - Metaphysica 8 (2):131-148.
    I consider here several versions of finitism or conceptions that try to work around postulating sets of infinite size. Restricting oneself to the so-called potential infinite seems to rest either on temporal readings of infinity (or infinite series) or on anti-realistic background assumptions. Both these motivations may be considered problematic. Quine’s virtual set theory points out where strong assumptions of infinity enter into number theory, but is implicitly committed to infinity anyway. The approaches centring on the indefinitely large and the (...)
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  40. Constructive Mathematics and Unbounded Operators — a Reply to Hellman.Douglas S. Bridges - 1995 - 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.
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  41. Book Review:Cantorian Set Theory and Limitation of Size Michael Hallett. [REVIEW]Robert Bunn - 1988 - Philosophy of Science 55 (3):461-.
    The usual objections to infinite numbers, and classes, and series, and the notion that the infinite as such is self-contradictory, may... be dismissed as groundless. There remains, however, a very grave difficulty, connected with the contradiction [of the class of all classes not members of themselves]. This difficulty does not concern the infinite as such, but only certain very large infinite classes.
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  42. ""Philosophical Foundation of the" Transfinite" in G. Cantor and the Question of Infinity.Manuel Cabada Castro - 2009 - Pensamiento 65 (246):669-711.
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  43. O Envolvimento Do Infinito No Finito.Adelino Cardoso (ed.) - 2006 - Centro de Filosofia da Universidade de Lisboa.
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  44. 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 (...)
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  45. Some Considerations on Infinity in Physics.Rovelli Carlo - 2011 - In Michał Heller & W. H. Woodin (eds.), Infinity: New Research Frontiers. Cambridge University Press. pp. 167--175.
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  46. On the Infinite in Mereology with Plural Quantification.Massimiliano Carrara & Enrico Martino - 2010 - 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 (...)
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  47. Aristotle and Cantor: On the Mathematical Infinite.Joseph S. Catalano - 1969 - Modern Schoolman 46 (3):264-267.
  48. Infinite Spaces Walter Benjamin and the Spurious Creations of Capitalism.Mark Cauchi - 2003 - Angelaki 8 (3):23 – 39.
  49. Traversing the Infinite Through Augustine and Derrida.Mark Cauchi - 2003 - In Philip Goodchild (ed.), Difference in Philosophy of Religion. Ashgate. pp. 45--57.
  50. Proof and Infinity: Response to André Porto.O. Chateaubriand - 2008 - Manuscrito 31 (1):45-49.
    The main issue André Porto raises in his paper concerns the use of dot notation to indicate an infinite set of hypotheses. Whereas I agree that one cannot extract a unique infinite expansion from a finite initial segment, in my response I argue that this holds for finite expansions as well. I further explain how my remarks on infinite proof structures are neither motivated by the impact of Gödel’s incompleteness theorems on Hilbert’s program, nor by a negative view of strict (...)
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