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  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.
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  2. B. Allen (2004). Infinity and Perspective. Common Knowledge 10 (2):366-366.
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  3. R. E. Allen (1974). Unity and Infinity: Parmenides 142b-145a. Review of Metaphysics 27 (4):697 - 725.
  4. 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 (...)
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  5. Joseph Almog (1999). Nothing, Something, Infinity. Journal of Philosophy 96 (9):462-478.
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  6. Joseph Almog (1999). Nothing, Something, Infinity. Journal of Philosophy 96 (9):462.
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  7. Logique A. Analyse (2008). Some Attempts at a Direct Reduction of the Infinite to the (Large) Finite Luca Bellotti. Logique Et Analyse 51:3.
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  8. 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.
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  9. W. S. Anglin (1997). The Philosophy of Mathematics the Invisible Art.
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  10. Hippocrates George Apostle (1952). Aristotle's Philosophy of Mathematics. University of Chicago Press.
  11. Morton F. Arnsdorf (1997). Keys to Infinity by Clifford A. Pickover. Perspectives in Biology and Medicine 40 (3):459-463.
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  12. Svante Arrhenius (1911). Comment on His "Infinity of the Universe." By Paul Carus. The Monist 21:285.
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  13. Svante Arrhenius (1911). Infinity of the Universe. The Monist 21 (2):161-173.
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  14. Sidney C. Bailin (1985). An Analysis of Finitism and the Justification of Set Theory.
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  15. Steven Barbone (1995). Infinity in Descartes. Philosophical Inquiry 17 (3-4):23-38.
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  16. Arabinda Basu (1974). The Infinite Zero. In Aurobindo Ghose, Srinivasa Iyengar & R. K. (eds.), Sri Aurobindo: A Centenary Tribute. Sri Aurobindo Ashram Press. pp. 310.
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  17. Libor Behounek (ed.) (2004). Logica Yearbook 2003.
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  18. J. Benardete (1979). The Infinite in Mathematics. Review of Metaphysics 32 (4):761-762.
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  19. José A. Benardete (1964). Infinity: An Essay in Metaphysics. Clarendon Press.
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  20. Vieri Benci, Mauro Di Nasso & Marco Forti (2006). An Aristotelian Notion of Size. 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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  21. 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 (...)
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  22. Sophie Berman (1993). Infinity in Descartes. 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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  23. Jose Bernadete (1964). Infinity: An Essay in Metaphysics. Clarendon Press.
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  24. Joël Biard & J. Celeyrette (eds.) (2005). De la Théologie aux Mathématiques: L'Infini au XIVe Siècle. Belles Lettres.
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  25. Marcel Bodea (2001). On The Infinite / Sur L’Infini. 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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  26. Bernard Bolanzo, Hourya Sinaceur, Bernard Bolzano & Centre National des Lettres (1993). Les Paradoxes de L'Infini.
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  27. Bernard Bolzano (1950). 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] Routledge and Kegan Paul.
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  28. Johannes Brachtendorf (ed.) (2008). Unendlichkeit: Interdisziplinäre Perspektiven. Mohr Siebeck.
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  29. 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 (...)
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  30. Manuel Bremer (2007). Varieties of Finitism. 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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  31. 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.
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  32. Robert Bunn (1988). Book Review:Cantorian Set Theory and Limitation of Size Michael Hallett. [REVIEW] 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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  33. Manuel Cabada Castro (2009). ""Philosophical Foundation of the" Transfinite" in G. Cantor and the Question of Infinity. Pensamiento 65 (246):669-711.
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  34. Adelino Cardoso (ed.) (2006). O Envolvimento Do Infinito No Finito. Centro de Filosofia da Universidade de Lisboa.
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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.
    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. Rovelli Carlo (2011). Some Considerations on Infinity in Physics. In Michał Heller & W. H. Woodin (eds.), Infinity: New Research Frontiers. Cambridge University Press. pp. 167--175.
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  37. 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 (...)
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  38. Joseph S. Catalano (1969). Aristotle and Cantor: On the Mathematical Infinite. Modern Schoolman 46 (3):264-267.
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  39. Mark Cauchi (2003). Infinite Spaces Walter Benjamin and the Spurious Creations of Capitalism. Angelaki 8 (3):23 – 39.
  40. Mark Cauchi (2003). Traversing the Infinite Through Augustine and Derrida. In Philip Goodchild (ed.), Difference in Philosophy of Religion. Ashgate. pp. 45--57.
  41. David J. Chalmers, Pick a Number Between Zero and Infinity.
    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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  42. Ram Chandra (1963). Towards Infinity. [Shahjahanpur, Shri Ram Chandra Mission.
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  43. Michael Clark (1992). An Introduction to Infinity. Cogito 6 (1):18-23.
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  44. Brian Clegg (2003). Infinity: The Quest to Think the Unthinkable. 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 small; (...)
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  45. Charles W. Cobb (1915). On the Notion of Infinity. Journal of Philosophy, Psychology and Scientific Methods 12 (16):438-443.
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  46. H. Cohen Daniel, Commentary on Ami Mamolo on Argumentation and Infinity.
    There is more to mathematics than proofs; there are also arguments, which means that mathematicians are human arguers complete with their biases. Among those biases is a preference for beauty, It is a bias insofar as it is a deaprture from objectivity, but it is benign, accounting for the popularity of Cantor's "Paradise" of non-denumerable infinities as a travel destination for mathematicians and the relatively little interest in Robinson's infinitesimals.
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  47. Tim Crowther, On Describing the Total Universe as the Non-Self-Similar Fractal (NSSF) Set.
    One conceptual question has been puzzling people for a long time: As the observable universe has been expanding, what has it been expanding into and where did it come from? In this essay I will combine the two questions above to one: What is the Total Universe? I will begin attempt to develop such a description by examining the linguistic human limitations because I believe that this language barrier between our evolved language and a description of the total universe can (...)
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  48. Daniel O. Dahlstrom, David T. Ozar & Leo Sweeney (eds.) (1981). Infinity. National Office of the American Catholic Philosophical Association, Catholic University of America.
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  49. John E. Dakin (1929). Rhythmic Infinity. New York: W. Neale.
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  50. J. W. Dauben (1979). Georg Cantor: His Mathematics and Philosophy of the Infinite. Hup.
    One of the greatest revolutions in mathematics occurred when Georg Cantor (1845-1918) promulgated his theory of transfinite sets.
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