Results for 'infinity'

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  1. 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.  36
    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. 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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  4.  1
    Infinity and Perspective.Howard H. Newman Professor of Philosophy Karsten Harries & Karsten Harries - 2001 - MIT Press.
    Bronze Award Winner for Philosophy in the ForeWord Magazine Book of the Year Awards. Much postmodern rhetoric, suggests Karsten Harries, can be understood as a symptom of our civilization's discontent, born of regret that we are no longer able to experience our world as a cosmos that assigns us our place. But dissatisfaction with the modern world may also spring from a conviction that modernism has failed to confront the challenge of an inevitably open future. Such conviction has frequently led (...)
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  5. 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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  6. 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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  7.  3
    Infinity: A Very Short Introduction.Ian Stewart - 2017 - Oxford, United Kingdom: 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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  8.  1
    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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  9.  32
    Infinity and Metaphysics.Daniel Nolan - 2009 - In Robin Le Poidevin, Peter Simons, Andrew McGonigal & Ross Cameron (eds.), The Routledge Companion to Metaphysics. New York, NY, USA: Routledge. pp. 430-439.
    This introduction to the roles infinity plays in metaphysics includes discussion of the nature of infinity itself; infinite space and time, both in extent and in divisibility; infinite regresses; and a list of some other topics in metaphysics where infinity plays a significant role.
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  10.  91
    Infinity and the foundations of linguistics.Ryan M. 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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  11. Beyond infinity: an expedition to the outer limits of mathematics.Eugenia Cheng - 2017 - New York: Basic Books.
    A mathematician and scientist in residence at the School of the Art Institute of Chicago helps readers explore the concept of infinity through unique concepts including chessboards, a chicken-sandwich sandwich and the creation of infinite cookies from an infinite dough ball.
     
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  12.  43
    To Infinity and Beyond: A Cultural History of the Infinite.Eli Maor - 1987 - Princeton: 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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  13.  28
    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.
  14.  3
    Infinity.Pablo Bernasconi - 2021 - Oklahoma City & Greensboro: Penny Candy Books.
    What is infinity? It's reading the last line of a book and imagining the rest. No, wait, it's the instruction manual for the machine that operates the sun and the stars. In unexpected observations, captivating images, and even some equations, celebrated Argentinian author-illustrator Pablo Bernasconi, finalist for the 2018 Hans Christian Andersen Award, offers up verses about what infinity could mean to all of us. Winner of the Grand Prize from the Asociación de Literatura Infantil y Juvenil de (...)
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  15.  3
    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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  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.
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  17. 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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  18. 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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  19. 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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  20.  1
    Infinity, What is It?Marnie Luce - 1969 - Minneapolis, Lerner Publications Co..
    Explains and gives examples of the mathematical concept of infinity.
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  21. 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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  22.  94
    Infinity in Mathematics: Is Cantor Necessary?Solomon Feferman - 1989 - Philosophical Topics 17 (2):23-45.
  23. Infinity: New Research Frontiers.Rudy Rucker, Wolfgang Achtner, Enrico Bombieri, Edward Nelson, W. Hugh Woodin & Harvey M. Friedman - 2011 - Cambridge University Press.
    This interdisciplinary study of infinity explores the concept through the prism of mathematics and then offers more expansive investigations in areas beyond mathematical boundaries to reflect the broader, deeper implications of infinity for human intellectual thought. More than a dozen world-renowned researchers in the fields of mathematics, physics, cosmology, philosophy, and theology offer a rich intellectual exchange among various current viewpoints, rather than a static picture of accepted views on infinity.The book starts with a historical examination of (...)
     
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  24.  49
    Benign Infinity.Matthias Steup - 2019 - In Cherie Braden, Rodrigo Borges & Branden Fitelson (eds.), Themes From Klein. Springer Verlag. pp. 235-57.
    According to infinitism, all justification comes from an infinite series of reasons. Peter Klein defends infinitism as the correct solution to the regress problem by rejecting two alternative solutions: foundationalism and coherentism. I focus on Klein's argument against foundationalism, which relies on the premise that there is no justification without meta-justification. This premise is incompatible with dogmatic foundationalism as defended by Michael Huemer and Time Pryor. It does not, however, conflict with non-dogmatic foundationalism. Whereas dogmatic foundationalism rejects the need for (...)
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  25.  6
    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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  26.  71
    Infinity: An Essay in Metaphysics.Jose Benardete - 1964 - Clarendon Press.
  27.  55
    Approaching Infinity[REVIEW]Christopher M. P. Tomaszewski - 2018 - Review of Metaphysics 71 (3):579-580.
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  28.  6
    Infinity and continuum in the alternative set theory.Kateřina Trlifajová - 2021 - European Journal for Philosophy of Science 12 (1):1-23.
    Alternative set theory was created by the Czech mathematician Petr Vopěnka in 1979 as an alternative to Cantor’s set theory. Vopěnka criticised Cantor’s approach for its loss of correspondence with the real world. Alternative set theory can be partially axiomatised and regarded as a nonstandard theory of natural numbers. However, its intention is much wider. It attempts to retain a correspondence between mathematical notions and phenomena of the natural world. Through infinity, Vopěnka grasps the phenomena of vagueness. Infinite sets (...)
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  29.  13
    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 - Cham: 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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  30.  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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  31. Choice, Infinity, and Negation: Both Set-Theory and Quantum-Information Viewpoints to Negation.Vasil Penchev - 2020 - Logic and Philosophy of Mathematics eJournal 12 (14):1-3.
    The concepts of choice, negation, and infinity are considered jointly. The link is the quantity of information interpreted as the quantity of choices measured in units of elementary choice: a bit is an elementary choice between two equally probable alternatives. “Negation” supposes a choice between it and confirmation. Thus quantity of information can be also interpreted as quantity of negations. The disjunctive choice between confirmation and negation as to infinity can be chosen or not in turn: This corresponds (...)
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  32.  36
    Divine Infinity in Greek and Medieval Thought. [REVIEW]William E. Carroll - 1994 - Review of Metaphysics 48 (1):170-171.
    This book reflects the commitment of an academic lifetime to the study of infinity. Most of the essays gathered here have been published before, and, in keeping with the breadth and depth of Sweeney's erudition on the subject, they contain a wealth of information on primary and secondary sources in the history of infinity.
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  33. Infinity.Eric Steinhart - 2007 - In Encyclopedia of American Philosophy. Routledge.
    This article deals with the concept of infinity in classical American philosophy. It focuses on the philosophical and technical developments of infinity in the 19th Century American thinkers Royce and Peirce.
     
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  34.  3
    Introduction: Infinity in Early Modern Philosophy.Ohad Nachtomy & Reed Winegar - 2018 - In 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.), Infinity in Early Modern Philosophy. Springer Verlag. pp. 1-8.
    In his Pensées, Blaise Pascal gives vivid voice to both the wonder and anxiety that many early modern thinkers felt towards infinity. Contemplating our place between the infinite expanse of space and the infinite divisibility of matter, Pascal writes.
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  35.  14
    Infinities as Natural Places.Juliano C. S. 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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  36. 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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  37. Ethics and Infinity.Emmanuel Lévinas & Philippe Nemo - 1985
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  38. 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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  39. Infinity goes up on trial: Must immortality be meaningless?Timothy Chappell - 2009 - European Journal of Philosophy 17 (1):30-44.
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  40. 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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  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.  89
    Infinity, Causation, and Paradox, by Alexander Pruss.Kenny Easwaran - 2019 - Mind 129 (516):1287-1291.
    _ Infinity, Causation, and Paradox _, by PrussAlexander. Oxford: Oxford University Press, 2018. Pp. xiii + 207.
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  43.  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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  44.  93
    Infinity in ontology and mind.Nino B. Cocchiarella - 2008 - Axiomathes 18 (1):1-24.
    Two fundamental categories of any ontology are the category of objects and the category of universals. We discuss the question whether either of these categories can be infinite or not. In the category of objects, the subcategory of physical objects is examined within the context of different cosmological theories regarding the different kinds of fundamental objects in the universe. Abstract objects are discussed in terms of sets and the intensional objects of conceptual realism. The category of universals is discussed in (...)
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  45. Finitude, Infinity and Time: A Study in Hegel's Idea of System.Mitchell S. Aboulafia - 1978 - Dissertation, Boston College
     
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  46.  29
    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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  47. Infinity in ethics.Peter Vallentyne - unknown - Routledge Encyclopedia of Philosophy.
    Puzzles can arise in ethical theory (as well as decision theory) when infinity is involved. The puzzles arise primarily in theories—such as consequentialist theories—that appeal to the value of actions or states of affairs. Section 1 addresses the question of whether one source of value (such as major aesthetic pleasures) can be infinitely more valuable than another (such as minor gustatory pleasures). An affirmative answer is given by appealing to the notion of lexicographic priority. Section 2 address the question (...)
     
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  48.  34
    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).
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  49.  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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  50. Infinity: New Research Frontiers.Michał Heller & W. H. Woodin (eds.) - 2011 - Cambridge University Press.
    Machine generated contents note: Introduction Rudy Rucker; Part I. Perspectives on Infinity from History: 1. Infinity as a transformative concept in science and theology Wolfgang Achtner; Part II. Perspectives on Infinity from Mathematics: 2. The mathematical infinity Enrico Bombieri; 3. Warning signs of a possible collapse of contemporary mathematics Edward Nelson; Part III. Technical Perspectives on Infinity from Advanced Mathematics: 4. The realm of the infinite W. Hugh Woodin; 5. A potential subtlety concerning the distinction (...)
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