Results for 'infinity'

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  1.  25
    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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  2.  64
    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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  3. 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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  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 (...)
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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. Totality and Infinity.Emmanuel Levinas - 1961/1969 - Pittsburgh: Duquesne University Press.
     
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  7.  10
    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.
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  8.  79
    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 (...)
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  9.  53
    Infinity: An Essay in Metaphysics.J. Benardete - 1964 - Clarendon Press.
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  10. 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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  11. 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 ...
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  12. 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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  13. 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 (...)
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  14. 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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  15. Infinity Goes Up on Trial: Must Immortality Be Meaningless?Timothy Chappell - 2009 - European Journal of Philosophy 17 (1):30-44.
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  16. 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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  17. 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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  18.  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 (...)
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  19. Ethics and Infinity.Emmanuel Lévinas & Philippe Nemo - 1985
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  20. 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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  21.  27
    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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  22. 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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  23.  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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  24.  85
    Infinity in Mathematics: Is Cantor Necessary?Solomon Feferman - 1989 - Philosophical Topics 17 (2):23-45.
  25.  33
    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.
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  26.  72
    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 (...)
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  27.  21
    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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  28. Infinity and Kant's Conception of the "Possibility of Experience".Charles Parsons - 1964 - Philosophical Review 73 (2):182-197.
  29.  42
    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 (...)
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  30. 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 (...)
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  31.  57
    Aristotelian Infinity.Jaakko Hintikka - 1966 - Philosophical Review 75 (2):197-218.
  32. 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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  33.  62
    Infinity and Continuity in Ancient and Medieval Thought.Norman Kretzmann (ed.) - 1982 - Cornell University Press.
  34.  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.
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  35. Descartes on the Infinity of Space Vs. Time.Geoffrey Gorham - 2018 - In Ohad Nachtomy & Reed Winegar (eds.), Infinity in Early Modern Philosophy. Berlin: Brill. pp. 45-61.
    In two rarely discussed passages – from unpublished notes on the Principles of Philosophy and a 1647 letter to Chanut – Descartes argues that the question of the infinite extension of space is importantly different from the infinity of time. In both passages, he is anxious to block the application of his well-known argument for the indefinite extension of space to time, in order to avoid the theologically problematic implication that the world has no beginning. Descartes concedes that we (...)
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  36. 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 (...)
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  37.  37
    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 (...)
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  38. 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 (...)
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  39.  65
    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 ...
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  40.  32
    Strong Axioms of Infinity and Elementary Embeddings.Robert M. Solovay - 1978 - Annals of Mathematical Logic 13 (1):73.
  41. 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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  42. Infinity in Pascal's Wager.Graham Oppy - 2018 - In Paul Bartha & Lawrence Pasternack (eds.), Pascal's Wager. Cambridge, UK: pp. 260-77.
    Bartha (2012) conjectures that, if we meet all of the other objections to Pascal’s wager, then the many-Gods objection is already met. Moreover, he shows that, if all other objections to Pascal’s wager are already met, then, in a choice between a Jealous God, an Indifferent God, a Very Nice God, a Very Perverse God, the full range of Nice Gods, the full range of Perverse Gods, and no God, you should wager on the Jealous God. I argue that his (...)
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  43.  92
    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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  44.  91
    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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  45. Infinity in Cosmology.Michał Heller - 2008 - Dialogue and Universalism 18 (9-10):77-87.
    The issue of infinity appeared in cosmology in the form of a question on spatial and time finiteness or infinity of the universe. Recently, more and more talking is going on about “other universes” (different ones from “our”), the number of which may be infinite. Speculations on this topic emerged in effect of the discussions on the issue of the anthropic principle, and the so-called inflation scenario. In truth, this kind of speculations are hardly recognized as scientific theories, (...)
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  46. 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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  47.  74
    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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  48. 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 (...)
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  49. 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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  50.  1
    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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