Results for 'Infinity'

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  1.  37
    “ ‘A Substance Consisting of an Infinity of Attributes’: Spinoza on the Infinity of Attributes” in Ohad Nachtomy and Reed Wieneger (Eds.), Infinity in Early Modern Philosophy (Springer, Forthcoming).Yitzhak Melamed - 2018 - In Reed Winegar & Ohad Nachtomy (eds.), Infinity in Early Modern Philosophy. Springer.
    Though Spinoza's definition of God at the beginning of the Ethics unequivocally asserts that God has infinitely many attributes, the reader of the Ethics will find only two of these attributes discussed in any detail in Parts Two through Five of the book. Addressing this intriguing gap between the infinity of attributes asserted in E1d6 and the discussion merely of the two attributes of Extension and Thought in the rest of the book, Jonathan Bennett writes: Spinoza seems to imply (...)
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  2. 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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  3. Mathematical Platonism and the Nature of Infinity.Gilbert B. Côté - 2013 - Open Journal of Philosophy 3 (3):372-375.
    An analysis of the counter-intuitive properties of infinity as understood differently in mathematics, classical physics and quantum physics allows the consideration of various paradoxes under a new light (e.g. Zeno’s dichotomy, Torricelli’s trumpet, and the weirdness of quantum physics). It provides strong support for the reality of abstractness and mathematical Platonism, and a plausible reason why there is something rather than nothing in the concrete universe. The conclusions are far reaching for science and philosophy.
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  4.  24
    The Infinity From Nothing Paradox and the Immovable Object Meets the Irresistible Force.Nicholas Shackel - forthcoming - European Journal for Philosophy of Science:1-17.
    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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  5. Hasdai Crescas and Spinoza on Actual Infinity and the Infinity of God’s Attributes.Yitzhak Melamed - 2014 - In Steven Nadler (ed.), Spinoza and Jewish Philosophy. Cambridge University Press. pp. 204-215.
    The seventeenth century was an important period in the conceptual development of the notion of the infinite. In 1643, Evangelista Torricelli (1608-1647)—Galileo’s successor in the chair of mathematics in Florence—communicated his proof of a solid of infinite length but finite volume. Many of the leading metaphysicians of the time, notably Spinoza and Leibniz, came out in defense of actual infinity, rejecting the Aristotelian ban on it, which had been almost universally accepted for two millennia. Though it would be another (...)
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  6.  15
    The Fault in Us: Ethics, Infinity, and Celestial Bodies.Donovan O. Schaefer - 2016 - Zygon 51 (3):783-796.
    Catherine Keller's Cloud of the Impossible knits together process theology and relational ontology with quantum mechanics. In quantum physics, she finds a new resource for undoing the architecture of classical metaphysics and its location of autonomous human subjects as the primary gears of ethical agency. Keller swarms theology with the quantum perspective, focusing in particular on the phenomenon of quantum entanglement, by which quantum particles are found to remain influential over each other long after they have been physically separated—what Albert (...)
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  7. Review of Oppy's Philosophical Perspectives on Infinity[REVIEW]Anne Newstead - 2007 - Australasian Journal of Philosophy 85 (4):679-695.
    This is a book review of Oppy's "Philosophical Perspectives on Infinity", which is of interest to those in metaphysics, epistemology, philosophy of science, mathematics, and philosophy of religion.
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  8. 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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  9.  50
    Defending the Indispensability Argument: Atoms, Infinity and the Continuum.Eduardo Castro - 2013 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 44 (1):41-61.
    This paper defends the Quine-Putnam mathematical indispensability argument against two objections raised by Penelope Maddy. The objections concern scientific practices regarding the development of the atomic theory and the role of applied mathematics in the continuum and infinity. I present two alternative accounts by Stephen Brush and Alan Chalmers on the atomic theory. I argue that these two theories are consistent with Quine’s theory of scientific confirmation. I advance some novel versions of the indispensability argument. I argue that these (...)
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  10.  54
    In Search of $$\Aleph _{0}$$ ℵ 0 : How Infinity Can Be Created.Markus Pantsar - 2015 - Synthese 192 (8):2489-2511.
    In this paper I develop a philosophical account of actual mathematical infinity that does not demand ontologically or epistemologically problematic assumptions. The account is based on a simple metaphor in which we think of indefinitely continuing processes as defining objects. It is shown that such a metaphor is valid in terms of mathematical practice, as well as in line with empirical data on arithmetical cognition.
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  11.  4
    Mereology and Infinity.Karl-Georg Niebergall - 2016 - Logic and Logical Philosophy 25 (3):309-350.
    This paper deals with the treatment of infinity and finiteness in mereology. After an overview of some first-order mereological theories, finiteness axioms are introduced along with a mereological definition of “x is finite” in terms of which the axioms themselves are derivable in each of those theories. The finiteness axioms also provide the background for definitions of “ T makes an assumption of infinity”. In addition, extensions of mereological theories by the axioms are investigated for their own sake. (...)
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  12.  66
    Science, Religion, and Infinity.Graham Oppy - 2012 - In The Blackwell Companion to Science and Christianity. Wiley. pp. 430-440.
    This chapter contains sections titled: * Brief History * How We Talk * Science and Infinity * Religion and Infinity * Concluding Remarks * Notes * References * Further Reading.
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  13.  40
    When Series Go in Indefinitum, Ad Infinitum and in Infinitum Concepts of Infinity in Kant’s Antinomy of Pure Reason.Silvia De Bianchi - 2015 - Synthese 192 (8):2395-2412.
    In the section of the Antinomy of pure Reason Kant presents three notions of infinity. By investigating these concepts of infinity, this paper highlights important ‘building blocks’ of the structure of the mathematical antinomies, such as the ability of reason of producing ascending and descending series, as well as the notions of given and givable series. These structural features are discussed in order to clarify Ernst Zermelo’s reading of Kant’s antinomy, according to which the latter is deeply rooted (...)
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  14.  24
    A Pantheist in Spite of Himself: Craig, Hegel, and Divine Infinity.Russell W. Dumke - 2016 - International Journal for Philosophy of Religion 80 (3):243-257.
    In his 2006 paper `Pantheists in Spite of Themselves: God and Infinity in Contemporary Theology,’ William Lane Craig examines the work of Wolfhart Pannenberg, Philip Clayton, and F. LeRon Shults, whose conceptions of God are influenced by Hegel. Craig shows that these thinkers’ Hegelian formulations lead to monism, despite their attempts to avoid it. He then attempts to refute Hegelian thinking by appealing to Cantor. I argue that that this refutation fails because Cantor and Hegel are far more amicable (...)
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  15.  64
    Infinity in Ontology and Mind.Nino 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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  16.  51
    The Axiom of Infinity and Transformations J: V→V.Paul Corazza - 2010 - Bulletin of Symbolic Logic 16 (1):37-84.
    We suggest a new approach for addressing the problem of establishing an axiomatic foundation for large cardinals. An axiom asserting the existence of a large cardinal can naturally be viewed as a strong Axiom of Infinity. However, it has not been clear on the basis of our knowledge of ω itself, or of generally agreed upon intuitions about the true nature of the mathematical universe, what the right strengthening of the Axiom of Infinity is—which large cardinals ought to (...)
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  17.  25
    A Theory of Sets with the Negation of the Axiom of Infinity.Stefano Baratella & Ruggero Ferro - 1993 - Mathematical Logic Quarterly 39 (1):338-352.
    In this paper we introduce a theory of finite sets FST with a strong negation of the axiom of infinity asserting that every set is provably bijective with a natural number. We study in detail the role of the axioms of Power Set, Choice, Regularity in FST, pointing out the relative dependences or independences among them. FST is shown to be provably equivalent to a fragment of Alternative Set Theory. Furthermore, the introduction of FST is motivated in view of (...)
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  18.  16
    Mathematical, Philosophical and Semantic Considerations on Infinity : General Concepts.José-Luis Usó-Doménech, Josué Antonio Nescolarde Selva & Mónica Belmonte Requena - 2016 - Foundations of Science 21 (4):615-630.
    In the Reality we know, we cannot say if something is infinite whether we are doing Physics, Biology, Sociology or Economics. This means we have to be careful using this concept. Infinite structures do not exist in the physical world as far as we know. So what do mathematicians mean when they assert the existence of ω? There is no universally accepted philosophy of mathematics but the most common belief is that mathematics touches on another worldly absolute truth. Many mathematicians (...)
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  19.  5
    Motility, Potentiality, and Infinity—A Semiotic Hypothesis on Nature and Religion.Massimo Leone - 2012 - Biosemiotics 5 (3):369-389.
    Against any obscurantist stand, denying the interest of natural sciences for the comprehension of human meaning and language, but also against any reductionist hypothesis, frustrating the specificity of the semiotic point of view on nature, the paper argues that the deepest dynamic at the basis of meaning consists in its being a mechanism of ‘potentiality navigation’ within a universe generally characterized by motility. On the one hand, such a hypothesis widens the sphere of meaning to all beings somehow endowed with (...)
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  20. Actual Versus Potential Infinity (BPhil Manuscript.).Anne Newstead - 1997 - Dissertation, University of Oxford
    Does mathematical practice require the existence of actual infinities, or are potential infinities enough? Contrasting points of view are examined in depth, concentrating on Aristotle’s arguments against actual infinities, Cantor’s attempts to refute Aristotle, and concluding with Zermelo’s assertion of the primacy of potential infinity in mathematics.
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  21. 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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  22.  10
    Approaching Infinity[REVIEW]Christopher M. P. Tomaszewski - 2018 - Review of Metaphysics 71 (3):579-580.
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  23.  21
    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. Actualised Infinity: Before-Effect and Nullify-Effect.Steffen Borge - 2003 - Disputatio 14:1 - 17.
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  25.  30
    The Logic of Categorematic and Syncategorematic Infinity.Sara L. Uckelman - 2015 - Synthese 192 (8):2361-2377.
    The medieval distinction between categorematic and syncategorematic words is usually given as the distinction between words which have signification or meaning in isolation from other words and those which have signification only when combined with other words . Some words, however, are classified as both categorematic and syncategorematic. One such word is Latin infinita ‘infinite’. Because infinita can be either categorematic or syncategorematic, it is possible to form sophisms using infinita whose solutions turn on the distinction between categorematic and syncategorematic (...)
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  26.  45
    Paradox and Potential Infinity.Charles McCarty - 2013 - Journal of Philosophical Logic 42 (1):195-219.
    We describe a variety of sets internal to models of intuitionistic set theory that (1) manifest some of the crucial behaviors of potentially infinite sets as described in the foundational literature going back to Aristotle, and (2) provide models for systems of predicative arithmetic. We close with a brief discussion of Church’s Thesis for predicative arithmetic.
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  27.  29
    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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  28.  21
    Infinity Between Mathematics and Apologetics: Pascal’s Notion of Infinite Distance.João Figueiredo Nobre Cortese - 2015 - Synthese 192 (8):2379-2393.
    In this paper I will examine what Blaise Pascal means by “infinite distance”, both in his works on projective geometry and in the apologetics of the Pensées’s. I suggest that there is a difference of meaning in these two uses of “infinite distance”, and that the Pensées’s use of it also bears relations to the mathematical concept of heterogeneity. I also consider the relation between the finite and the infinite and the acceptance of paradoxical relations by Pascal.
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  29.  3
    In the Beginning Was the Apeiron: Infinity in Greek Philosophy. [REVIEW]Jason W. Carter - 2012 - Ancient Philosophy 32 (1):167-171.
  30. Infinity, What is It?Marnie Luce - 1969 - Minneapolis, Lerner Publications Co..
     
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  31. 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.
  32.  12
    Infinity and the Mind: The Science and Philosophy of the Infinite.Rudy vB Rucker - 1982 - 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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  33.  16
    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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  34.  64
    Actual and Potential Infinity.Øystein Linnebo & Stewart Shapiro - forthcoming - Noûs.
    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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  35. Strong Axioms of Infinity and the Debate About Realism.Kai Hauser & W. Hugh Woodin - 2014 - Journal of Philosophy 111 (8):397-419.
    One of the most distinctive and intriguing developments of modern set theory has been the realization that, despite widely divergent incentives for strengthening the standard axioms, there is essentially only one way of ascending the higher reaches of infinity. To the mathematical realist the unexpected convergence suggests that all these axiomatic extensions describe different aspects of the same underlying reality.
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  36.  43
    Reflecting on Absolute Infinity.Philip Welch & Leon Horsten - 2016 - Journal of Philosophy 113 (2):89-111.
    This article is concerned with reflection principles in the context of Cantor’s conception of the set-theoretic universe. We argue that within such a conception reflection principles can be formulated that confer intrinsic plausibility to strong axioms of infinity.
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  37.  3
    Decidable Fragments of the Simple Theory of Types with Infinity and $Mathrm{NF}$.Anuj Dawar, Thomas Forster & Zachiri McKenzie - 2017 - Notre Dame Journal of Formal Logic 58 (3):433-451.
    We identify complete fragments of the simple theory of types with infinity and Quine’s new foundations set theory. We show that TSTI decides every sentence ϕ in the language of type theory that is in one of the following forms: ϕ=∀x1r1⋯∀xkrk∃y1s1⋯∃ylslθ where the superscripts denote the types of the variables, s1>⋯>sl, and θ is quantifier-free, ϕ=∀x1r1⋯∀xkrk∃y1s⋯∃ylsθ where the superscripts denote the types of the variables and θ is quantifier-free. This shows that NF decides every stratified sentence ϕ in the (...)
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  38.  3
    König's Infinity Lemma and Beth's Tree Theorem.George Weaver - 2017 - History and Philosophy of Logic 38 (1):48-56.
    König, D. [1926. ‘Sur les correspondances multivoques des ensembles’, Fundamenta Mathematica, 8, 114–34] includes a result subsequently called König's Infinity Lemma. Konig, D. [1927. ‘Über eine Schlussweise aus dem Endlichen ins Unendliche’, Acta Litterarum ac Scientiarum, Szeged, 3, 121–30] includes a graph theoretic formulation: an infinite, locally finite and connected graph includes an infinite path. Contemporary applications of the infinity lemma in logic frequently refer to a consequence of the infinity lemma: an infinite, locally finite tree with (...)
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  39.  19
    The Strength of Extensionality II—Weak Weak Set Theories Without Infinity.Kentaro Sato - 2011 - Annals of Pure and Applied Logic 162 (8):579-646.
    By obtaining several new results on Cook-style two-sorted bounded arithmetic, this paper measures the strengths of the axiom of extensionality and of other weak fundamental set-theoretic axioms in the absence of the axiom of infinity, following the author’s previous work [K. Sato, The strength of extensionality I — weak weak set theories with infinity, Annals of Pure and Applied Logic 157 234–268] which measures them in the presence. These investigations provide a uniform framework in which three different kinds (...)
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  40. Worlds Apart: On the Possibility of an Actual Infinity.Josh Dever - unknown
    Cosmological arguments attempt to prove the existence of God by appeal to the necessity of a first cause. Schematically, a cosmological argument will thus appear as: (1) All contingent beings have a cause of existence. (2) There can be no infinite causal chains. (3) Therefore, there must be some non-contingent First Cause. Cosmological arguments come in two species, depending on their justification of the second premiss. Non-temporal cosmological arguments, such as those of Aristotle and Aquinas, view causation as requiring explanatory (...)
     
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  41. Pick a Number Between Zero and Infinity.David J. Chalmers - manuscript
    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.  13
    The Strength of Extensionality I—Weak Weak Set Theories with Infinity.Kentaro Sato - 2009 - Annals of Pure and Applied Logic 157 (2-3):234-268.
    We measure, in the presence of the axiom of infinity, the proof-theoretic strength of the axioms of set theory which make the theory look really like a “theory of sets”, namely, the axiom of extensionality Ext, separation axioms and the axiom of regularity Reg . We first introduce a weak weak set theory as a base over which to clarify the strength of these axioms. We then prove the following results about proof-theoretic ordinals:1. and ,2. and . We also (...)
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  43.  97
    Intuition and Infinity: A Kantian Theme with Echoes in the Foundations of Mathematics.Carl Posy - 2008 - Royal Institute of Philosophy Supplement 63:165-193.
    Kant says patently conflicting things about infinity and our grasp of it. Infinite space is a good case in point. In his solution to the First Antinomy, he denies that we can grasp the spatial universe as infinite, and therefore that this universe can be infinite; while in the Aesthetic he says just the opposite: ‘Space is represented as a given infinite magnitude’ (A25/B39). And he rests these upon consistently opposite grounds. In the Antinomy we are told that we (...)
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  44.  15
    Transcendence and Salvation in Levinas’s Time and the Other and Totality and Infinity.Marc A. Cohen - 2014 - Levinas Studies 9:53-66.
    This short essay argues for a thematic connection between Emmanuel Levinas’s Time and the Other and his Totality and Infinity. Time and the Other directly addresses the problem of salvation, and this concern with salvation can be traced through Totality and Infinity, where it is implicit in Levinas’s conception of desire—so there is a religious concern at the core of that (purportedly) secular work. And this thematic connection suggests a further interpretive question about the role of fecundity in (...)
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  45. The Concept of Infinity in Modern Cosmology.Massimiliano Badino - unknown
    The aim of this paper is not only to deal with the concept of infinity, but also to develop some considerations about the epistemological status of cosmology. These problems are connected because from an epistemological point of view, cosmology, meant as the study of the universe as a whole, is not merely a physical (or empirical) science. On the contrary it has an unavoidable metaphysical character which can be found in questions like “why is there this universe (or a (...)
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  46. « Review Of: Mary P. Nichols, Socrates On Friendship And Community: Reflections On Plato’s Symposium, Phaedrus, And Lysis ; And Laurence D. Cooper, Eros In Plato, Rousseau, And Nietzsche: The Politics Of Infinity ». [REVIEW]David Konstan - 2010 - Plato: The Internet Journal of the International Plato Society 10.
    Mary P. Nichols, Socrates on Friendship and Community: Reflections on Plato’s Symposium, Phaedrus, and Lysis. Cambridge: Cambridge University Press, 2008. Pp. viii + 229. ISBN 978-0-521-89973-4. Laurence D. Cooper, Eros in Plato, Rousseau, and Nietzsche: The Politics of Infinity. University Park: The Pennsylvania State University Press, 2008. Pp. xii + 357. ISBN 978-0-271-03330-3.
     
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  47.  51
    Movie Review Of: The Man Who Knew Infinity.Gary James Jason - 2016 - Liberty 6.
    This is a review of the biopic of the great mathematician Ramanujan, 'The Man Who Knew Infinity'(2016).
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  48.  76
    Logicism and the Problem of Infinity: The Number of Numbers.G. Landini - 2011 - 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 (...)
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  49.  67
    Komentarz do kwestii 7 "O nieskończoności Boga" (Introduction to Question 7 of Thomas Aquinas' Summa Theologiae "The Infinity of God").Zbigniew Nerczuk - 1999 - In Gabriela Kurylewicz, Mikołaj Olszewski & Zbigniew Nerczuk (eds.), Tomasz z Akwinu, Traktat o Bogu. Znak. pp. 491-512.
    This is the introduction to the Question 7 (The infinity of God) of St. Thomas Aquinas "Summa Theologiae".
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  50.  94
    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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