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  1. added 2020-02-12
    God and Science Are Infinite.John Linus O'Sullivan - forthcoming - AuthorsDen.
    Abstract: Standing half wave particles at light speed twice in expansion-contraction comprise a static universe where two transverse fields 90° out of phase are the square of distance from each other. The universe has a static concept of time since the infinite universe is a static universe without a beginning or end. The square of distance is a point of reversal in expansion-contraction between the fields as a means to conserve energy. Photons on expansion in the electric field create matter (...)
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  2. added 2019-08-23
    Wittgenstein on Cantor's Proof.Chrysoula Gitsoulis - 2018 - In Gabriele M. Mras, Paul Weingartner & Bernhard Ritter (eds.), Philosophy of Logic and Mathematics: Contributions of the 41st International Wittgenstein Symposium. pp. 67-69.
    Cantor’s proof that the reals are uncountable forms a central pillar in the edifices of higher order recursion theory and set theory. It also has important applications in model theory, and in the foundations of topology and analysis. Due partly to these factors, and to the simplicity and elegance of the proof, it has come to be accepted as part of the ABC’s of mathematics. But even if as an Archimedean point it supports tomes of mathematical theory, there is a (...)
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  3. added 2019-04-29
    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 be derivable? (...)
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  4. added 2018-11-21
    Why Believe Infinite Sets Exist?Andrei Mărăşoiu - 2018 - Axiomathes 28 (4):447-460.
    The axiom of infinity states that infinite sets exist. I will argue that this axiom lacks justification. I start by showing that the axiom is not self-evident, so it needs separate justification. Following Maddy’s :481–511, 1988) distinction, I argue that the axiom of infinity lacks both intrinsic and extrinsic justification. Crucial to my project is Skolem’s From Frege to Gödel: a source book in mathematical logic, 1879–1931, Cambridge, Harvard University Press, pp. 290–301, 1922) distinction between a theory of real sets, (...)
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  5. added 2018-09-29
    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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  6. added 2017-04-15
    What is the Infinite?Øystein Linnebo - 2013 - The Philosophers' Magazine 61:42-47.
    The paper discusses some different conceptions of the infinity, from Aristotle to Georg Cantor (1845-1918) and beyond. The ancient distinction between actual and potential infinity is explained, along with some arguments against the possibility of actually infinite collections. These arguments were eventually rejected by most philosophers and mathematicians as a result of Cantor’s elegant and successful theory of actually infinite collections.
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  7. added 2016-06-12
    History and Philosophy of Infinity: Selected Papers From the Conference “Foundations of the Formal Sciences VIII” Held at Corpus Christi College, Cambridge, England, 20–23 September 2013.Brendan P. Larvor, Benedikt Löwe & Dirk Schlimm - 2015 - Synthese 192 (8):2339-2344.
  8. added 2015-09-05
    Infinitely Complex Machines.Eric Steinhart - 2007 - In Intelligent Computing Everywhere. Springer. pp. 25-43.
    Infinite machines (IMs) can do supertasks. A supertask is an infinite series of operations done in some finite time. Whether or not our universe contains any IMs, they are worthy of study as upper bounds on finite machines. We introduce IMs and describe some of their physical and psychological aspects. An accelerating Turing machine (an ATM) is a Turing machine that performs every next operation twice as fast. It can carry out infinitely many operations in finite time. Many ATMs can (...)
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  9. added 2015-06-29
    Is the Dream Solution of the Continuum Hypothesis Attainable?Joel David Hamkins - 2015 - Notre Dame Journal of Formal Logic 56 (1):135-145.
    The dream solution of the continuum hypothesis would be a solution by which we settle the continuum hypothesis on the basis of a newly discovered fundamental principle of set theory, a missing axiom, widely regarded as true. Such a dream solution would indeed be a solution, since we would all accept the new axiom along with its consequences. In this article, however, I argue that such a dream solution to $\mathrm {CH}$ is unattainable.
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  10. added 2014-06-04
    Dialogue on Alternating Consciousness: From Perception to Infinities and Back to Free Will.Claus Janew - 2014 - Journal of Consciousness Exploration and Research 5 (4):351-391.
    Can we trace back consciousness, reality, awareness, and free will to a single basic structure without giving up any of them? Can the universe exist in both real and individual ways without being composed of both? This dialogue founds consciousness and freedom of choice on the basis of a new reality concept that also includes the infinite as far as we understand it. Just the simplest distinction contains consciousness. It is not static, but a constant alternation of perspectives. From its (...)
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  11. added 2011-02-01
    Taming the Infinite. [REVIEW]M. Potter - 1996 - British Journal for the Philosophy of Science 47 (4):609-619.
    A critique of Shaughan Lavine's attempt in /Understanding the Infinite/ to reduce talk about the infinite to finitely comprehensible terms.
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  12. added 2011-01-06
    The Case Against Infinity.Kip Sewell - manuscript
    Infinity and infinite sets, as traditionally defined in mathematics, are shown to be logical absurdities. To maintain logical consistency, mathematics ought to abandon the traditional notion of infinity. It is proposed that infinity should be replaced with the concept of “indefiniteness”. This further implies that other fields drawing on mathematics, such as physics and cosmology, ought to reject theories that postulate infinities of space and time. It is concluded that however indefinite our calculations of space and time become, the Universe (...)
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  13. added 2008-12-31
    Hilbert's Machine and the Axiom of Infinity.Antonio Leon - manuscript
    Hilbert's machine is a supertask machine inspired by Hilbert's Hotel whose functioning leads to a contradiction that compromises the Axiom of Infinity.
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  14. added 2008-12-31
    Properties, Abstracts, and the Axiom of Infinity.Herbert Hochberg - 1977 - Journal of Philosophical Logic 6 (1):193 - 207.
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  15. added 2008-12-31
    Reduction of Arithmetic to Logic Based on the Theory of Types Without the Axiom of Infinity and the Typical Ambiguity of Arithmetical Constants.Ludwik Borkowski - 1958 - Studia Logica 8 (1):283 - 297.
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  16. added 2008-12-31
    On Ω-Inconsistency and a so-Called Axiom of Infinity.W. V. Quine - 1953 - Journal of Symbolic Logic 18 (2):119-124.
  17. added 2008-12-31
    The Axiom of Infinity in Quine's New Foundations.J. Barkley Rosser - 1952 - Journal of Symbolic Logic 17 (4):238-242.
    We use NF to designate the system known as Quine's New Foundations, and NF + AF to designate the same system with a suitable axiom of infinity adjoined. We use ML to designate the revised system appearing in the third printing of Quine's “Mathematical Logic”. This system ML is just the systemPproposed by Wang in [4], and essentially includes NF as a part.The pripcipal results of the present paper are:A. In NF the axiom of infinity is equivalent to the definability (...)
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