Results for 'infinity'

128 found
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  1.  65
    “ ‘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.  65
    Descartes on the Infinity of Space Vs. Time.Geoffrey Gorham - 2018 - In Ohad Nachtomy & Reed Winegar (eds.), Infinity in Early Modern Philosophy. Berlin: Brill.
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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. 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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  5. 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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  6.  55
    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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  7. 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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  8.  34
    Infinite Leap: The Case Against Infinity.Jonathan Livingstone - manuscript
    Infinity exists as a concept but has no existence in actuality. For infinity to have existence in actuality either time or space have to already be infinite. Unless something is already infinite, the only way to become infinite is by an 'infinity leap' in an infinitely small moment, and this is not possible. Neither does infinitely small have an existence since anything larger than zero is not infinitely small. Therefore infinity has no existence in actuality.
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  9. 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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  10. Actualised Infinity: Before-Effect and Nullify-Effect.Steffen Borge - 2003 - Disputatio 1 (14):1 - 17.
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  11. Solving Ordinary Differential Equations by Working with Infinitesimals Numerically on the Infinity Computer.Yaroslav Sergeyev - 2013 - Applied Mathematics and Computation 219 (22):10668–10681.
    There exists a huge number of numerical methods that iteratively construct approximations to the solution y(x) of an ordinary differential equation (ODE) y′(x) = f(x,y) starting from an initial value y_0=y(x_0) and using a finite approximation step h that influences the accuracy of the obtained approximation. In this paper, a new framework for solving ODEs is presented for a new kind of a computer – the Infinity Computer (it has been patented and its working prototype exists). The new computer (...)
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  12.  96
    Higher Order Numerical Differentiation on the Infinity Computer.Yaroslav Sergeyev - 2011 - Optimization Letters 5 (4):575-585.
    There exist many applications where it is necessary to approximate numerically derivatives of a function which is given by a computer procedure. In particular, all the fields of optimization have a special interest in such a kind of information. In this paper, a new way to do this is presented for a new kind of a computer - the Infinity Computer - able to work numerically with finite, infinite, and infinitesimal number. It is proved that the Infinity Computer (...)
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  13.  55
    Wittgenstein And Labyrinth Of ‘Actual Infinity’: The Critique Of Transfinite Set Theory.Valérie Lynn Therrien - 2012 - Ithaque 10:43-65.
    In order to explain Wittgenstein’s account of the reality of completed infinity in mathematics, a brief overview of Cantor’s initial injection of the idea into set- theory, its trajectory and the philosophic implications he attributed to it will be presented. Subsequently, we will first expound Wittgenstein’s grammatical critique of the use of the term ‘infinity’ in common parlance and its conversion into a notion of an actually existing infinite ‘set’. Secondly, we will delve into Wittgenstein’s technical critique of (...)
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  14.  54
    Immortality, Infinity and the Limitations of God.Alexey Prokofyev - manuscript
    I tried to describe Infinity as a major natural conundrum known to man. The booklet also contains answers to some eternal questions, such as the meaning of life, faith, etc. I am especially proud of my Morality section.
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  15.  24
    The Idea of Infinity in its Physical and Spiritual Meanings.Graham Nicholson - manuscript
    Abstract -/- The concept of infinity is of ancient origins and has puzzled deep thinkers ever since up to the present day. Infinity remains somewhat of a mystery in a physical world in which our comprehension is largely framed around the concept of boundaries. This is partly because we live in a physical world that is governed by certain dimensions or limits – width, breadth, depth, mass, space, age and time. To our ordinary understanding, it is a seemingly (...)
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  16. Life and Infinity.NuyGnues Eel - 2014 - Dissertation,
    Can life be visually represented as a circle? Hegel states that true infinity, when visualized, takes the shape of a circle. The dissertation begins with a hypothesis, "does the progression to the true infinite reflect the notion of life itself?" Then, Hegel's notion of infinity is expanded and applied to the notion of life. This work is trying to explain human evolution and life itself.
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  17. 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 (...)
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  18.  43
    Independence of the Grossone-Based Infinity Methodology From Non-Standard Analysis and Comments Upon Logical Fallacies in Some Texts Asserting the Opposite.Yaroslav D. Sergeyev - 2019 - Foundations of Science 24 (1):153-170.
    This paper considers non-standard analysis and a recently introduced computational methodology based on the notion of ①. The latter approach was developed with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework and in all the situations requiring these notions. Non-standard analysis is a classical purely symbolic technique that works with ultrafilters, external and internal sets, standard and non-standard numbers, etc. In its turn, the ①-based methodology does not use any of these (...)
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  19.  96
    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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  20. Formalization and Infinity.André Porto - 2008 - Manuscrito 31 (1):25-43.
    This article discusses some of Chateaubriand’s views on the connections between the ideas of formalization and infinity, as presented in chapters 19 and 20 of Logical Forms. We basically agree with his criticisms of the standard construal of these connections, a view we named “formal proofs as ultimate provings”, but we suggest an alternative way of picturing that connection based on some ideas of the late Wittgenstein.
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  21.  82
    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.), Św. 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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  22.  9
    On the Reconciliation Between Infinity and Zero - Another 'Theory of Everything' Based on Nothing?Louis Taylor - manuscript
    Is there room enough in all creation for an 'Empty Universe Theory'? How should we view the realm in which we exist? Are the natures of matter and energy, their compositions and relationships with each other the fundamental key to the understanding of everything or is it something else? A thought on the true nature of the realm we really inhabit with some basic mathematical description of the relationship between the finite and the absolute as we are capable of understanding (...)
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  23.  29
    Infinity and the Problem of Evil.John Leslie - 2019 - European Journal for Philosophy of Religion 11 (2):111-117.
    God seemingly had a duty to create minds each of infinite worth through possessing God-like knowledge. People might object that God’s own infinite worth was all that was needed, or that no mind that God created could have truly infinite worth; however, such objections fail. Yet this does not generate an unsolvable Problem of Evil. We could exist inside an infinite mind that was one among endlessly many, perhaps all created by Platonic Necessity. “God” might be our name for this (...)
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  24. Cantor on Infinity in Nature, Number, and the Divine Mind.Anne Newstead - 2009 - American Catholic Philosophical Quarterly 83 (4):533-553.
    The mathematician Georg Cantor strongly believed in the existence of actually infinite numbers and sets. Cantor’s “actualism” went against the Aristotelian tradition in metaphysics and mathematics. Under the pressures to defend his theory, his metaphysics changed from Spinozistic monism to Leibnizian voluntarist dualism. The factor motivating this change was two-fold: the desire to avoid antinomies associated with the notion of a universal collection and the desire to avoid the heresy of necessitarian pantheism. We document the changes in Cantor’s thought with (...)
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  25. 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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  26.  51
    Dutch Books and Infinity.Brian Weatherson - manuscript
    Peter Walley argues that a vague credal state need not be representable by a set of probability functions that could represent precise credal states, because he believes that the members of the representor set need not be countably additive. I argue that the states he defends are in a way incoherent.
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  27. Interpretation of Percolation in Terms of Infinity Computations.Yaroslav Sergeyev, Dmitri Iudin & Masaschi Hayakawa - 2012 - Applied Mathematics and Computation 218 (16):8099-8111.
    In this paper, a number of traditional models related to the percolation theory has been considered by means of new computational methodology that does not use Cantor’s ideas and describes infinite and infinitesimal numbers in accordance with the principle ‘The part is less than the whole’. It gives a possibility to work with finite, infinite, and infinitesimal quantities numerically by using a new kind of a compute - the Infinity Computer – introduced recently in [18]. The new approach does (...)
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  28.  60
    What Is A Number? Re-Thinking Derrida's Concept of Infinity.Joshua Soffer - 2007 - Journal of the British Society for Phenomenology 38 (2):202-220.
    Iterability, the repetition which alters the idealization it reproduces, is the engine of deconstructive movement. The fact that all experience is transformative-dissimulative in its essence does not, however, mean that the momentum of change is the same for all situations. Derrida adapts Husserl's distinction between a bound and a free ideality to draw up a contrast between mechanical mathematical calculation, whose in-principle infinite enumerability is supposedly meaningless, empty of content, and therefore not in itself subject to alteration through contextual change, (...)
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  29.  76
    Reseña a: Levinas’s Existential Analític, a commentary on Totality and Infinity. James R. Mensch. Northwestern University Press. [REVIEW]Esteban J. Beltrán Ulate - 2016 - Phenomenological Reviews 1 (1).
    Totalidad e Infinito (TI) resulta ser una obra compleja. Ante el estilo de Levinas para la exposición de sus ideas, resulta oportuno contar con un apoyo para los nuevos lectores, con el objetivo de poder indagar en aspectos que podrían pasar desapercibidos. El trabajo desarrollado por James R. Mensch, profesor de Filosofía de la Charles University en República Checa y de Saint Francis Xavier University en Canadá, le permite incorporarse dentro de la lista de comentadores destacados de Levinas. El acercamiento (...)
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  30. Evolution At the Surface of Euclid:Elements of A Long Infinity in Motion Along Space.Marvin E. Kirsh - 2011 - International Journal of the Arts and Sciences 4 (2):71-96.
    It is modernly debated whether application of the free will has potential to cause harm to nature. Power possessed to the discourse, sensory/perceptual, physical influences on life experience by the slow moving machinery of change is a viral element in the problems of civilization; failed resolution of historical paradox involving mind and matter is a recurring source of problems. Reference is taken from the writing of Euclid in which a oneness of nature as an indivisible point of thought is made (...)
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  31. Mathematical Infinity, Its Inventors, Discoverers, Detractors, Defenders, Masters, Victims, Users, and Spectators.Edward G. Belaga - manuscript
    "The definitive clarification of the nature of the infinite has become necessary, not merely for the special interests of the individual sciences, but rather for the honour of the human understanding itself. The infinite has always stirred the emotions of mankind more deeply than any other question; the infinite has stimulated and fertilized reason as few other ideas have ; but also the infinite, more than other notion, is in need of clarification." (David Hilbert 1925).
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  32. Locke and the Scholastics on Theological Discourse.Walter Ott - 1997 - Locke Studies 28 (1):51-66.
    On the face of it, Locke rejects the scholastics' main tool for making sense of talk of God, namely, analogy. Instead, Locke claims that we generate an idea of God by 'enlarging' our ideas of some attributes (such as knowledge) with the idea of infinity. Through an analysis of Locke's idea of infinity, I argue that he is in fact not so distant from the scholastics and in particular must rely on analogy of inequality.
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  33.  41
    A Geneticist's Roadmap to Sanity.Gilbert B. Côté - manuscript
    World news can be discouraging these days. In order to counteract the effects of fake news and corruption, scientists have a duty to present the truth and propose ethical solutions acceptable to the world at large. -/- By starting from scratch, we can lay down the scientific principles underlying our very existence, and reach reasonable conclusions on all major topics including quantum physics, infinity, timelessness, free will, mathematical Platonism, triple-aspect monism, ethics and religion, all the way to creation and (...)
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  34. Why Spinoza is Not an Eleatic Monist (Or Why Diversity Exists).Yitzhak Y. Melamed - 2011 - In Philip Goff (ed.), Spinoza on Monism. Palgrave.
    “Why did God create the World?” is one of the traditional questions of theology. In the twentieth century this question was rephrased in a secularized manner as “Why is there something rather than nothing?” While creation - at least in its traditional, temporal, sense - has little place in Spinoza’s system, a variant of the same questions puts Spinoza’s system under significant pressure. According to Spinoza, God, or the substance, has infinitely many modes. This infinity of modes follow from (...)
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  35. Finitism and the Beginning of the Universe.Stephen Puryear - 2014 - Australasian Journal of Philosophy 92 (4):619-629.
    Many philosophers have argued that the past must be finite in duration because otherwise reaching the present moment would have involved something impossible, namely, the sequential occurrence of an actual infinity of events. In reply, some philosophers have objected that there can be nothing amiss in such an occurrence, since actually infinite sequences are ‘traversed’ all the time in nature, for example, whenever an object moves from one location in space to another. This essay focuses on one of the (...)
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  36. Distance and Dissimilarity.Ben Blumson - 2018 - Philosophical Papers 48 (2):211-239.
    This paper considers whether an analogy between distance and dissimilarlity supports the thesis that degree of dissimilarity is distance in a metric space. A straightforward way to justify the thesis would be to define degree of dissimilarity as a function of number of properties in common and not in common. But, infamously, this approach has problems with infinity. An alternative approach would be to prove representation and uniqueness theorems, according to which if comparative dissimilarity meets certain qualitative conditions, then (...)
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  37. Finitism, Divisibilty, and the Beginning of the Universe: Replies to Loke and Dumsday.Stephen Puryear - 2016 - Australasian Journal of Philosophy 94 (4):808-813.
    Some philosophers contend that the past must be finite in duration, because otherwise reaching the present would have involved the sequential occurrence of an actual infinity of events, which they regard as impossible. I recently developed a new objection to this finitist argument, to which Andrew Ter Ern Loke and Travis Dumsday have replied. Here I respond to the three main points raised in their replies.
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  38. Waismann's Critique of Wittgenstein.Anthony Birch - 2007 - Analysis and Metaphysics 6 (2007):263-272.
    Friedrich Waismann, a little-known mathematician and onetime student of Wittgenstein's, provides answers to problems that vexed Wittgenstein in his attempt to explicate the foundations of mathematics through an analysis of its practice. Waismann argues in favor of mathematical intuition and the reality of infinity with a Wittgensteinian twist. Waismann's arguments lead toward an approach to the foundation of mathematics that takes into consideration the language and practice of experts.
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  39. The Indefinite Within Descartes' Mathematical Physics.Françoise Monnoyeur-Broitman - 2013 - Eidos: Revista de Filosofía de la Universidad Del Norte 19:107-122.
    Descartes' philosophy contains an intriguing notion of the infinite, a concept labeled by the philosopher as indefinite. Even though Descartes clearly defined this term on several occasions in the correspondence with his contemporaries, as well as in his Principles of Philosophy, numerous problems about its meaning have arisen over the years. Most commentators reject the view that the indefinite could mean a real thing and, instead, identify it with an Aristotelian potential infinite. In the first part of this article, I (...)
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  40. The Actual Infinite as a Day or the Games.Pascal Massie - 2007 - Review of Metaphysics 60 (3):573-596.
    It is commonly assumed that Aristotle denies any real existence to infinity. Nothing is actually infinite. If, in order to resolve Zeno’s paradoxes, Aristotle must talk of infinity, it is only in the sense of a potentiality that can never be actualized. Aristotle’s solution has been both praised for its subtlety and blamed for entailing a limitation of mathematic. His understanding of the infinite as simply indefinite (the “bad infinite” that fails to reach its accomplishment), his conception of (...)
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  41. Existence Is Evidence of Immortality.Michael Huemer - manuscript
    Time may be infinite in both directions. If it is, then, if persons could live at most once in all of time, the probability that you would be alive now would be zero. But if persons can live more than once, the probability that you would be alive now would be nonzero. Since you are alive now, with certainty, either the past is finite, or persons can live more than once.
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  42.  80
    Los límites del universo creado: La asimilación tomista de la doctrina aristotélica en torno al problema de la infinitud.Ana Maria Carmen Minecan - 2015 - Disputatio. Philosophical Research Bulletin 4 (5):119--143.
    [ES] El presente artículo estudia el influjo de los tratados físicos de Aristóteles sobre la concepción tomista en torno al lugar del infinito en el cosmos creado. Se analiza la posición sostenida por el Aquinate respecto a cuatro aspectos fundamentales de la teoría aristotélica en torno al infinito: existencia de una sustancia infinita, existencia de un cuerpo infinito, existencia de un infinito en acto y la infinitud del tiempo. Asimismo se expone el empleo de la teoría aristotélica del movimiento y (...)
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  43. Religious Topics in the 21st Century.Yoji K. Gondor, Joseph Krenz & Joseph Krecz - manuscript
    Abstract: With all the obstacles and challenges it has suffered, the modern religion is an integral part of our society. Are the religions and the new technical developments in any form of reasonable harmony? There is nothing greater than infinity, nothing more mysterious than the infinite space or time, and nothing more mysterious than the Creator. In this way, it seems that there is a symbolic correlation connecting the concept of infinity and the transcendental vision of the mighty (...)
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  44.  87
    Infinite Barbarians.Daniel Nolan - 2019 - Ratio 32 (3):173-181.
    This paper discusses an infinite regress that looms behind a certain kind of historical explanation. The movement of one barbarian group is often explained by the movement of others, but those movements in turn call for an explanation. While their explanation can again be the movement of yet another group of barbarians, if this sort of explanation does not stop somewhere we are left with an infinite regress of barbarians. While that regress would be vicious, it cannot be accommodated by (...)
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  45. Aristotelian Finitism.Tamer Nawar - 2015 - Synthese 192 (8):2345-2360.
    It is widely known that Aristotle rules out the existence of actual infinities but allows for potential infinities. However, precisely why Aristotle should deny the existence of actual infinities remains somewhat obscure and has received relatively little attention in the secondary literature. In this paper I investigate the motivations of Aristotle’s finitism and offer a careful examination of some of the arguments considered by Aristotle both in favour of and against the existence of actual infinities. I argue that Aristotle has (...)
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  46.  78
    A Paradox of Evidential Equivalence.David Builes - forthcoming - Mind:fzz046.
    Our evidence can be about different subject matters. In fact, necessarily equivalent pieces of evidence can be about different subject matters. Does the hyperintensionality of ‘aboutness’ engender any hyperintensionality at the level of rational credence? In this paper, I present a case which seems to suggest that the answer is ‘yes’. In particular, I argue that our intuitive notions of 'independent' evidence and 'inadmissible' evidence are sensitive to aboutness in a hyperintensional way. We are thus left with a paradox. While (...)
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  47. The Tristram Shandy Paradox.Graham Oppy - 2002 - Philosophia Christi 4 (2):335-349.
    This paper is a response to David Oderberg's discussion of the Tristram Shandy paradox. I defend the claim that the Tristram Shandy paradox does not support the claim that it is impossible that the past is infinite.
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  48. Fair Infinite Lotteries.Sylvia Wenmackers & Leon Horsten - 2013 - Synthese 190 (1):37-61.
    This article discusses how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. Techniques and ideas from non-standard analysis are brought to bear on the problem.
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  49.  86
    The Cantorian Bubble.Jeremy Gwiazda - manuscript
    The purpose of this paper is to suggest that we are in the midst of a Cantorian bubble, just as, for example, there was a dot com bubble in the late 1990’s.
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  50. Kant on the Logical Form of Singular Judgments.Huaping Lu-Adler - 2014 - Kantian Review 19 (3):367-92.
    At A71/B96–7 Kant explains that singular judgements are ‘special’ because they stand to the general ones as Einheit to Unendlichkeit. The reference to Einheit brings to mind the category of unity and hence raises a spectre of circularity in Kant’s explanation. I aim to remove this spectre by interpreting the Einheit-Unendlichkeit contrast in light of the logical distinctions among universal, particular and singular judgments shared by Kant and his logician predecessors. This interpretation has a further implication for resolving a controversy (...)
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