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The Infinite

Routledge (1990)

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  1. Being and Becoming and the Immanence-Transcendence Relation in Evelyn Underhill’s Mystical Philosophy.Peter Gan Chong Beng - 2011 - Sophia 50 (3):375-389.
    If mysticism, as Coventry Patmore defines it, is 'the science of ultimates,' in what way would mysticism explain the possibility of a profound relationship between ultimate reality as infinite and proximate reality as finite ? This paper attempts to address that question through the lens of Evelyn Underhill’s philosophy of mysticism. The paper fundamentally works at framing two of Hegel’s triadic patterns of dialectic against the being-becoming binary as engaged by Underhill. This application helps unveil the relation of transcendence with (...)
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  • A Look at the Staccato Run.Jon Pérez Laraudogoitia - 2006 - Synthese 148 (2):433-441.
    This paper considers a recent criticism of the physical possibility of super-tasks which involves Achilles's staccato run. It is held that the criticism fails and that the underlying fallacy can be linked with interesting developments in the modern literature on physical supertasks.
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  • Throwing Darts, Time, and the Infinite.Jeremy Gwiazda - 2013 - Erkenntnis 78 (5):971-975.
    In this paper, I present a puzzle involving special relativity and the random selection of real numbers. In a manner to be specified, darts thrown later hit reals further into a fixed well-ordering than darts thrown earlier. Special relativity is then invoked to create a puzzle. I consider four ways of responding to this puzzle which, I suggest, fail. I then propose a resolution to the puzzle, which relies on the distinction between the potential infinite and the actual infinite. I (...)
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  • Functions and Shapes in the Light of the International System of Units.Ingvar Johansson - 2008 - Metaphysica 9 (1):93-117.
    Famously, Galilei made the ontological claim that the book of nature is written in the language of mathematics. Probably, if only implicitly, most contemporary natural scientists share his view. This paper, in contradistinction, argues that nature is only partly written in the language of mathematics; partly, it is written in the language of functions and partly in a very simple purely qualitative language, too. During the argumentation, three more specific but in themselves interesting theses are put forward: first (in Section (...)
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  • Knowledge of Proofs.Peter Pagin - 1994 - Topoi 13 (2):93-100.
    If proofs are nothing more than truth makers, then there is no force in the standard argument against classical logic (there is no guarantee that there is either a proof forA or a proof fornot A). The standard intuitionistic conception of a mathematical proof is stronger: there are epistemic constraints on proofs. But the idea that proofs must be recognizable as such by us, with our actual capacities, is incompatible with the standard intuitionistic explanations of the meanings of the logical (...)
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  • The Inverse Spaceship Paradox.J. P. Laraudogoitia - 2011 - Synthese 178 (3):429-435.
    In this article I propose what I call the inverse spaceship paradox. The article's interest lies in the fact that, contrary to what appears to be an implicit agreement in the literature on indeterminism, it shows that coming from infinity can be a perfectly predictable and therefore deterministic process in a classical universe.
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  • Varieties of Finitism.Manuel Bremer - 2007 - Metaphysica 8 (2):131-148.
    I consider here several versions of finitism or conceptions that try to work around postulating sets of infinite size. Restricting oneself to the so-called potential infinite seems to rest either on temporal readings of infinity (or infinite series) or on anti-realistic background assumptions. Both these motivations may be considered problematic. Quine’s virtual set theory points out where strong assumptions of infinity enter into number theory, but is implicitly committed to infinity anyway. The approaches centring on the indefinitely large and the (...)
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  • A Debate About Anderson's Logic.A. W. Stewart✠ - 2009 - History and Philosophy of Logic 30 (2):157-169.
    This article is about the history of logic in Australia. Douglas Gasking (1911?1994) undertook to translate the logical terminology of John Anderson (1893?1962) into that of Ludwig Wittgenstein's (1921) Tractatus. At the time Gilbert Ryle (1900?1976), and more recently David Armstrong, recommended the result to students; but it is reasonable to have misgivings about Gasking as a guide to either Anderson or Wittgenstein. The historical interest of the debate Gasking initiated is that it yielded surprisingly little information about Anderson's traditional (...)
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  • Ramsey on Saying and Whistling: A Discordant Note.Richard Holton & Huw Price - 2003 - Noûs 37 (2):325–341.
    In 'General Propositions and Causality' Ramsey rejects his earlier view that universal generalizations are infinite conjunctions, arguing that they are not genuine propositions at all. We argue that his new position is unstable. The issues about infinity that lead Ramsey to the new view are essentially those underlying Wittgenstein's rule-following considerations. If they show that generalizations are not genuine propositions, they show that there are no genuine propositions. The connection raises interesting historical questions about the direction of influence between Ramsey (...)
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  • Royce's Model of the Absolute. Steinhart - 2012 - Transactions of the Charles S. Peirce Society 48 (3):356.
    At the end of the 19th century, Josiah Royce participated in what has come to be called the great debate (Royce, 1897; Armour, 2005).1 The great debate concerned issues in metaphysical theology, and, since metaphysics was primarily idealistic, it dealt considerably with the relations between the divine Self and lesser selves. After the great debate, Royce developed his idealism in his Gifford Lectures (1898-1900). These were published as The World and the Individual. At the end of the first volume, Royce (...)
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  • ‘We Can't Whistle It Either’: Legend and Reality.Cora Diamond - 2011 - European Journal of Philosophy 19 (3):335-356.
    : There is a famous quip of F.P. Ramsey's, which is my second epigraph. According to a widespread legend, the quip is a criticism of Wittgenstein's treatment in the Tractatus of what cannot be said. The remark is indeed Ramsey's, but he didn't mean what he is taken to mean in the legend. His quip, looked at in context, means something quite different. The legend is sometimes taken to provide support for a reading of the Tractatus according to which the (...)
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  • Measuring the Size of Infinite Collections of Natural Numbers: Was Cantor’s Theory of Infinite Number Inevitable?: Measuring the Size of Infinite Collections of Natural Numbers.Paolo Mancosu - 2009 - Review of Symbolic Logic 2 (4):612-646.
    Cantor’s theory of cardinal numbers offers a way to generalize arithmetic from finite sets to infinite sets using the notion of one-to-one association between two sets. As is well known, all countable infinite sets have the same ‘size’ in this account, namely that of the cardinality of the natural numbers. However, throughout the history of reflections on infinity another powerful intuition has played a major role: if a collection A is properly included in a collection B then the ‘size’ of (...)
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  • On Finitism and the Beginning of the Universe: A Reply to Stephen Puryear.Andrew Ter Ern Loke - 2016 - Australasian Journal of Philosophy 94 (3):591-595.
    ABSTRACTStephen Puryear argues that William Lane Craig's view, that time as duration is logically prior to the potentially infinite divisions that we make of it, involves the idea that time is prior to any parts we conceive within it. He objects that PWT entails the Priority of the Whole with respect to Events, and that it subverts the argument, used by proponents of the Kalam Cosmological Argument such as Craig, against an eternal past based on the impossibility of traversing an (...)
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  • The Extent of the Present.William Craig - 2000 - International Studies in the Philosophy of Science 14 (2):165 – 185.
    One of the principal objections to a tensed or dynamic theory of time is the ancient puzzle about the extent of the present. Three alternative conceptions of the extent of the present are considered: an instantaneous present, an atomic present, and a non-metrical present. The first conception is difficult to reconcile with the objectivity of temporal becoming posited by a dynamic theory of time. The second conception solves that problem, but only at the expense of making change discontinuous. The third (...)
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  • 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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  • With and Without End.Peter Cave - 2007 - Philosophical Investigations 30 (2):105–126.
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  • The Cheated God: Death and Personal Time.Roy Sorensen - 2005 - Analysis 65 (2):119–125.
  • Ineffability and Reflections: An Outline of the Concept of Knowledge.A. W. Moore - 1993 - European Journal of Philosophy 1 (3):285-308.
  • Wittgenstein on Set Theory and the Enormously Big.Ryan Dawson - 2016 - Philosophical Investigations 39 (4):313-334.
    Wittgenstein's conception of infinity can be seen as continuing the tradition of the potential infinite that begins with Aristotle. Transfinite cardinals in set theory might seem to render the potential infinite defunct with the actual infinite now given mathematical legitimacy. But Wittgenstein's remarks on set theory argue that the philosophical notion of the actual infinite remains philosophical and is not given a mathematical status as a result of set theory. The philosophical notion of the actual infinite is not to be (...)
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