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The Infinite

Philosophical Quarterly 41 (164):348 (1990)

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  1. Some Remarks on Wittgenstein’s Philosophy of Mathematics.Richard Startup - 2020 - Open Journal of Philosophy 10 (1):45-65.
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  • 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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  • 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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  • 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 of three (...)
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  • Minima Sensibilia: Against the Dynamic Snapshot Model of Temporal Experience.Jack Shardlow - 2019 - European Journal of Philosophy 27 (3):741-757.
    In our wakeful conscious lives, the experience of time and dynamic temporal phenomena—such as continuous motion and change—appears to be ubiquitous. How is it that temporality is woven into our conscious experience? Is it through perceptual experience presenting a series of instantaneous states of the world, which combine together—in a sense which would need to be specified—to give us experience of dynamic temporal phenomena? In this paper, I argue that this is not the case. -/- Several authors have recently proposed (...)
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  • On Alain Badiou’s ‘Critique of Religion’.Mads Peter Karlsen - 2018 - International Journal of Philosophy and Theology 79 (1-2):36-59.
    This paper examines Alain Badiou’s critical engagement with religion. It is argued that there are two central points at which religion enters the scene of Badiou’s philosophy. First, in his critique, the ‘motif of finitude’ Badiou repeatedly refers to religion, claiming that ‘the obsession with finitude is a remnant of the tyranny of the sacred’. Second, Badiou stages his attempt to regenerate philosophy against the proclamation of its end as a confrontation with the religion, through philosophy’s detachment from the poetization (...)
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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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  • What Are Observables in Hamiltonian Theories? Testing Definitions with Empirical Equivalence.J. Brian Pitts - unknown
    Change seems missing in Hamiltonian General Relativity's observables. The typical definition takes observables to have $0$ Poisson bracket with \emph{each} first-class constraint. Another definition aims to recover Lagrangian-equivalence: observables have $0$ Poisson bracket with the gauge generator $G$, a \emph{tuned sum} of first-class constraints. Empirically equivalent theories have equivalent observables. That platitude provides a test of definitions using de Broglie's massive electromagnetism. The non-gauge ``Proca'' formulation has no first-class constraints, so everything is observable. The gauge ``Stueckelberg'' formulation has first-class constraints, (...)
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  • The Labours of Zeno – a Supertask Indeed?Barbara M. Sattler - 2019 - Ancient Philosophy Today 1 (1):1-17.
    It is usually supposed that, with his dichotomy paradox, Zeno gave birth to the modern so-called supertask debate – the debate of whether carrying out an infinite sequence of actions or operations...
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  • The Paradox of Beginning: Hegel, Kierkegaard and Philosophical Inquiry.Daniel Watts - 2007 - Inquiry: An Interdisciplinary Journal of Philosophy 50 (1):5 – 33.
    This paper reconsiders certain of Kierkegaard's criticisms of Hegel's theoretical philosophy in the light of recent interpretations of the latter. The paper seeks to show how these criticisms, far from being merely parochial or rhetorical, turn on central issues concerning the nature of thought and what it is to think. I begin by introducing Hegel's conception of "pure thought" as this is distinguished by his commitment to certain general requirements on a properly philosophical form of inquiry. I then outline Hegel's (...)
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  • The Metaphysics of Mortals: Death, Immortality, and Personal Time.Cody Gilmore - 2016 - Philosophical Studies 173 (12):3271-3299.
    Personal time, as opposed to external time, has a certain role to play in the correct account of death and immortality. But saying exactly what that role is, and what role remains for external time, is not straightforward. I formulate and defend accounts of death and immortality that specify these roles precisely.
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  • Stupne Nekonzistentnosti.Ladislav Kvasz - 2012 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 19:95-115.
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  • Classical Particle Dynamics, Indeterminism and a Supertask.Jon Pérez Laraudogoitia - 1997 - British Journal for the Philosophy of Science 48 (1):49-54.
    In this paper a model in particle dynamics of a well-known supertask is constructed. As a consequence, a new and simple result about the failure of determinism of classical particle dynamics can be proved which is related to the non-existence of boundary conditions at spatial infinity. This result is much more accessible to the non-technical reader than similar ones in the scientific literature.
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  • Putnam on Reference and Constructible Sets.Michael Levin - 1997 - British Journal for the Philosophy of Science 48 (1):55-67.
    Putnam argues that, by ‘reinterpretation’, the Axiom of Constructibility can be saved from empirical refutation. This paper contends that this argument fails, a failure which leaves Putnam's sweeping appeal to the Lowenheim –Skolem Theorem inadequately motivated.
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  • Sts: A Structural Theory Of Sets.A. Baltag - 1999 - Logic Journal of the IGPL 7 (4):481-515.
    We explore a non-classical, universal set theory, based on a purely 'structural' conception of sets. A set is a transfinite process of unfolding of an arbitrary binary structure, with identity of sets given by the observational equivalence between such processes. We formalize these notions using infinitary modal logic, which provides partial descriptions for set structures up to observational equivalence. We describe the comprehension and topological properties of the resulting set-theory, and we use it to give non-classical solutions to classical paradoxes, (...)
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  • Priest on the Paradox of the Gods.Jon P.Érez Laraudogoitia - 2000 - Analysis 60 (2):152-155.
  • Erik-Jon Gaizka, the Magician of Infinity.J. Perez Laraudogoitia - 2010 - Analysis 70 (3):451-456.
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  • Prompting Challenges.John Turri - 2010 - Analysis 70 (3):456-462.
  • Argument-Forms Which Turn Invalid Over Infinite Domains: Physicalism as Supertask?Catherine Legg - 2008 - Contemporary Pragmatism 5 (1):1-11.
    Argument-forms exist which are valid over finite but not infinite domains. Despite understanding of this by formal logicians, philosophers can be observed treating as valid arguments which are in fact invalid over infinite domains. In support of this claim I will first present an argument against the classical pragmatist theory of truth by Mark Johnston. Then, more ambitiously, I will suggest the fallacy lurks in certain arguments for physicalism taken for granted by many philosophers today.
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  • A Modern Analysis of Divine Infinity.Eric Steinhart - 2009 - Theology and Science 7 (3):261-274.
    Mathematics is obviously important in the sciences. And so it is likely to be equally important in any effort that aims to understand God in a scientifically significant way or that aims to clarify the relations between science and theology. The degree to which God has any perfection is absolutely infinite. We use contemporary mathematics to precisely define that absolute infinity. For any perfection, we use transfinite recursion to define an endlessly ascending series of degrees of that perfection. That series (...)
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  • Structure and Categoricity: Determinacy of Reference and Truth Value in the Philosophy of Mathematics.Tim Button & Sean Walsh - 2016 - Philosophia Mathematica 24 (3):283-307.
    This article surveys recent literature by Parsons, McGee, Shapiro and others on the significance of categoricity arguments in the philosophy of mathematics. After discussing whether categoricity arguments are sufficient to secure reference to mathematical structures up to isomorphism, we assess what exactly is achieved by recent ‘internal’ renditions of the famous categoricity arguments for arithmetic and set theory.
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  • 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 than (...)
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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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  • Naturalising Badiou: Mathematical Ontology and Structural Realism.Fabio Gironi - unknown
    This thesis offers a naturalist revision of Alain Badiou’s philosophy. This goal is pursued through an encounter of Badiou’s mathematical ontology and theory of truth with contemporary trends in philosophy of mathematics and philosophy of science. I take issue with Badiou’s inability to elucidate the link between the empirical and the ontological, and his residual reliance on a Heideggerian project of fundamental ontology, which undermines his own immanentist principles. I will argue for both a bottom-up naturalisation of Badiou’s philosophical approach (...)
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  • Empirical Equivalence, Artificial Gauge Freedom and a Generalized Kretschmann Objection.J. Brian Pitts - unknown
    Einstein considered general covariance to characterize the novelty of his General Theory of Relativity (GTR), but Kretschmann thought it merely a formal feature that any theory could have. The claim that GTR is ``already parametrized'' suggests analyzing substantive general covariance as formal general covariance achieved without hiding preferred coordinates as scalar ``clock fields,'' much as Einstein construed general covariance as the lack of preferred coordinates. Physicists often install gauge symmetries artificially with additional fields, as in the transition from Proca's to (...)
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  • Scientific Phenomena and Patterns in Data.Pascal Ströing - 2018 - Dissertation, LMU München
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  • Brains in Vats and Model Theory.Tim Button - forthcoming - In Sanford Goldberg (ed.), The Brain in a Vat. Cambridge University Press.
    Hilary Putnam’s BIV argument first occurred to him when ‘thinking about a theorem in modern logic, the “Skolem–Löwenheim Theorem”’ (Putnam 1981: 7). One of my aims in this paper is to explore the connection between the argument and the Theorem. But I also want to draw some further connections. In particular, I think that Putnam’s BIV argument provides us with an impressively versatile template for dealing with sceptical challenges. Indeed, this template allows us to unify some of Putnam’s most enduring (...)
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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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  • Why Live Forever? What Metaphysics Can Contribute.Aaron Segal - 2018 - Erkenntnis 83 (2):185-204.
    I suggest a way in which metaphysics might cure us of our desire for immortality. Supposing that time is composed of instants, or even that time could be composed of instants, leads to the conclusion that there is nothing good that immortality offers, nothing we might reasonably want, that is in principle unavailable to a mere mortal. My argument proceeds in three stages. First, I suggest a necessary condition for a feature to ground the desirability of a life or a (...)
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  • Why Skeptics Paint, or Imagining “Skepoiesis”: Un-Knowing and Re-Knowing Aesthetics Martin Ovens.Martin Ovens - 2014 - Journal of Aesthetics and Phenomenology 1 (1):33-61.
    ABSTRACTTwo distinct domains of philosophic enquiry are selected in order to disclose the core dynamics and concerns of a particular mode of “aesthetic skepsis”. Aspects of philosophy of cosmology and philosophy of infinity are considered in ways that serve to discipline the diminution of “belief” and the cultivation of creativity. The journey begins with a skeptic ego that is phenomenologically “empty” but wedded to a rhetoric of “darkness and light.” The result is a skepsis that needs to recapture and reconfigure (...)
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  • 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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