Results for 'Infinite totality'

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  1.  10
    Levinas' Critique of Heidegger in Totality and Infinite.Eduardo Sabrovsky - 2011 - Ideas Y Valores 60 (145):55-68.
    The article examines the critique of Being and Time formulated by Levinas in Totality and Infinite, a critique centered on Heidegger’s omission of two fundamental forms of being in the world: enjoyment and inhabiting. This omission is symptomatic: as a critique of modernity, Being and Time internalizes and ontologizes the prevalence of the equipmentality that characterizes our era far more than scientific objectivism does. Thus, a certain type of pragmatism would constitute the keystone of Being and Time as (...)
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  2. Kant on Complete Determination and Infinite Judgement.Nicholas F. Stang - 2012 - British Journal for the History of Philosophy 20 (6):1117-1139.
    In the Transcendental Ideal Kant discusses the principle of complete determination: for every object and every predicate A, the object is either determinately A or not-A. He claims this principle is synthetic, but it appears to follow from the principle of excluded middle, which is analytic. He also makes a puzzling claim in support of its syntheticity: that it represents individual objects as deriving their possibility from the whole of possibility. This raises a puzzle about why Kant regarded it as (...)
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  3. On the Concept of Finitism.Luca Incurvati - 2015 - Synthese 192 (8):2413-2436.
    At the most general level, the concept of finitism is typically characterized by saying that finitistic mathematics is that part of mathematics which does not appeal to completed infinite totalities and is endowed with some epistemological property that makes it secure or privileged. This paper argues that this characterization can in fact be sharpened in various ways, giving rise to different conceptions of finitism. The paper investigates these conceptions and shows that they sanction different portions of mathematics as finitistic.
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  4.  32
    What is the Nature of Mathematical–Logical Objects?Stathis Livadas - 2017 - Axiomathes 27 (1):79-112.
    This article deals with a question of a most general, comprehensive and profound content as it is the nature of mathematical–logical objects insofar as these are considered objects of knowledge and more specifically objects of formal mathematical theories. As objects of formal theories they are dealt with in the sense they have acquired primarily from the beginnings of the systematic study of mathematical foundations in connection with logic dating from the works of G. Cantor and G. Frege in the last (...)
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  5.  38
    Subjek En Etiese Verantwoordelikheidsbesef: Die Idee van Die Oneindige in Levinas Se Totality and Infinity.Sampie Terreblanche - 2000 - South African Journal of Philosophy 19 (2):133-150.
    Subject and the realisation of ethical responsibility – The Idea of the In finite in Levinas' Totality and Infinity. In Totality and Infinity Emmanuel Levinas writes about the categorical character of the ethical responsibility that the subject owes to the other. The confrontation with the suffering other puts the subject's natural self-interest into question, and brings him/her to realise an ethical responsibility of which s/he cannot unburden himself/herself. The question arises as to what in the constitution of the (...)
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  6.  37
    Erratum: Aspects of the Infinite in Kant.A. W. Moore - 1988 - Mind 97 (387):501-s-501.
    The wrong version of my article ‘Aspects of the Infinite in Kant’ was printed in the last issue of Mind (pp. 205–23). I should like to correct an error that thereby appeared on page 207. In A430–2/B458–60 of the Critique of Pure Reason Kant does not deny that what is (mathematically) infinite should be what I called an actual measurable totality—if, by its measure, we mean ‘the multiplicity of given units which it contains’. His point is simply (...)
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  7.  20
    Totality and Infinity, Alterity, and Relation: From Levinas to Glissant.Bernadette Cailler - 2011 - Journal of French and Francophone Philosophy 19 (1):135-151.
    Totality and Infinity , the title of a well-known work by Emmanuel Levinas, takes up a word which readers of Poetic Intention and of many other texts of Édouard Glissant’s will easily recognize: a term sometimes used in a sense that is clearly positive, sometimes in a sense that is not quite as positive, such as when, for instance, he compares “totalizing Reason” to the “Montaigne’s tolerant relativism.” In his final collection of essays, Traité du tout-monde, Poétique IV , (...)
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  8. The Structure and Justification of Infinite Responsibility in the Philosophy of Emmanuel Levinas.Diane Perpich - 1997 - Dissertation, The University of Chicago
    On standard accounts of responsibility, one is thought to be responsible for one's own actions or affairs. Levinas' philosophy speaks of a responsibility that goes beyond my actions and their consequences to an infinite, irrecusable, asymmetrical responsibility for the other human. In the dissertation, I present a defense of Levinasian responsibility and argue that distinctive of Levinas' thought as an ethics is the manner in which it maintains the absolute and unexceptionable character of responsibility, while simultaneously putting into question (...)
     
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  9. Totality and Infinity.Emmanuel Levinas - 1961/1969 - Pittsburgh: Duquesne University Press.
  10. The Neighbor and the Infinite: Marion and Levinas on the Encounter Between Self, Human Other, and God. [REVIEW]Christina M. Gschwandtner - 2007 - Continental Philosophy Review 40 (3):231-249.
    In this article I examine Jean-Luc Marion's two-fold criticism of Emmanuel Levinas’ philosophy of other and self, namely that Levinas remains unable to overcome ontological difference in Totality and Infinity and does so successfully only with the notion of the appeal in Otherwise than Being and that his account of alterity is ambiguous in failing to distinguish clearly between human and divine other. I outline Levinas’ response to this criticism and then critically examine Marion's own account of subjectivity that (...)
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  11.  24
    ¿ Qué Un Otro Otro.Miguel Gutiérrez - 2008 - Ideas Y Valores 57 (136):105-115.
    Lévinas is one of the most important thinkers of the 20th century and, perhaps, the philosopher who has attempted to think of difference most seriously. In this effort, he encountered the limits of language itself, as well as the difficulties it poses for thinking the other, difference, outside the ..
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  12.  10
    La crítica de Lévinas a Heidegger en Totalidad e infinito.Eduardo Sabrovsky - 2011 - Ideas Y Valores 60 (145):55-68.
    Se pretende dar cuenta de la crítica a Ser y tiempo que Lévinas formula en Totalidad e infinito, crítica centrada en la omisión de dos formas primordiales de estancia en el mundo: el goce y el habitar. Tal omisión es sintomática: Ser y tiempo, al querer ser una crítica de la modernidad, internaliza ..
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  13.  62
    Totality and Infinity: An Essay on Exteriority.Emmanuel Levinas - 1969 - Distribution for the U.S. And Canada, Kluwer Boston.
    INTRODUCTION Ever since the beginning of the modern phenomenological movement disciplined attention has been paid to various patterns of human experience as ...
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  14.  47
    On the Space-Time Ontology of Physical Theories.Kenneth L. Manders - 1982 - Philosophy of Science 49 (4):575-590.
    In the correspondence with Clarke, Leibniz proposes to construe physical theory in terms of physical (spatio-temporal) relations between physical objects, thus avoiding incorporation of infinite totalities of abstract entities (such as Newtonian space) in physical ontology. It has generally been felt that this proposal cannot be carried out. I demonstrate an equivalence between formulations postulating space-time as an infinite totality and formulations allowing only possible spatio-temporal relations of physical (point-) objects. The resulting rigorous formulations of physical theory (...)
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  15.  49
    Surveyability and the Sorites Paradox.Mark Addis - 1995 - Philosophia Mathematica 3 (2):157-165.
    Some issues raised by the notion of surveyability and how it is represented mathematically are explored. Wright considers the sense in which the positive integers are surveyable and suggests that their structure will be a weakly finite, but weakly infinite, totality. One way to expose the incoherence of this account is by applying Wittgenstein's distinction between intensional and extensional to it. Criticism of the idea of a surveyable proof shows the notion's lack of clarity. It is suggested that (...)
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  16.  21
    Bernays, Dooyeweerd and Gödel – the Remarkable Convergence in Their Reflections on the Foundations of Mathematics.Dfm Strauss - 2011 - South African Journal of Philosophy 30 (1):70-94.
    In spite of differences the thought of Bernays, Dooyeweerd and Gödel evinces a remarkable convergence. This is particularly the case in respect of the acknowledgement of the difference between the discrete and the continuous, the foundational position of number and the fact that the idea of continuity is derived from space (geometry – Bernays). What is furthermore similar is the recognition of what is primitive (and indefinable) as well as the account of the coherence of what is unique, such as (...)
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  17. Logic, Semantics, and Possible Worlds.Matthew William Mckeon - 1994 - Dissertation, The University of Connecticut
    The general issue addressed in this dissertation is: what do the models of formal model-theoretic semantics represent? In chapter 2, I argue that those of first-order classical logic represent meaning assignments in possible worlds. This motivates an inquiry into what the interpretations of first-order quantified model logic represent, and in Chapter 3 I argue that they represent meaning assignments in possible universes of possible worlds. A possible universe is unpacked as one way model reality might be. The problem arises here (...)
     
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  18. How Probable is an Infinite Sequence of Heads? A Reply to Williamson.Ruth Weintraub - 2008 - Analysis 68 (299):247-250.
    It is possible that a fair coin tossed infinitely many times will always land heads. So the probability of such a sequence of outcomes should, intuitively, be positive, albeit miniscule: 0 probability ought to be reserved for impossible events. And, furthermore, since the tosses are independent and the probability of heads (and tails) on a single toss is half, all sequences are equiprobable. But Williamson has adduced an argument that purports to show that our intuitions notwithstanding, the probability of an (...)
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  19.  49
    Picturing the Infinite.Jeremy Gwiazda - manuscript
    The purpose of this note is to contrast a Cantorian outlook with a non-Cantorian one and to present a picture that provides support for the latter. In particular, I suggest that: i) infinite hyperreal numbers are the (actual, determined) infinite numbers, ii) ω is merely potentially infinite, and iii) infinitesimals should not be used in the di Finetti lottery. Though most Cantorians will likely maintain a Cantorian outlook, the picture is meant to motivate the obvious nature of (...)
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  20. Boring Infinite Descent.Tuomas E. Tahko - 2014 - Metaphilosophy 45 (2):257-269.
    In formal ontology, infinite regresses are generally considered a bad sign. One debate where such regresses come into play is the debate about fundamentality. Arguments in favour of some type of fundamentalism are many, but they generally share the idea that infinite chains of ontological dependence must be ruled out. Some motivations for this view are assessed in this article, with the conclusion that such infinite chains may not always be vicious. Indeed, there may even be room (...)
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  21. Deflationism and Tarski's Paradise.Jeffrey Ketland - 1999 - Mind 108 (429):69-94.
    Deflationsism about truth is a pot-pourri, variously claiming that truth is redundant, or is constituted by the totality of 'T-sentences', or is a purely logical device (required solely for disquotational purposes or for re-expressing finitarily infinite conjunctions and/or disjunctions). In 1980, Hartry Field proposed what might be called a 'deflationary theory of mathematics', in which it is alleged that all uses of mathematics within science are dispensable. Field's criterion for the dispensability of mathematics turns on a property of (...)
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  22. Infinite Modes.Kristina Meshelski - 2015 - In Andre Santos Campos (ed.), Spinoza: Basic Concepts. Imprint Academic. pp. 43-54.
    In this chapter I explain Spinoza's concept of "infinite modes". After some brief background on Spinoza's thoughts on infinity, I provide reasons to think that Immediate Infinite Modes are identical to the attributes, and that Mediate Infinite Modes are merely totalities of finite modes. I conclude with some considerations against the alternative view that infinite modes are laws of nature.
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  23. 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 (...)
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  24. And so On...: Reasoning with Infinite Diagrams.Solomon Feferman - 2012 - Synthese 186 (1):371 - 386.
    This paper presents examples of infinite diagrams (as well as infinite limits of finite diagrams) whose use is more or less essential for understanding and accepting various proofs in higher mathematics. The significance of these is discussed with respect to the thesis that every proof can be formalized, and a "pre" form of this thesis that every proof can be presented in everyday statements-only form.
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  25. The Hypercategorematic Infinite.Maria Rosa Antognazza - 2015 - The Leibniz Review 25:5-30.
    This paper aims to show that a proper understanding of what Leibniz meant by “hypercategorematic infinite” sheds light on some fundamental aspects of his conceptions of God and of the relationship between God and created simple substances or monads. After revisiting Leibniz’s distinction between (i) syncategorematic infinite, (ii) categorematic infinite, and (iii) actual infinite, I examine his claim that the hypercategorematic infinite is “God himself” in conjunction with other key statements about God. I then discuss (...)
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  26. The Infinite.A. W. MOORE - 1990 - Routledge.
    Anyone who has pondered the limitlessness of space and time, or the endlessness of numbers, or the perfection of God will recognize the special fascination of this question. Adrian Moore's historical study of the infinite covers all its aspects, from the mathematical to the mystical.
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  27. Infinite Regress Arguments.Jan Willem Wieland - 2013 - Springer.
    This book on infinite regress arguments provides (i) an up-to-date overview of the literature on the topic, (ii) ready-to-use insights for all domains of philosophy, and (iii) two case studies to illustrate these insights in some detail. Infinite regress arguments play an important role in all domains of philosophy. There are infinite regresses of reasons, obligations, rules, and disputes, and all are supposed to have their own moral. Yet most of them are involved in controversy. Hence the (...)
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  28.  66
    Infinite Time Turing Machines.Joel David Hamkins - 2002 - Minds and Machines 12 (4):567-604.
    Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time. By doing so, they provide a natural model of infinitary computability, a theoretical setting for the analysis of the power and limitations of supertask algorithms.
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  29.  95
    The Kalām Cosmological Argument and the Infinite God Objection.Jacobus Erasmus & Anné Hendrik Verhoef - 2015 - Sophia 54 (4):411-427.
    In this article, we evaluate various responses to a noteworthy objection, namely, the infinite God objection to the kalām cosmological argument. As regards this objection, the proponents of the kalām argument face a dilemma—either an actual infinite cannot exist or God cannot be infinite. More precisely, this objection claims that God’s omniscience entails the existence of an actual infinite with God knowing an actually infinite number of future events or abstract objects, such as mathematical truths. (...)
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  30. Infinite Regress Arguments.Jan Willem Wieland - 2013 - Acta Analytica 28 (1):95-109.
    Infinite regress arguments play an important role in many distinct philosophical debates. Yet, exactly how they are to be used to demonstrate anything is a matter of serious controversy. In this paper I take up this metaphilosophical debate, and demonstrate how infinite regress arguments can be used for two different purposes: either they can refute a universally quantified proposition (as the Paradox Theory says), or they can demonstrate that a solution never solves a given problem (as the Failure (...)
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  31.  51
    Infinite Regress - Virtue or Vice?Anna-Sofia Maurin - 2007 - Hommage À Wlodek.
    In this paper I argue that the infinite regress of resemblance is vicious in the guise it is given by Russell but that it is virtuous if generated in a (contemporary) trope theoretical framework. To explain why this is so I investigate the infinite regress argument. I find that there is but one interesting and substantial way in which the distinction between vicious and virtuous regresses can be understood: The Dependence Understanding. I argue, furthermore, that to be able (...)
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  32. Achievements and Fallacies in Hume's Account of Infinite Divisibility.James Franklin - 1994 - Hume Studies 20 (1):85-101.
    Throughout history, almost all mathematicians, physicists and philosophers have been of the opinion that space and time are infinitely divisible. That is, it is usually believed that space and time do not consist of atoms, but that any piece of space and time of non-zero size, however small, can itself be divided into still smaller parts. This assumption is included in geometry, as in Euclid, and also in the Euclidean and non- Euclidean geometries used in modern physics. Of the few (...)
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  33.  60
    Infinite Time Turing Machines.Joel David Hamkins & Andy Lewis - 2000 - Journal of Symbolic Logic 65 (2):567-604.
    Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time. By doing so, they provide a natural model of infinitary computability, a theoretical setting for the analysis of the power and limitations of supertask algorithms.
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  34.  36
    Indeterminacy of Fair Infinite Lotteries.Philip Kremer - 2014 - Synthese 191 (8):1757-1760.
    In ‘Fair Infinite Lotteries’ (FIL), Wenmackers and Horsten use non-standard analysis to construct a family of nicely-behaved hyperrational-valued probability measures on sets of natural numbers. Each probability measure in FIL is determined by a free ultrafilter on the natural numbers: distinct free ultrafilters determine distinct probability measures. The authors reply to a worry about a consequent ‘arbitrariness’ by remarking, “A different choice of free ultrafilter produces a different ... probability function with the same standard part but infinitesimal differences.” They (...)
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  35. Infinite Numbers Are Large Finite Numbers.Jeremy Gwiazda - unknown
    In this paper, I suggest that infinite numbers are large finite numbers, and that infinite numbers, properly understood, are 1) of the structure omega + (omega* + omega)Ө + omega*, and 2) the part is smaller than the whole. I present an explanation of these claims in terms of epistemic limitations. I then consider the importance, part of which is demonstrating the contradiction that lies at the heart of Cantorian set theory: the natural numbers are too large to (...)
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  36.  11
    Not Wholly Finite: The Dual Aspect of Finite Modes in Spinoza.Noa Shein - 2018 - Philosophia 46 (2):433-451.
    Spinoza’s bold claim that there exists only a single infinite substance entails that finite things pose a deep challenge: How can Spinoza account for their finitude and their plurality? Taking finite bodies as a test case for finite modes in general I articulate the necessary conditions for the existence of finite things. The key to my argument is the recognition that Spinoza’s account of finite bodies reflects both Cartesian and Hobbesian influences. This recognition leads to the surprising realization there (...)
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  37.  59
    Self-Awareness (Svasaṃvedana) and Infinite Regresses: A Comparison of Arguments by Dignāga and Dharmakīrti.Birgit Kellner - 2011 - Journal of Indian Philosophy 39 (4-5):411-426.
    This paper compares and contrasts two infinite regress arguments against higher-order theories of consciousness that were put forward by the Buddhist epistemologists Dignāga (ca. 480–540 CE) and Dharmakīrti (ca. 600–660). The two arguments differ considerably from each other, and they also differ from the infinite regress argument that scholars usually attribute to Dignāga or his followers. The analysis shows that the two philosophers, in these arguments, work with different assumptions for why an object-cognition must be cognised: for Dignāga (...)
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  38. Minds Within Minds: An Infinite Descent of Mentality in a Physical World.Christopher Brown - 2017 - Erkenntnis 82 (6):1339-1350.
    Physicalism is frequently understood as the thesis that everything depends upon a fundamental physical level. This standard formulation of physicalism has a rarely noted and arguably unacceptable consequence—it makes physicalism come out false in worlds which have no fundamental level, for instance worlds containing things which can infinitely decompose into smaller and smaller parts. If physicalism is false, it should not be for this reason. Thus far, there is only one proposed solution to this problem, and it comes from the (...)
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  39. The Problem of Endless Joy: Is Infinite Utility Too Much for Utilitarianism?: J. L. A. Garcia and M. T. Nelson.J. L. A. Garcia - 1994 - Utilitas 6 (2):183-192.
    What if human joy went on endlessly? Suppose, for example, that each human generation were followed by another, or that the Western religions are right when they teach that each human being lives eternally after death. If any such possibility is true in the actual world, then an agent might sometimes be so situated that more than one course of action would produce an infinite amount of utility. Deciding whether to have a child born this year rather than next (...)
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  40.  41
    Leibniz on Infinite Numbers, Infinite Wholes, and Composite Substances.Adam Harmer - 2014 - British Journal for the History of Philosophy 22 (2):236-259.
    Leibniz claims that nature is actually infinite but rejects infinite number. Are his mathematical commitments out of step with his metaphysical ones? It is widely accepted that Leibniz has a viable response to this problem: there can be infinitely many created substances, but no infinite number of them. But there is a second problem that has not been satisfactorily resolved. It has been suggested that Leibniz’s argument against the world soul relies on his rejection of infinite (...)
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  41. On Multiverses and Infinite Numbers.Jeremy Gwiazda - 2014 - In Klaas Kraay (ed.), God and the Multiverse. Routledge. pp. 162-173.
    A multiverse is comprised of many universes, which quickly leads to the question: How many universes? There are either finitely many or infinitely many universes. The purpose of this paper is to discuss two conceptions of infinite number and their relationship to multiverses. The first conception is the standard Cantorian view. But recent work has suggested a second conception of infinite number, on which infinite numbers behave very much like finite numbers. I will argue that that this (...)
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  42.  61
    Agonistic World Projects: Transcendentalism Versus Naturalism.László Tengelyi - 2013 - Journal of Speculative Philosophy 27 (3):236-252.
    Kantian transcendental philosophy has shown that we can never decide the question of whether or not the world is infinite in space and time, because, in the field of appearance, the world as a totality of concordant experience "does not exist as [an unconditioned] whole, either of infinite or of finite magnitude."1 However, appearances are encountered in a world, in which one aspect of a thing always invites us to consider others, indicating thereby a road to infinity. (...)
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  43.  28
    Infinite Decisions and Rationally Negligible Probabilities.Nicholas J. J. Smith - 2016 - Mind (500):1-14.
    I have argued for a picture of decision theory centred on the principle of Rationally Negligible Probabilities. Isaacs argues against this picture on the grounds that it has an untenable implication. I first examine whether my view really has this implication; this involves a discussion of the legitimacy or otherwise of infinite decisions. I then examine whether the implication is really undesirable and conclude that it is not.
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  44. Infinite Regresses of Justification.Oliver Black - 1988 - International Philosophical Quarterly 28 (4):421-437.
    This paper uses a schema for infinite regress arguments to provide a solution to the problem of the infinite regress of justification. The solution turns on the falsity of two claims: that a belief is justified only if some belief is a reason for it, and that the reason relation is transitive.
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  45. Die Lehre des Erscheinens bei Jan Patočka.Ana Cecilia Santos - 2007 - Studia Phaenomenologica 7:303-329.
    In this article the author attempts to establish whether we can find a “theory of appearance” in the philosophy of Jan Patočka. The “appearance” for Patočka is basically composed of two elements. First there is a “primeval movement” which accounts for an infinite possibility of phenomena. The second element is the relation of this movement with an “addressee”, the subjectivity. If we begin to analyse the unity of these two elements we fundamentally come across three problems: what is it (...)
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  46.  18
    On the Infinite God Objection: A Reply to Jacobus Erasmus and Anné Hendrik Verhoef.Andrew Loke - 2016 - Sophia 55 (2):263-272.
    Erasmus and Verhoef suggest that a promising response to the infinite God objection to the Kalām cosmological argument include showing that abstract objects do not exist; actually infinite knowledge is impossible; and redefining omniscience as : for any proposition p, if God consciously thinks about p, God will either accept p as true if and only if p is true, or accept p as false if and only if p is false. I argue that there is insufficient motivation (...)
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  47.  55
    Aristotle on the Infinite.Ursula Coope - 2012 - In Christopher Shields (ed.), Oxford Handbook of Aristotle. Oxford University Press. pp. 267.
    In Physics, Aristotle starts his positive account of the infinite by raising a problem: “[I]f one supposes it not to exist, many impossible things result, and equally if one supposes it to exist.” His views on time, extended magnitudes, and number imply that there must be some sense in which the infinite exists, for he holds that time has no beginning or end, magnitudes are infinitely divisible, and there is no highest number. In Aristotle's view, a plurality cannot (...)
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  48. The Cofinality of the Infinite Symmetric Group and Groupwise Density.Jörg Brendle & Maria Losada - 2003 - Journal of Symbolic Logic 68 (4):1354-1361.
    We show that g ≤ c(Sym(ω)) where g is the groupwise density number and c(Sym(ω)) is the cofinality of the infinite symmetric group. This solves (the second half of) a problem addressed by Thomas.
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  49.  57
    What is an Infinite Regress Argument?Claude Gratton - 1996 - Informal Logic 18 (2).
    I describe the general structure of most infinite regress arguments; introduce some basic vocabulary; present a working hypothesis of the nature and derivation of an infinite regress; apply this working hypothesis to various infinite regress arguments to explain why they fail to entail an infinite regress; describe a common mistake in attempting to derive certain infinite regresses; and examine how infinite regresses function as a premise.
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  50. Paradoxes of the Infinite.Bernard Bolzano - 1950 - London: Routledge and Kegan Paul.
    Paradoxes of the Infinite presents one of the most insightful, yet strangely unacknowledged, mathematical treatises of the 19 th century: Dr Bernard Bolzano’s Paradoxien . This volume contains an adept translation of the work itself by Donald A. Steele S.J., and in addition an historical introduction, which includes a brief biography as well as an evaluation of Bolzano the mathematician, logician and physicist.
     
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