Results for 'Infinite'

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  1. 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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  2. Infinite Prospects.Jeffrey Sanford Russell & Yoaav Isaacs - forthcoming - Philosophy and Phenomenological Research.
    People with the kind of preferences that give rise to the St. Petersburg paradox are problematic---but not because there is anything wrong with infinite utilities. Rather, such people cannot assign the St. Petersburg gamble any value that any kind of outcome could possibly have. Their preferences also violate an infinitary generalization of Savage's Sure Thing Principle, which we call the *Countable Sure Thing Principle*, as well as an infinitary generalization of von Neumann and Morgenstern's Independence axiom, which we call (...)
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  3.  85
    Infinite Aggregation and Risk.Hayden Wilkinson - manuscript
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  4. Infinite Value and the Best of All Possible Worlds.Nevin Climenhaga - 2018 - Philosophy and Phenomenological Research 97 (2):367-392.
    A common argument for atheism runs as follows: God would not create a world worse than other worlds he could have created instead. However, if God exists, he could have created a better world than this one. Therefore, God does not exist. In this paper I challenge the second premise of this argument. I argue that if God exists, our world will continue without end, with God continuing to create value-bearers, and sustaining and perfecting the value-bearers he has already created. (...)
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  5. 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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  6. 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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  7. Infinite Utility.James Cain - 1995 - Australasian Journal of Philosophy 73 (3):401 – 404.
    Suppose we wish to decide which of a pair of actions has better consequences in a case in which both actions result in infinite utility. Peter Vallentyne and others have proposed that one action has better consequences than a second if there is a time after which the cumulative utility of the first action always outstrips the cumulative utility of the second. I argue against this principle, in particular I show how cases may arise in which up to any (...)
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  8. Spinoza’s ‘Infinite Modes’ Reconsidered.Kristin Primus - 2019 - Journal of Modern Philosophy 1 (1):1-29.
    My two principal aims in this essay are interconnected. One aim is to provide a new interpretation of the ‘infinite modes’ in Spinoza’s Ethics. I argue that for Spinoza, God, conceived as the one infinite and eternal substance, is not to be understood as causing two kinds of modes, some infinite and eternal and the rest finite and non-eternal. That there cannot be such a bifurcation of divine effects is what I take the ‘infinite mode’ propositions, (...)
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  9. 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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  10. Infinite Paths to Infinite Reality: Sri Ramakrishna and Cross-Cultural Philosophy of Religion.Ayon Maharaj - 2018 - New York, NY, USA: Oxford University Press.
    This book examines the philosophy of the nineteenth-century Indian mystic Sri Ramakrishna and brings him into dialogue with Western philosophers of religion, primarily in the recent analytic tradition. Sri Ramakrishna’s expansive conception of God as the impersonal-personal Infinite Reality, Maharaj argues, opens up an entirely new paradigm for addressing central topics in the philosophy of religion, including divine infinitude, religious diversity, the nature and epistemology of mystical experience, and the problem of evil.
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  11. On Infinite Number and Distance.Jeremy Gwiazda - 2012 - Constructivist Foundations 7 (2):126-130.
    Context: The infinite has long been an area of philosophical and mathematical investigation. There are many puzzles and paradoxes that involve the infinite. Problem: The goal of this paper is to answer the question: Which objects are the infinite numbers (when order is taken into account)? Though not currently considered a problem, I believe that it is of primary importance to identify properly the infinite numbers. Method: The main method that I employ is conceptual analysis. In (...)
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  12. Infinite Analysis, Lucky Proof, and Guaranteed Proof in Leibniz.Gonzalo Rodriguez-Pereyra & Paul Lodge - 2011 - Archiv für Geschichte der Philosophie 93 (2):222-236.
    According to one of Leibniz's theories of contingency a proposition is contingent if and only if it cannot be proved in a finite number of steps. It has been argued that this faces the Problem of Lucky Proof , namely that we could begin by analysing the concept ‘Peter’ by saying that ‘Peter is a denier of Christ and …’, thereby having proved the proposition ‘Peter denies Christ’ in a finite number of steps. It also faces a more general but (...)
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  13. 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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  14. Infinite Responsibility in the Bedpan: Response Ethics, Care Ethics, and the Phenomenology of Caregiving.Joel Michael Reynolds - 2016 - Hypatia 31 (4):779-794.
    Drawing upon the practice of caregiving and the insights of feminist care ethics, I offer a phenomenology of caregiving through the work of Eva Feder Kittay and Emmanuel Lévinas. I argue that caregiving is a material dialectic of embodied response involving moments of leveling, attention, and interruption. In this light, the Levinasian opposition between responding to another's singularity and leveling it via parity-based principles is belied in the experience of care. Contra much of response ethics’ and care ethics’ respective literatures, (...)
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  15.  84
    Infinite Graphs in Systematic Biology, with an Application to the Species Problem.Samuel A. Alexander - 2013 - Acta Biotheoretica 61 (2):181--201.
    We argue that C. Darwin and more recently W. Hennig worked at times under the simplifying assumption of an eternal biosphere. So motivated, we explicitly consider the consequences which follow mathematically from this assumption, and the infinite graphs it leads to. This assumption admits certain clusters of organisms which have some ideal theoretical properties of species, shining some light onto the species problem. We prove a dualization of a law of T.A. Knight and C. Darwin, and sketch a decomposition (...)
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  16. The Relatively Infinite Value of the Environment.Paul Bartha & C. Tyler DesRoches - 2017 - Australasian Journal of Philosophy 95 (2):328-353.
    Some environmental ethicists and economists argue that attributing infinite value to the environment is a good way to represent an absolute obligation to protect it. Others argue against modelling the value of the environment in this way: the assignment of infinite value leads to immense technical and philosophical difficulties that undermine the environmentalist project. First, there is a problem of discrimination: saving a large region of habitat is better than saving a small region; yet if both outcomes have (...)
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  17.  97
    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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  18. Taking Stock of Infinite Value: Pascal’s Wager and Relative Utilities.Paul Bartha - 2007 - Synthese 154 (1):5-52.
    Among recent objections to Pascal's Wager, two are especially compelling. The first is that decision theory, and specifically the requirement of maximizing expected utility, is incompatible with infinite utility values. The second is that even if infinite utility values are admitted, the argument of the Wager is invalid provided that we allow mixed strategies. Furthermore, Hájek has shown that reformulations of Pascal's Wager that address these criticisms inevitably lead to arguments that are philosophically unsatisfying and historically unfaithful. Both (...)
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  19. Complexity, Existence and Infinite Analysis.Giovanni Merlo - 2012 - The Leibniz Review 22:9-36.
    According to Leibniz’s infinite-analysis account of contingency, any derivative truth is contingent if and only if it does not admit of a finite proof. Following a tradition that goes back at least as far as Bertrand Russell, several interpreters have been tempted to explain this biconditional in terms of two other principles: first, that a derivative truth is contingent if and only if it contains infinitely complex concepts and, second, that a derivative truth contains infinitely complex concepts if and (...)
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  20.  26
    Pareto Principles in Infinite Ethics.Amanda Askell - 2018 - Dissertation, New York University
    It is possible that the world contains infinitely many agents that have positive and negative levels of well-being. Theories have been developed to ethically rank such worlds based on the well-being levels of the agents in those worlds or other qualitative properties of the worlds in question, such as the distribution of agents across spacetime. In this thesis I argue that such ethical rankings ought to be consistent with the Pareto principle, which says that if two worlds contain the same (...)
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  21. 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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  22. The Paradox of Infinite Given Magnitude: Why Kantian Epistemology Needs Metaphysical Space.Lydia Patton - 2011 - Kant-Studien 102 (3):273-289.
    Kant's account of space as an infinite given magnitude in the Critique of Pure Reason is paradoxical, since infinite magnitudes go beyond the limits of possible experience. Michael Friedman's and Charles Parsons's accounts make sense of geometrical construction, but I argue that they do not resolve the paradox. I argue that metaphysical space is based on the ability of the subject to generate distinctly oriented spatial magnitudes of invariant scalar quantity through translation or rotation. The set of determinately (...)
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  23. Overgeneration in the Higher Infinite.Salvatore Florio & Luca Incurvati - forthcoming - In Gil Sagi & Jack Woods (eds.), The Semantic Conception of Logic: Essays on Consequence, Invariance, and Meaning. Cambridge: Cambridge University Press.
    The Overgeneration Argument is a prominent objection against the model-theoretic account of logical consequence for second-order languages. In previous work we have offered a reconstruction of this argument which locates its source in the conflict between the neutrality of second-order logic and its alleged entanglement with mathematics. Some cases of this conflict concern small large cardinals. In this article, we show that in these cases the conflict can be resolved by moving from a set-theoretic implementation of the model-theoretic account to (...)
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  24. 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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  25.  87
    Brentanian Inner Consciousness and the Infinite Regress Problem.Andrea Marchesi - 2019 - Dialectica 73 (1-2):129-147.
    By “Brentanian inner consciousness” I mean the conception of inner consciousness developed by Franz Brentano. The aim of this paper is threefold: first, to present Brentano’s account of inner consciousness; second, to discuss this account in light of the mereology outlined by Brentano himself; and third, to decide whether this account incurs an infinite regress. In this regard, I distinguish two kinds of infinite regress: external infinite regress and internal infinite regress. I contend that the most (...)
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  26. The Finite and the Infinite in Frege's Grundgesetze der Arithmetik.Richard Heck - 1998 - In Matthias Schirn (ed.), Philosophy of Mathematics Today. Oxford University Press.
    Discusses Frege's formal definitions and characterizations of infinite and finite sets. Speculates that Frege might have discovered the "oddity" in Dedekind's famous proof that all infinite sets are Dedekind infinite and, in doing so, stumbled across an axiom of countable choice.
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  27. 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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  28. On the Infinite in Mereology with Plural Quantification.Massimiliano Carrara & Enrico Martino - 2011 - Review of Symbolic Logic 4 (1):54-62.
    In Lewis reconstructs set theory using mereology and plural quantification (MPQ). In his recontruction he assumes from the beginning that there is an infinite plurality of atoms, whose size is equivalent to that of the set theoretical universe. Since this assumption is far beyond the basic axioms of mereology, it might seem that MPQ do not play any role in order to guarantee the existence of a large infinity of objects. However, we intend to demonstrate that mereology and plural (...)
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  29. A Generalised Lottery Paradox for Infinite Probability Spaces.Martin Smith - 2010 - British Journal for the Philosophy of Science 61 (4):821-831.
    Many epistemologists have responded to the lottery paradox by proposing formal rules according to which high probability defeasibly warrants acceptance. Douven and Williamson present an ingenious argument purporting to show that such rules invariably trivialise, in that they reduce to the claim that a probability of 1 warrants acceptance. Douven and Williamson’s argument does, however, rest upon significant assumptions – amongst them a relatively strong structural assumption to the effect that the underlying probability space is both finite and uniform. In (...)
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  30. There Must Be A First: Why Thomas Aquinas Rejects Infinite, Essentially Ordered, Causal Series.Caleb Cohoe - 2013 - British Journal for the History of Philosophy 21 (5):838 - 856.
    Several of Thomas Aquinas's proofs for the existence of God rely on the claim that causal series cannot proceed in infinitum. I argue that Aquinas has good reason to hold this claim given his conception of causation. Because he holds that effects are ontologically dependent on their causes, he holds that the relevant causal series are wholly derivative: the later members of such series serve as causes only insofar as they have been caused by and are effects of the earlier (...)
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  31.  58
    Are Infinite Explanations Self-Explanatory?Alexandre Billon - forthcoming - Erkenntnis.
    Consider an infinite series whose items are each explained by their immediate successor. Does such an infinite explanation explain the whole series or does it leave something to be explained? Hume arguably claimed that it does fully explain the whole series. Leibniz, however, designed a very telling objection against this claim, an objection involving an infinite series of book copies. In this paper, I argue that the Humean claim can, in certain cases, be saved from the Leibnizian (...)
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  32. 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 (...)
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  33. Infinite Descent.T. Scott Dixon - 2020 - In Michael J. Raven (ed.), The Routledge Handbook of Metaphysical Grounding. New York, USA: Routledge. pp. 244-58.
    Once one accepts that certain things metaphysically depend upon, or are metaphysically explained by, other things, it is natural to begin to wonder whether these chains of dependence or explanation must come to an end. This essay surveys the work that has been done on this issue—the issue of grounding and infinite descent. I frame the discussion around two questions: (1) What is infinite descent of ground? and (2) Is infinite descent of ground possible? In addressing the (...)
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  34. 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 (...)
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  35.  91
    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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  36. 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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  37.  70
    Infinite Judgements and Transcendental Logic.Ekin Erkan, Anna Longo & Madeleine Collier - 2020 - Cosmos and History : The Journal of Natural and Social Philosophy 20 (2):391-415.
    The infinite judgement has long been forgotten and yet, as I am about to demonstrate, it may be urgent to revive it for its critical and productive potential. An infinite judgement is neither analytic nor synthetic; it does not produce logical truths, nor true representations, but it establishes the genetic conditions of real objects and the concepts appropriate to them. It is through infinite judgements that we reach the principle of transcendental logic, in the depths of which (...)
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  38. Infinitely Complex Machines.Eric Steinhart - 2007 - In Intelligent Computing Everywhere. Springer. pp. 25-43.
    Infinite machines (IMs) can do supertasks. A supertask is an infinite series of operations done in some finite time. Whether or not our universe contains any IMs, they are worthy of study as upper bounds on finite machines. We introduce IMs and describe some of their physical and psychological aspects. An accelerating Turing machine (an ATM) is a Turing machine that performs every next operation twice as fast. It can carry out infinitely many operations in finite time. Many (...)
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  39.  80
    The Infinite Regress of Optimization.Philippe Mongin - 1991 - Behavioral and Brain Sciences 14 (2):229-230.
    A comment on Paul Schoemaker's target article in Behavioral and Brain Sciences, 14 (1991), p. 205-215, "The Quest for Optimality: A Positive Heuristic of Science?" (https://doi.org/10.1017/S0140525X00066140). This comment argues that the optimizing model of decision leads to an infinite regress, once internal costs of decision (i.e., information and computation costs) are duly taken into account.
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  40. Realism and the Infinite.Paul Livingston - 2013 - Speculations (IV):99-107.
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  41. Infinite options, intransitive value, and supererogation.Daniel Muñoz - 2020 - Philosophical Studies 178 (6):2063-2075.
    Supererogatory acts are those that lie “beyond the call of duty.” There are two standard ways to define this idea more precisely. Although the definitions are often seen as equivalent, I argue that they can diverge when options are infinite, or when there are cycles of better options; moreover, each definition is acceptable in only one case. I consider two ways out of this dilemma.
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  42.  62
    L’infinité et l’idéalité du fini : une lecture sur la théorie de la véritable infinité dans la Science de la logique.Arif Yildiz - 2020 - In D. Ferrer F. Orsini M. Bordignon A. Bavaresco C. Iber (ed.), A Autobiografia do Pensamento. A Ciência da Lógica de Hegel. Brasília - Brasilia, Federal District, Brazil: pp. 143-166.
    Le passage spéculatif de la catégorie du mauvais infini dans le véritable infini reste l’un des plus importants dans la Science de la logique. Comme il est bien connu, ce passage est expliqué par Hegel à travers sa théorie de l’idéalité du fini. Pourtant, du fait de sa structure complexe, le surgissement du véritable infini au sein du fini par l’idéalisation peut être considéré comme un processus abstrait, consistant seulement à supprimer la dualité de l’infinité. Cet article se propose donc (...)
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  43. Easy Ontology, Application Conditions and Infinite Regress.Andrew Brenner - 2018 - Analysis 78 (4):605-614.
    In a number of recent publications Thomasson has defended a deflationary approach to ontological disputes, according to which ontological disputes are relatively easy to settle, by either conceptual analysis, or conceptual analysis in conjunction with empirical investigation. Thomasson’s “easy” approach to ontology is intended to derail many prominent ontological disputes. In this paper I present an objection to Thomasson’s approach to ontology. Thomasson’s approach to existence assertions means that she is committed to the view that application conditions associated with any (...)
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  44. Taking Reductionism to the Limit: How to Rebut the Antireductionist Argument From Infinite Limits.Juha Saatsi & Alexander Reutlinger - 2017 - Philosophy of Science (3):455-482.
    This paper analyses the anti-reductionist argument from renormalisation group explanations of universality, and shows how it can be rebutted if one assumes that the explanation in question is captured by the counterfactual dependence account of explanation.
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  45. L'infinité des nombres premiers : une étude de cas de la pureté des méthodes.Andrew Arana - 2011 - Les Etudes Philosophiques 97 (2):193.
    Une preuve est pure si, en gros, elle ne réfère dans son développement qu’à ce qui est « proche » de, ou « intrinsèque » à l’énoncé à prouver. L’infinité des nombres premiers, un théorème classique de l’arithmétique, est un cas d’étude particulièrement riche pour les recherches philosophiques sur la pureté. Deux preuves différentes de ce résultat sont ici considérées, à savoir la preuve euclidienne classique et une preuve « topologique » plus récente proposée par Furstenberg. D’un point de vue (...)
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  46. Autonomy and The Paradox of Self-Creation: Infinite Regresses, Finite Selves, and the Limits of Authenticity.Robert Noggle - 2008 - In James Stacey Taylor (ed.), Personal Autonomy: New Essays on Personal Autonomy and its Role in Contemporary Moral Philosophy. Cambridge University Press.
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  47. 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 (...). I suggest that certain structures, such as a well-ordering of the reals, or the natural numbers, are examples of the potential infinite, whereas infinite integers in a nonstandard model of arithmetic are examples of the actual infinite. (shrink)
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  48. No Successfull Infinite Regress.Laureano Luna - 2014 - Logic and Logical Philosophy 23 (2):189-201.
    We model infinite regress structures -not arguments- by means of ungrounded recursively defined functions in order to show that no such structure can perform the task of providing determination to the items composing it, that is, that no determination process containing an infinite regress structure is successful.
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  49.  61
    The Infinite in Giordano Bruno. With a Translation of His Dialogue, Concerning the Cause, Principle, and One.G. B. & Sidney Greenberg - 1951 - Journal of Philosophy 48 (11):369.
    Una visión de la película de Lars Von Trier: Anticristo.
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  50.  39
    Avoiding Infinite Regress: Posterior Analytics I 22.Breno Zuppolini - 2019 - Manuscrito 42 (4):122-156.
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