Search results for 'Infinite' (try it on Scholar)

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  1. Tuomas E. Tahko (2014). Boring Infinite Descent. 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.  46
    Maria Rosa Antognazza (forthcoming). The Hypercategorematic Infinite. The Leibniz Review 25.
    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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  3. Nicholas Stang (2012). Kant on Complete Determination and Infinite Judgement. 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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  4.  46
    Jacobus Erasmus & Anné Hendrik Verhoef (2015). The Kalām Cosmological Argument and the Infinite God Objection. 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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  5. Jeremy Gwiazda, Infinite Numbers Are Large Finite Numbers.
    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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  6. Jeremy Gwiazda (2014). On Multiverses and Infinite Numbers. In Klaas Kraay (ed.), God and the Multiverse. Routledge 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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  7.  51
    Solomon Feferman (2012). And so On...: Reasoning with Infinite Diagrams. 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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  8. Jörg Brendle & Maria Losada (2003). The Cofinality of the Infinite Symmetric Group and Groupwise Density. 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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  9. Jan Willem Wieland (2013). Infinite Regress Arguments. 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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  10.  16
    Kristina Meshelski (2015). Infinite Modes. In Andre Santos Campos (ed.), Spinoza: Basic Concepts. Imprint Academic 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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  11. Iulian D. Toader (2015). Against Harmony: Infinite Idealizations and Causal Explanation. In Iulian D. Toader, Gabriel Sandu & Ilie Pȃrvu (eds.), Romanian Studies in Philosophy of Science. Boston Studies in the Philosophy and History of Science, Vol. 313, 291-301.
    This paper discusses the idea that some of the causal factors that are responsible for the production of a natural phenomenon are explanatorily irrelevant and, thus, may be omitted or distorted. It argues against Craig Callender’s suggestion that the standard explanation of phase transitions in statistical mechanics may be considered a causal explanation, in Michael Strevens’ sense, as a distortion that can nevertheless successfully represent causal relations.
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  12.  99
    Laureano Luna (2014). No Successfull Infinite Regress. 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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  13. Paul Bartha (2007). Taking Stock of Infinite Value: Pascal's Wager and Relative Utilities. 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 (Philosophical Review 112, 2003) has shown that reformulations of Pascal’s Wager that address these criticisms inevitably lead to arguments that are philosophically unsatisfying (...)
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  14. Steven M. Duncan, Why There Can't Be a Self-Explanatory Series of Infinite Past Events.
    Based on a recently published essay by Jeremy Gwiazda, I argue that the possibility that the present state of the universe is the product of an actually infinite series of causally-ordered prior events is impossible in principle, and thus that a major criticism of the Secunda Via of St. Thomas is baseless after all.
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  15. A. W. Moore (1990). The Infinite. Routledge.
    This historical study of the infinite covers all its aspects from the mathematical to the mystical. Anyone who has ever pondered the limitlessness of space and time, or the endlessness of numbers, or the perfection of God will recognize the special fascination of the subject. Beginning with an entertaining account of the main paradoxes of the infinite, including those of Zeno, A.W. Moore traces the history of the topic from Aristotle to Kant, Hegel, Cantor, and Wittgenstein.
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  16.  43
    Joel David Hamkins (2002). Infinite Time Turing Machines. 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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  17.  64
    Ruth Weintraub (2008). How Probable is an Infinite Sequence of Heads? A Reply to Williamson. 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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  18.  2
    Andrew Ter Ern Loke (forthcoming). On the Infinite God Objection: A Reply to Jacobus Erasmus and Anné Hendrik Verhoef. Sophia:1-10.
    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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  19.  5
    Luc Lauwers (forthcoming). Infinite Lotteries, Large and Small Sets. Synthese:1-7.
    One result of this note is about the nonconstructivity of countably infinite lotteries: even if we impose very weak conditions on the assignment of probabilities to subsets of natural numbers we cannot prove the existence of such assignments constructively, i.e., without something such as the axiom of choice. This is a corollary to a more general theorem about large-small filters, a concept that extends the concept of free ultrafilters. The main theorem is that proving the existence of large-small filters (...)
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  20. Jan Willem Wieland (2014). Infinite Regress Arguments. 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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  21.  43
    Jeremy Gwiazda, Paradoxes of the Infinite Rest on Conceptual Confusion.
    The purpose of this paper is to dissolve paradoxes of the infinite by correctly identifying the infinite natural numbers.
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  22.  32
    Birgit Kellner (2011). Self-Awareness (Svasaṃvedana) and Infinite Regresses: A Comparison of Arguments by Dignāga and Dharmakīrti. [REVIEW] 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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  23.  20
    Catherine Legg (2008). Argument-Forms Which Turn Invalid Over Infinite Domains: Physicalism as Supertask? 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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  24.  27
    Claude Gratton (1996). What is an Infinite Regress Argument? 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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  25.  28
    Thomas Holden (2002). Infinite Divisibility and Actual Parts in Hume’s Treatise. Hume Studies 28 (1):3-25.
    According to a standard interpretation of Hume’s argument against infinite divisibility, Hume is raising a purely formal problem for mathematical constructions of infinite divisibility, divorced from all thought of the stuffing or filling of actual physical continua. I resist this. Hume’s argument must be understood in the context of a popular early modern account of the metaphysical status of the parts of physical quantities. This interpretation disarms the standard mathematical objections to Hume’s reasoning; I also defend it on (...)
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  26.  63
    Christophe Grellard (2007). Scepticism, Demonstration and the Infinite Regress Argument (Nicholas of Autrecourt and John Buridan). Vivarium 45 (s 2-3):328-342.
    The aim of this paper is to examine the medieval posterity of the Aristotelian and Pyrrhonian treatments of the infinite regress argument. We show that there are some possible Pyrrhonian elements in Autrecourt's epistemology when he argues that the truth of our principles is merely hypothetical. By contrast, Buridan's criticisms of Autrecourt rely heavily on Aristotelian material. Both exemplify a use of scepticism.
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  27.  50
    J. L. A. Garcia & Mark T. Nelson (1994). The Problem of Endless Joy: Is Infinite Utility Too Much for Utilitarianism? Utilitas 6 (2):183.
    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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  28.  8
    Murdoch J. Gabbay (2012). Finite and Infinite Support in Nominal Algebra and Logic: Nominal Completeness Theorems for Free. Journal of Symbolic Logic 77 (3):828-852.
    By operations on models we show how to relate completeness with respect to permissivenominal models to completeness with respect to nominal models with finite support. Models with finite support are a special case of permissive-nominal models, so the construction hinges on generating from an instance of the latter, some instance of the former in which sufficiently many inequalities are preserved between elements. We do this using an infinite generalisation of nominal atoms-abstraction. The results are of interest in their own (...)
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  29.  23
    Adam Harmer (2014). Leibniz on Infinite Numbers, Infinite Wholes, and Composite Substances. 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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  30.  70
    Jon Roffe (2007). The Errant Name: Badiou and Deleuze on Individuation, Causality and Infinite Modes in Spinoza. [REVIEW] Continental Philosophy Review 40 (4):389-406.
    Although Alain Badiou dedicates a number of texts to the philosophy of Benedict de Spinoza throughout his work—after all, the author of a systematic philosophy of being more geometrico must be a point of reference for the philosopher who claims that “mathematics = ontology”—the reading offered in Meditation Ten of his key work Being and Event presents the most significant moment of this engagement. Here, Badiou proposes a reading of Spinoza’s ontology that foregrounds a concept that is as central to, (...)
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  31.  45
    Joel David Hamkins & Andy Lewis (2000). Infinite Time Turing Machines. 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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  32.  12
    D. E. Seabold & J. D. Hamkins (2001). Infinite Time Turing Machines With Only One Tape. Mathematical Logic Quarterly 47 (2):271-287.
    Infinite time Turing machines with only one tape are in many respects fully as powerful as their multi-tape cousins. In particular, the two models of machine give rise to the same class of decidable sets, the same degree structure and, at least for partial functions f : ℝ → ℕ, the same class of computable functions. Nevertheless, there are infinite time computable functions f : ℝ → ℝ that are not one-tape computable, and so the two models of (...)
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  33.  10
    Simon D. Smith (2015). Kant’s Mathematical Sublime and the Role of the Infinite: Reply to Crowther. Kantian Review 20 (1):99-120.
    This paper offers an analysis of KantNature is thus sublime in those of its appearances the intuition of which brings with them the idea of its infinitys interpretation of this species of aesthetic experience, and I reject his interpretation as not being reflective of Kant’s actual position. I go on to show that the experience of the mathematical sublime is necessarily connected with the progression of the imagination in its move towards the infinite.
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  34.  20
    İskender Taşdelen (2014). A Counterfactual Analysis of Infinite Regress Arguments. Acta Analytica 29 (2):195-213.
    I propose a counterfactual theory of infinite regress arguments. Most theories of infinite regress arguments present infinite regresses in terms of indicative conditionals. These theories direct us to seek conditions under which an infinite regress generates an infinite inadmissible set. Since in ordinary language infinite regresses are usually expressed by means of infinite sequences of counterfactuals, it is natural to expect that an analysis of infinite regress arguments should be based on a (...)
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  35.  10
    João Figueiredo Nobre Cortese (2015). Infinity Between Mathematics and Apologetics: Pascal’s Notion of Infinite Distance. Synthese 192 (8):2379-2393.
    In this paper I will examine what Blaise Pascal means by “infinite distance”, both in his works on projective geometry and in the apologetics of the Pensées’s. I suggest that there is a difference of meaning in these two uses of “infinite distance”, and that the Pensées’s use of it also bears relations to the mathematical concept of heterogeneity. I also consider the relation between the finite and the infinite and the acceptance of paradoxical relations by Pascal.
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  36.  16
    Claude Gratton (1994). Circular Definitions, Circular Explanations, and Infinite Regresses. Argumentation 8 (3):295-308.
    This paper discusses some of the ways in which circular definitions and circular explanations entail or fail to entail infinite regresses. And since not all infinite regresses are vicious, a few criteria of viciousness are examined in order to determine when the entailment of a regress refutes a circular definition or a circular explanation.
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  37.  21
    Stefano Aguzzoli & Agata Ciabattoni (2000). Finiteness in Infinite-Valued Łukasiewicz Logic. Journal of Logic, Language and Information 9 (1):5-29.
    In this paper we deepen Mundici's analysis on reducibility of the decision problem from infinite-valued ukasiewicz logic to a suitable m-valued ukasiewicz logic m , where m only depends on the length of the formulas to be proved. Using geometrical arguments we find a better upper bound for the least integer m such that a formula is valid in if and only if it is also valid in m. We also reduce the notion of logical consequence in to the (...)
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  38.  38
    Verónica Becher & Santiago Figueira (2005). Kolmogorov Complexity for Possibly Infinite Computations. Journal of Logic, Language and Information 14 (2):133-148.
    In this paper we study the Kolmogorov complexity for non-effective computations, that is, either halting or non-halting computations on Turing machines. This complexity function is defined as the length of the shortest input that produce a desired output via a possibly non-halting computation. Clearly this function gives a lower bound of the classical Kolmogorov complexity. In particular, if the machine is allowed to overwrite its output, this complexity coincides with the classical Kolmogorov complexity for halting computations relative to the first (...)
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  39.  15
    Pierre Cartier (2012). How to Take Advantage of the Blur Between the Finite and the Infinite. Logica Universalis 6 (1-2):217-226.
    In this paper is presented and discussed the notion of true finite by opposition to the notion of theoretical finite. Examples from mathematics and physics are given. Fermat’s infinite descent principle is challenged.
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  40.  11
    René Woudenberg & Ronald Meester (2014). Infinite Epistemic Regresses and Internalism. Metaphilosophy 45 (2):221-231.
    This article seeks to state, first, what traditionally has been assumed must be the case in order for an infinite epistemic regress to arise. It identifies three assumptions. Next it discusses Jeanne Peijnenburg's and David Atkinson's setting up of their argument for the claim that some infinite epistemic regresses can actually be completed and hence that, in addition to foundationalism, coherentism, and infinitism, there is yet another solution (if only a partial one) to the traditional epistemic regress problem. (...)
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  41. Bernard Bolzano (1950). Paradoxes of the Infinite. London, Routledge and 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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  42.  4
    Michel Blay (1999). Reasoning with the Infinite: From the Closed World to the Mathematical Universe. University of Chicago Press.
    "One of Michael Blay's many fine achievements in Reasoning with the Infinite is to make us realize how velocity, and later instantaneous velocity, came to play a vital part in the development of a rigorous mathematical science of motion. ...
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  43.  9
    Ansten Mørch Klev (2009). Infinite Time Extensions of Kleene's {Mathcal{O}}. Archive for Mathematical Logic 48 (7):691-703.
    Using infinite time Turing machines we define two successive extensions of Kleene’s ${\mathcal{O}}$ and characterize both their height and their complexity. Specifically, we first prove that the one extension—which we will call ${\mathcal{O}^{+}}$ —has height equal to the supremum of the writable ordinals, and that the other extension—which we will call ${\mathcal{O}}^{++}$ —has height equal to the supremum of the eventually writable ordinals. Next we prove that ${\mathcal{O}^+}$ is Turing computably isomorphic to the halting problem of infinite time (...)
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  44.  26
    Theodore Hailperin (2001). Potential Infinite Models and Ontologically Neutral Logic. Journal of Philosophical Logic 30 (1):79-96.
    The paper begins with a more carefully stated version of ontologically neutral (ON) logic, originally introduced in (Hailperin, 1997). A non-infinitistic semantics which includes a definition of potential infinite validity follows. It is shown, without appeal to the actual infinite, that this notion provides a necessary and sufficient condition for provability in ON logic.
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  45.  19
    Samuel Coskey & Joel David Hamkins (2010). Infinite Time Decidable Equivalence Relation Theory. Notre Dame Journal of Formal Logic 52 (2):203-228.
    We introduce an analogue of the theory of Borel equivalence relations in which we study equivalence relations that are decidable by an infinite time Turing machine. The Borel reductions are replaced by the more general class of infinite time computable functions. Many basic aspects of the classical theory remain intact, with the added bonus that it becomes sensible to study some special equivalence relations whose complexity is beyond Borel or even analytic. We also introduce an infinite time (...)
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  46.  9
    Philip Kremer (2014). Indeterminacy of Fair Infinite Lotteries. 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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  47.  8
    Miguel Sanchez-Mazas (1989). Essai de Représentation Par des Nombres Réels d'Une Analyse Infinite des Notions Individuelles Dans Une Infinité de Mondes Possibles. Argumentation 3 (1):75-96.
    The aim of this study is to try to make use of real numbers for representing an infinite analysis of individual notions in an infinity of possible worlds.As an introduction to the subject, the author shows, firstly, the possibility of representing Boole's lattice of universal notions by an associate Boole's lattice of rational numbers.But, in opposition to the universal notions, definable by a finite number of predicates, an individual notion, cannot admits this sort of definition, because each state of (...)
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  48.  9
    Henry W. Johnstone (1994). Question-Begging and Infinite Regress. Argumentation 8 (3):291-293.
    InMetaphysics Γ, Ch. 4, Aristotle speaks of both infinite regress and question-begging, but does not explicitly relate them. We get the impression that he thinks that to use one of these arguments to avoid the other is to jump from the frying-pan into the fire. This relationship is illustrated in terms of the ignorant belief that everything can be proved, and of attempts to prove the Law of Noncontradiction.
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  49.  2
    Jon Pérez Laraudogoitia (2015). On the Atkinson–Johnson Homogeneous Solution for Infinite Systems. Foundations of Physics 45 (5):496-506.
    This paper shows that the general homogeneous solution to equations of evolution for some infinite systems of particles subject to mutual binary collisions does not depend on a single arbitrary constant but on a potentially infinite number of such constants. This is because, as I demonstrate, a single self-excitation of a system of particles can depend on a potentially infinite number of parameters. The recent homogeneous solution obtained by Atkinson and Johnson, which depends on a single arbitrary (...)
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    Eli Maor (1987). To Infinity and Beyond: A Cultural History of the Infinite. Princeton University Press.
    Eli Maor examines the role of infinity in mathematics and geometry and its cultural impact on the arts and sciences. He evokes the profound intellectual impact the infinite has exercised on the human mind--from the "horror infiniti" of the Greeks to the works of M. C. Escher from the ornamental designs of the Moslems, to the sage Giordano Bruno, whose belief in an infinite universe led to his death at the hands of the Inquisition. But above all, the (...)
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