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

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  1. Jeremy Gwiazda, Infinite Numbers Are Large Finite Numbers.score: 24.0
    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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  2. P. Bartha (2007). Taking Stock of Infinite Value: Pascal's Wager and Relative Utilities. Synthese 154 (1):5 - 52.score: 24.0
    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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  3. Nicholas Stang (2012). Kant on Complete Determination and Infinite Judgement. British Journal for the History of Philosophy 20 (6):1117-1139.score: 24.0
    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. Steven M. Duncan, Why There Can't Be a Self-Explanatory Series of Infinite Past Events.score: 24.0
    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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  5. Jan Willem Wieland (2013). Infinite Regress Arguments. Acta Analytica 28 (1):95-109.score: 24.0
    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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  6. A. W. Moore (1990/2002). The Infinite. Routledge.score: 24.0
    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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  7. Tuomas E. Tahko (2014). Boring Infinite Descent. Metaphilosophy 45 (2):257-269.score: 24.0
    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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  8. 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.score: 24.0
    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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  9. Anne Ashley Davenport (1999). Measure of a Different Greatness: The Intensive Infinite, 1250-1650. Brill.score: 24.0
    This volume examines a selection of late medieval works devoted to the intensive infinite in order to draw a comprehensive picture of the context, character and ...
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  10. Christophe Grellard (2007). Scepticism, Demonstration and the Infinite Regress Argument (Nicholas of Autrecourt and John Buridan). Vivarium 45 (s 2-3):328-342.score: 24.0
    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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  11. Solomon Feferman (2012). And so On...: Reasoning with Infinite Diagrams. Synthese 186 (1):371 - 386.score: 24.0
    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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  12. Laureano Luna (2014). No Successfull Infinite Regress. Logic and Logical Philosophy 23 (2).score: 24.0
    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. Jan Willem Wieland (2014). Infinite Regress Arguments. Springer.score: 24.0
    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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  14. J. L. A. Garcia & Mark T. Nelson (1994). The Problem of Endless Joy: Is Infinite Utility Too Much for Utilitarianism? Utilitas 6 (02):183-.score: 24.0
    What if human joy (more technically, utility) 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 (or of disutility, or of both). Deciding whether to (...)
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  15. Joel David Hamkins & Andy Lewis (2000). Infinite Time Turing Machines. Journal of Symbolic Logic 65 (2):567-604.score: 24.0
    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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  16. Jeremy Gwiazda, Paradoxes of the Infinite Rest on Conceptual Confusion.score: 24.0
    The purpose of this paper is to dissolve paradoxes of the infinite by correctly identifying the infinite natural numbers.
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  17. Joel David Hamkins (2002). Infinite Time Turing Machines. Minds and Machines 12 (4):567-604.score: 24.0
    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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  18. 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.score: 24.0
    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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  19. Eli Maor (1987/1991). To Infinity and Beyond: A Cultural History of the Infinite. Princeton University Press.score: 24.0
    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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  20. Adam Harmer (2014). Leibniz on Infinite Numbers, Infinite Wholes, and Composite Substances. British Journal for the History of Philosophy 22 (2):236-259.score: 24.0
    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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  21. Stefano Aguzzoli & Agata Ciabattoni (2000). Finiteness in Infinite-Valued Łukasiewicz Logic. Journal of Logic, Language and Information 9 (1):5-29.score: 24.0
    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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  22. Samuel Coskey & Joel David Hamkins (2010). Infinite Time Decidable Equivalence Relation Theory. Notre Dame Journal of Formal Logic 52 (2):203-228.score: 24.0
    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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  23. İskender Taşdelen (2014). A Counterfactual Analysis of Infinite Regress Arguments. Acta Analytica 29 (2):195-213.score: 24.0
    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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  24. Verónica Becher & Santiago Figueira (2005). Kolmogorov Complexity for Possibly Infinite Computations. Journal of Logic, Language and Information 14 (2):133-148.score: 24.0
    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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  25. Theodore Hailperin (2001). Potential Infinite Models and Ontologically Neutral Logic. Journal of Philosophical Logic 30 (1):79-96.score: 24.0
    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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  26. Thomas Holden (2002). Infinite Divisibility and Actual Parts in Hume’s Treatise. Hume Studies 28 (1):3-25.score: 24.0
    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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  27. Claude Gratton (1996). What is an Infinite Regress Argument? Informal Logic 18 (2).score: 24.0
    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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  28. Henry W. Johnstone (1994). Question-Begging and Infinite Regress. Argumentation 8 (3):291-293.score: 24.0
    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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  29. Jörg Brendle & Maria Losada (2003). The Cofinality of the Infinite Symmetric Group and Groupwise Density. Journal of Symbolic Logic 68 (4):1354-1361.score: 24.0
    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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  30. 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.score: 24.0
    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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  31. Catherine Legg (2008). Argument-Forms Which Turn Invalid Over Infinite Domains: Physicalism as Supertask? Contemporary Pragmatism 5 (1):1-11.score: 24.0
    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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  32. Claude Gratton (1994). Circular Definitions, Circular Explanations, and Infinite Regresses. Argumentation 8 (3):295-308.score: 24.0
    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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  33. Pierre Cartier (2012). How to Take Advantage of the Blur Between the Finite and the Infinite. Logica Universalis 6 (1-2):217-226.score: 24.0
    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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  34. Jeremy Gwiazda (2014). On Multiverses and Infinite Numbers. In Klaas Kraay (ed.), God and the Multiverse. Routledge. 162-173.score: 24.0
    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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  35. Philip Kremer (2014). Indeterminacy of Fair Infinite Lotteries. Synthese 191 (8):1757-1760.score: 24.0
    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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  36. René Woudenberg & Ronald Meester (2014). Infinite Epistemic Regresses and Internalism. Metaphilosophy 45 (2):221-231.score: 24.0
    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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  37. Ansten Mørch Klev (2009). Infinite Time Extensions of Kleene's {Mathcal{O}}. Archive for Mathematical Logic 48 (7):691-703.score: 24.0
    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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  38. Miguel S.�Nchez-Mazas (1989). Essai de Repr�Sentation Par des Nombres R�Els d'Une Analyse Infinite des Notions Individuelles Dans Une Infinit� de Mondes Possibles. Argumentation 3 (1):75-96.score: 24.0
    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 (as Leibniz pointed out) admits this sort of definition, (...)
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  39. Bernard Bolzano (1950). Paradoxes of the Infinite. London, Routledge and Paul.score: 24.0
    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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  40. Yitzhak Y. Melamed (2012). “’Christus Secundum Spiritum’: Spinoza, Jesus, and the Infinite Intellect”. In Neta Stahl (ed.), The Jewish Jesus. Routledge.score: 21.0
  41. Caleb Cohoe (2013). There Must Be A First: Why Thomas Aquinas Rejects Infinite, Essentially Ordered, Causal Series. British Journal for the History of Philosophy 21 (5):838 - 856.score: 21.0
    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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  42. Christina M. Gschwandtner (2007). The Neighbor and the Infinite: Marion and Levinas on the Encounter Between Self, Human Other, and God. [REVIEW] Continental Philosophy Review 40 (3):231-249.score: 21.0
    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 attempts (...)
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  43. Infinite Ethics, Infinite Ethics.score: 21.0
    Aggregative consequentialism and several other popular moral theories are threatened with paralysis: when coupled with some plausible assumptions, they seem to imply that it is always ethically indifferent what you do. Modern cosmology teaches that the world might well contain an infinite number of happy and sad people and other candidate value-bearing locations. Aggregative ethics implies that such a world contains an infinite amount of positive value and an infinite amount of negative value. You can affect only (...)
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  44. Robert C. Koons (1993). Faith, Probability and Infinite Passion. Faith and Philosophy 10 (2):145-160.score: 21.0
    The logical treatment of the nature of religious belief (here I will concentrate on belief in Christianity) has been distorted by the acceptance of a false dilemma. On the one hand, many (e.g., Braithwaite, Hare) have placed the significance of religious belief entirely outside the realm of intellectual cognition. According to this view, religious statements do not express factual propositions: they are not made true or false by the ways things are. Religious belief consists in a certain attitude toward the (...)
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  45. Sven Ove Hansson (2012). Finite Contractions on Infinite Belief Sets. Studia Logica 100 (5):907-920.score: 21.0
    Contractions on belief sets that have no finite representation cannot be finite in the sense that only a finite number of sentences is removed. However, such contractions can be delimited so that the actual change takes place in a logically isolated, finite-based part of the belief set. A construction that answers to this principle is introduced, and is axiomatically characterized. It turns out to coincide with specified meet contraction.
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  46. Charles Sayward (1988). Is English Infinite? Philosophical Papers 17 (2):141-151.score: 21.0
    It is argued that English is finite. By this is meant that it contains only finitely many expressions. The conclusion is reached by arguing: (1) only finitely many expressions of English are tokenable; (2) if E is an expression of English, then E is tokenable.
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  47. Ursula Coope (2012). &Quot;aristotle on the Infinite&Quot;. In Christopher Shields (ed.), Oxford Handbook of Aristotle. Oxford University Press. 267.score: 21.0
  48. Ver�Nica Becher, Santiago Figueira, Andr� Nies & Silvana Picchi (2005). Program Size Complexity for Possibly Infinite Computations. Notre Dame Journal of Formal Logic 46 (1):51-64.score: 21.0
    We define a program size complexity function as a variant of the prefix-free Kolmogorov complexity, based on Turing monotone machines performing possibly unending computations. We consider definitions of randomness and triviality for sequences in relative to the complexity. We prove that the classes of Martin-Löf random sequences and -random sequences coincide and that the -trivial sequences are exactly the recursive ones. We also study some properties of and compare it with other complexity functions. In particular, is different from , the (...)
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  49. Kenji Fukuzaki (2012). Definability of the Ring of Integers in Some Infinite Algebraic Extensions of the Rationals. Mathematical Logic Quarterly 58 (4‐5):317-332.score: 21.0
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  50. D. E. Seabold & J. D. Hamkins (2001). Infinite Time Turing Machines With Only One Tape. Mathematical Logic Quarterly 47 (2):271-287.score: 21.0
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