Results for 'infinite descent'

949 found
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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 Descent.T. Scott Dixon - 2020 - In Michael J. Raven, The Routledge Handbook of Metaphysical Grounding. New York: 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? (...)
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  3. Minds Within Minds: An Infinite Descent of Mentality in a Physical World.Christopher Devlin Brown - 2017 - Erkenntnis 82 (6):1339-1350.
    Physicalism is frequently understood as the thesis that everything depends upon a fundamental physical level. This standard formulation of physicalism has a rarely noted and arguably unacceptable consequence—it makes physicalism come out false in worlds which have no fundamental level, for instance worlds containing things which can infinitely decompose into smaller and smaller parts. If physicalism is false, it should not be for this reason. Thus far, there is only one proposed solution to this problem, and it comes from the (...)
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  4. Physicalism, Foundationalism, and Infinite Descent.Jonas Werner - 2025 - Erkenntnis 90 (2):789-794.
    This paper contributes to answering the question how physicalism can be defined for a world without fundamental physical phenomena. In a recent paper in this journal, Torin Alter, Sam Coleman, and Robert J. Howell propose a necessary condition on physicalism. They argue that physicalism is true only if there is no infinitely descending chain of mentally constituted phenomena. I argue that this alleged necessary condition faces counterexamples. An infinitely descending chain of mentally constituted phenomena is compatible with physicalism. Afterwards I (...)
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  5.  42
    Finite Arithmetic with Infinite Descent.Yvon Gauthier - 1989 - Dialectica 43 (4):329-337.
    SummaryFinite, or Fermat arithmetic, as we call it, differs from Peano arithmetic in that it does not involve the existence of an infinite set or Peano's induction postulate. Fermat's method of infinite descent takes the place of bound induction, and we show that a con‐structivist interpretation of logical connectives and quantifiers can account for the predicative finitary nature of Fermat's arithmetic. A non‐set‐theoretic arithemetical logic thus seems best suited to a constructivist‐inspired number theory.
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  6. The method of infinite descent and the method of mathematical induction.Harriet F. Montague - 1944 - Philosophy of Science 11 (3):178-185.
    The purpose of this paper may be found in the following quotation. “Whenever an argument can be made to lead to a descending infinitude of natural numbers the hypothesis upon which the argument rests becomes untenable. This method of proof is called the method of infinite descent;.... It would be interesting and valuable to compare this method with the method of mathematical induction.”.
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    Historical and Foundational Details on the Method of Infinite Descent: Every Prime Number of the Form 4 n + 1 is the Sum of Two Squares.Paolo Bussotti & Raffaele Pisano - 2020 - Foundations of Science 25 (3):671-702.
    Pierre de Fermat is known as the inventor of modern number theory. He invented–improved many methods useful in this discipline. Fermat often claimed to have proved his most difficult theorems thanks to a method of his own invention: the infinite descent. He wrote of numerous applications of this procedure. Unfortunately, he left only one almost complete demonstration and an outline of another demonstration. The outline concerns the theorem that every prime number of the form 4n + 1 is (...)
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  8. Physicalism, Infinite Decomposition, and Constitution.Torin Alter, Sam Coleman & Robert J. Howell - 2022 - Erkenntnis (4):1735-1744.
    How could physicalism be true of a world in which there are no fundamental physical phenomena? A familiar answer, due to Barbara Gail Montero and others, is that physicalism could be true of such a world if that world does not contain an infinite descent of mentality. Christopher Devlin Brown has produced a counterexample to that solution. We show how to modify the solution to accommodate Brown’s example: physicalism could be true of a world without fundamental physical phenomena (...)
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  9. An infinitely descending chain of ground without a lower bound.Jon Erling Litland - 2016 - Philosophical Studies 173 (5):1361-1369.
    Using only uncontentious principles from the logic of ground I construct an infinitely descending chain of ground without a lower bound. I then compare the construction to the constructions due to Dixon and Rabin and Rabern.
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  10. La descente infinie, l’induction transfinie et le tiers exclu.Yvon Gauthier - 2009 - Dialogue 48 (1):1.
    ABSTRACT: It is argued that the equivalence, which is usually postulated to hold between infinite descent and transfinite induction in the foundations of arithmetic uses the law of excluded middle through the use of a double negation on the infinite set of natural numbers and therefore cannot be admitted in intuitionistic logic and mathematics, and a fortiori in more radical constructivist foundational schemes. Moreover it is shown that the infinite descent used in Dedekind-Peano arithmetic does (...)
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  11.  67
    How to take advantage of the blur between the finite and the infinite.Pierre Cartier - 2012 - 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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  12. Internal and external consistency of arithmetic.Yvon Gauthier - 2001 - Logica Trianguli 5:19-41.
    What Gödel referred to as “outer” consistency is contrasted with the “inner” consistency of arithmetic from a constructivist point of view. In the settheoretic setting of Peano arithmetic, the diagonal procedure leads out of the realm of natural numbers. It is shown that Hilbert’s programme of arithmetization points rather to an “internalisation” of consistency. The programme was continued by Herbrand, Gödel and Tarski. Tarski’s method of quantifier elimination and Gödel’s Dialectica interpretation are part and parcel of Hilbert’s finitist ideal which (...)
     
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  13. Fundamentality and Ontological Minimality.Tuomas E. Tahko - 2018 - In Ricki Bliss & Graham Priest, Reality and its Structure: Essays in Fundamentality. Oxford, UK: Oxford University Press. pp. 237-253.
    In this chapter, a generic definition of fundamentality as an ontological minimality thesis is sought and its applicability examined. Most discussions of fundamentality are focused on a mereological understanding of the hierarchical structure of reality, which may be combined with an atomistic, object-oriented metaphysics. But recent work in structuralism, for instance, calls for an alternative understanding and it is not immediately clear that the conception of fundamentality at work in structuralism is commensurable with the mereological conception. However, it is proposed (...)
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  14. Normativity all the way down: from normative realism to pannormism.Einar Duenger Bohn - 2018 - Synthese 195 (9):4107-4124.
    In this paper, I provide an argument for pannormism, the view according to which there are normative properties all the way down. In particular, I argue for what I call the trickling down principle, which says that if there is a metaphysically basic normative property, then, if whatever instantiates it has a ground, that ground instantiates it as well.
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  15.  11
    Internal Logic: Foundations of Mathematics from Kronecker to Hilbert.Yvon Gauthier - 2002 - Springer Verlag.
    Internal logic is the logic of content. The content is here arithmetic and the emphasis is on a constructive logic of arithmetic (arithmetical logic). Kronecker's general arithmetic of forms (polynomials) together with Fermat's infinite descent is put to use in an internal consistency proof. The view is developed in the context of a radical arithmetization of mathematics and logic and covers the many-faceted heritage of Kronecker's work, which includes not only Hilbert, but also Frege, Cantor, Dedekind, Husserl and (...)
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  16. Fermat’s Last Theorem Proved by Induction (and Accompanied by a Philosophical Comment).Vasil Penchev - 2020 - Metaphilosophy eJournal (Elsevier: SSRN) 12 (8):1-8.
    A proof of Fermat’s last theorem is demonstrated. It is very brief, simple, elementary, and absolutely arithmetical. The necessary premises for the proof are only: the three definitive properties of the relation of equality (identity, symmetry, and transitivity), modus tollens, axiom of induction, the proof of Fermat’s last theorem in the case of n = 3 as well as the premises necessary for the formulation of the theorem itself. It involves a modification of Fermat’s approach of infinite descent. (...)
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  17.  20
    Handbook of Mathematical Induction: Theory and Applications.David S. Gunderson - 2010 - Chapman & Hall/Crc.
    Handbook of Mathematical Induction: Theory and Applications shows how to find and write proofs via mathematical induction. This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application examples from nearly every area of mathematics. In the first part of the book, the author discusses different inductive techniques, including well-ordered sets, basic mathematical induction, strong induction, double induction, infinite descent, downward induction, and several variants. He then introduces ordinals and cardinals, (...)
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  18. The Universe As We Find It. By John Heil. [REVIEW]Tuomas E. Tahko - 2013 - Mind 122 (488):1095-1098.
    Book review of 'The Universe As We Find It' (2012, OUP). By John Heil.
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  19.  15
    Five Poems.Amit Majmudar - 2019 - Arion 27 (1):105-111.
    In lieu of an abstract, here is a brief excerpt of the content:Five Poems AMIT MAJMUDAR Observing Orpheus I hear the meaning turn back in his throat like Eurydice on the way up from the darkness. Music’s meaning is its making. As for me, I am one more animal in his entourage, learning a new thirst, finding a new south. None of us knew we had this instinct in us. If deserts hide wildflowers until first rain, bright ears are blossoming (...)
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  20.  52
    Eclipsing Art: Method and Metaphysics in Coleridge's "Biographia Literaria".Tim Milnes - 1999 - Journal of the History of Ideas 60 (1):125.
    In lieu of an abstract, here is a brief excerpt of the content:Eclipsing Art: Method and Metaphysics in Coleridge’s Biographia Literaria *Tim MilnesColeridge’s PredicamentIn his self-addressed “letter” which precipitates the abrupt end to the thirteenth chapter (and with it, the first volume) of the Biographia Literaria, Coleridge likens the current state of his argument to “the fragments of the winding steps of an old ruined tower.” 1 The suggestion of intellectual ascent in this is revealing and is echoed a few (...)
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  21.  9
    One of the Trinity Has Suffered: Balthasar's Theology of Divine Suffering in Dialogue.Joshua R. Brotherton & Joshua Brotherton - 2019 - Steubenville, OH, USA: Emmaus Academic.
    "The goal of this volume is to revise Hans Urs von Balthasar's theology of divine suffering, that is, his disputed discourse on the descent of Christ into hell and its implications for the Triune God, according to a robust contemporary Catholic theology. In order to accomplish such an appropriation, I have recourse not only to twentieth-century Thomistic theology, but also to the thought of Pope Emeritus Benedict XVI and Pope St. John Paul II. I seek to engage the best (...)
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  22.  26
    The Petrification of Cleopatra in Nineteenth Century Art.Margaret Malamud & Martha Malamud - 2020 - Arion 28 (1):31-51.
    In lieu of an abstract, here is a brief excerpt of the content:The Petrification of Cleopatra in Nineteenth Century Art MARGARET MALAMUD MARTHA MALAMUD What did Cleopatra look like? Was she a Roman, a Ptolemaic Greek, an Egyptian, an African? Was she a precocious child, a devastatingly beautiful seductress, an astute practitioner of imperial politics, a murderess, a longnosed blue-stocking? [Figure 1] Cleopatra is dead, but “Cleopatra ” exists in the eye of the beholder. What other human being has been (...)
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  23.  14
    Deep Mysteries: God, Christ, and Ourselves by Aidan Nichols (review).Gerard T. Mundy - 2023 - Nova et Vetera 21 (1):386-387.
    In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Deep Mysteries: God, Christ, and Ourselves by Aidan NicholsGerard T. MundyDeep Mysteries: God, Christ, and Ourselves by Aidan Nichols, O.P. (Lanham, MD: Lexington, 2020), vii + 133 pp.Basic Catholic teaching declares that God's will must be trusted and that perfect knowledge of all that is resides in the Creator. An implication of this claim is that all of God's work within time and history—in man's linearly conception of (...)
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  24. Jewish Themes in Spinoza's Philosophy (review).Yisrael Yehoshua Melamed - 2003 - Journal of the History of Philosophy 41 (3):417-418.
    In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 41.3 (2003) 417-418 [Access article in PDF] Heidi M. Ravven and Lenn E. Goodman, editors. Jewish Themes in Spinoza's Philosophy. Albany: The State University of New York Press, 2002. Pp. ix + 290. Cloth, $78.50. Paper, $26.95.The current anthology presents an important contribution to the study of Spinoza's relation to Jewish philosophy as well as to contemporary scholarship of Spinoza's metaphysics and political (...)
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  25. Infinite Beliefs'.Infinite Regresses - 2003 - In Winfried Löffler & Weingartner Paul, Knowledge and Belief. ALWS.
     
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  26. Infinite Ethics.Infinite Ethics - unknown
    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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  27. Continuity in Fourteenth Century Theories of Alteration.Infinite Indivisible - 1982 - In Norman Kretzmann, Infinity and continuity in ancient and medieval thought. Ithaca, N.Y.: Cornell University Press. pp. 231--257.
  28. Index to Volume X.Vincent Colapietro, Being as Dialectic, Kenneth Stikkers, Dale Jacquette, Adversus Adversus Regressum Against Infinite Regress Objections, Santosh Makkuni, Moral Luck, Practical Judgment, Leo J. Penta & On Power - 1996 - Journal of Speculative Philosophy 10 (4).
     
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  29. List of Contents: Volume 13, Number 3, June 2000.Semi-Infinite Rectangular Barrier, K. Dechoum, L. de la Pena, E. Santos, A. Schulze, G. Esposito, C. Stornaiolo & P. K. Anastasovski - 2000 - Foundations of Physics 30 (10).
  30.  18
    Millian Qualitative Superiorities and Utilitarianism, Part II.Vi Infinite Superiorities - 2009 - Utilitas 21 (2):2009.
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  31. Quentin Smith.Moral Realism, Infinite Spacetime & Imply Moral Nihilism - 2003 - In Heather Dyke, Time and Ethics: Essays at the Intersection. Kluwer Academic Publishers.
     
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  32. Benardete paradoxes, patchwork principles, and the infinite past.Joseph C. Schmid - 2024 - Synthese 203 (2):51.
    Benardete paradoxes involve a beginningless set each member of which satisfies some predicate just in case no earlier member satisfies it. Such paradoxes have been wielded on behalf of arguments for the impossibility of an infinite past. These arguments often deploy patchwork principles in support of their key linking premise. Here I argue that patchwork principles fail to justify this key premise.
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  33. Utilitarianism and infinite utility.Peter Vallentyne - 1993 - Australasian Journal of Philosophy 71 (2):212 – 217.
    Traditional act utilitarianism judges an action permissible just in case it produces as much aggregate utility as any alternative. It is often supposed that utilitarianism faces a serious problem if the future is infinitely long. For in that case, actions may produce an infinite amount of utility. And if that is so for most actions, then utilitarianism, it appears, loses most of its power to discriminate among actions. For, if most actions produce an infinite amount of utility, then (...)
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  34. List of Contents: Volume 11, Number 5, October 1998.S. Fujita, D. Nguyen, E. S. Nam, Phonon-Exchange Attraction, Type I. I. Superconductivity, Wave Cooper & Infinite Well - 1999 - Foundations of Physics 29 (1).
  35. 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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  36. 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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  37. 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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  38. Correction to John D. Norton “How to build an infinite lottery machine”.John D. Norton & Alexander R. Pruss - 2018 - European Journal for Philosophy of Science 8 (1):143-144.
    An infinite lottery machine is used as a foil for testing the reach of inductive inference, since inferences concerning it require novel extensions of probability. Its use is defensible if there is some sense in which the lottery is physically possible, even if exotic physics is needed. I argue that exotic physics is needed and describe several proposals that fail and at least one that succeeds well enough.
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  39. The Kalām Cosmological Argument and the Infinite God Objection.Jacobus Erasmus & Anné Hendrik Verhoef - 2015 - Sophia 54 (4):411-427.
    In this article, we evaluate various responses to a noteworthy objection, namely, the infinite God objection to the kalām cosmological argument. As regards this objection, the proponents of the kalām argument face a dilemma—either an actual infinite cannot exist or God cannot be infinite. More precisely, this objection claims that God’s omniscience entails the existence of an actual infinite with God knowing an actually infinite number of future events or abstract objects, such as mathematical truths. (...)
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  40. Ayer was born in London to parents of continental European descent. His fa-ther, Jules, was from a Swiss Calvinist.Isaiah Berlin - 2005 - In Siobhan Chapman & Christopher Routledge, Key thinkers in linguistics and the philosophy of language. Edinburgh: Edinburgh University Press. pp. 16.
     
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  41.  81
    Tableaux for łukasiewicz infinite-valued logic.Nicola Olivetti - 2003 - Studia Logica 73 (1):81 - 111.
    In this work we propose a labelled tableau method for ukasiewicz infinite-valued logic L . The method is based on the Kripke semantics of this logic developed by Urquhart [25] and Scott [24]. On the one hand, our method falls under the general paradigm of labelled deduction [8] and it is rather close to the tableau systems for sub-structural logics proposed in [4]. On the other hand, it provides a CoNP decision procedure for L validity by reducing the check (...)
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  42.  88
    « The Allegory Of The Cave: The Necessity Of The Philosopher’s Descent ».Georgia Mouroutsou - 2011 - Plato Journal 11.
  43. The problem of infinite matter in steady-state cosmology.Richard Schlegel - 1965 - Philosophy of Science 32 (1):21-31.
    The creation-of-matter hypothesis of the Bondi-Gold-Hoyle steady-state cosmology requires that in an infinite time to which the first transfinite number may be assigned the number of atoms of matter produced would be equal to the cardinal number of the set of mathematical points in the continuum. The existence of a set of finite atoms with that cardinal number is physically unacceptable. The argument for the production of a non-denumerable set of atoms, in infinite time, is given in terms (...)
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  44.  62
    Ramsey sentences for infinite theories.Herbert E. Hendry - 1975 - Philosophy of Science 42 (1):28.
    Ramsey's device [2], for eliminating theoretical terms from a theory assumes that the theory has only finitely many axioms. Paul Berent [1], has recently suggested a modification of Ramsey's method that is designed to cover the infinite case. But, his modified method is quite unlike Ramsey's in that it involves an ascent from the original theory to a suitable metatheory. Thus, it is perhaps of some interest to note that there is an extension of Ramsey's method that covers the (...)
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  45. (1 other version)Design Inferences in an Infinite Universe.Bradley Monton - 2009 - In Oxford Studies in Philosophy of Religion, Volume 2. Oxford University Press.
    How are inferences to design affected when one makes the (plausible) assumption that the universe is spatially infinite? I will show that arguments for the existence of God based on the improbable development of life don’t go through. I will also show that the model of design inferences promulgated by William Dembski is flawed. My model for design inferences has the (desirable) consequence that there are circumstances where a seeming miracle can count as evidence for the existence of God, (...)
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  46. Legal validity and the infinite regress.Oliver Black - 1996 - Law and Philosophy 15 (4):339 - 368.
    The following four theses all have some intuitive appeal: (I) There are valid norms. (II) A norm is valid only if justified by a valid norm. (III) Justification, on the class of norms, has an irreflexive proper ancestral. (IV) There is no infinite sequence of valid norms each of which is justified by its successor. However, at least one must be false, for (I)--(III) together entail the denial of (IV). There is thus a conflict between intuition and logical possibility. (...)
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  47. (1 other version)Aristotle's Theory of the Infinite.Abraham Edel - 1935 - Revue de Métaphysique et de Morale 42 (4):16-16.
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  48.  29
    The representation theorem for the algebras determined by the fragments of infinite-valued logic of Lukasiewicz.Barbara Wozniakowska - 1978 - Bulletin of the Section of Logic 7 (4):176-178.
    In this paper we shall give a characterization of D-algebras in terms of lattice ordered abelian groups. To make this paper self-contained we shall recall some notations from [4]. The symbols !; ^; _; serve as implication, conjunction, disjunction, and negation, respectively. By D we mean a set of connectives from the list above containing the implication connective !. By a D-formula we mean a formula built up in a usual way from an innite set of the propositional variables and (...)
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  49. 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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  50.  96
    Is life of infinite value?Dena S. Davis - 2001 - Kennedy Institute of Ethics Journal 11 (3):239-246.
    : It is possible and necessary to compare stretches of human life with other goods, such as the good of conserving resources for others. A minute of human life is not of infinite value; all else being equal, a minute of life is less valuable than 10 years of the same life. Nevertheless, this ability to evaluate human life does not necessarily lead to total commodification of human life.
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