Results for 'infinity'

372 found
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  1. Aristotelian Infinity.John Bowin - 2007 - Oxford Studies in Ancient Philosophy 32:233-250.
    Bowin begins with an apparent paradox about Aristotelian infinity: Aristotle clearly says that infinity exists only potentially and not actually. However, Aristotle appears to say two different things about the nature of that potential existence. On the one hand, he seems to say that the potentiality is like that of a process that might occur but isn't right now. Aristotle uses the Olympics as an example: they might be occurring, but they aren't just now. On the other hand, (...)
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  2. Choice, Infinity, and Negation: Both Set-Theory and Quantum-Information Viewpoints to Negation.Vasil Penchev - 2020 - Logic and Philosophy of Mathematics eJournal 12 (14):1-3.
    The concepts of choice, negation, and infinity are considered jointly. The link is the quantity of information interpreted as the quantity of choices measured in units of elementary choice: a bit is an elementary choice between two equally probable alternatives. “Negation” supposes a choice between it and confirmation. Thus quantity of information can be also interpreted as quantity of negations. The disjunctive choice between confirmation and negation as to infinity can be chosen or not in turn: This corresponds (...)
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  3. The Infinity from Nothing paradox and the Immovable Object meets the Irresistible Force.Nicholas Shackel - 2018 - European Journal for Philosophy of Science 8 (3):417-433.
    In this paper I present a novel supertask in a Newtonian universe that destroys and creates infinite masses and energies, showing thereby that we can have infinite indeterminism. Previous supertasks have managed only to destroy or create finite masses and energies, thereby giving cases of only finite indeterminism. In the Nothing from Infinity paradox we will see an infinitude of finite masses and an infinitude of energy disappear entirely, and do so despite the conservation of energy in all collisions. (...)
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  4. Numerical infinities applied for studying Riemann series theorem and Ramanujan summation.Yaroslav Sergeyev - 2018 - In AIP Conference Proceedings 1978. AIP. pp. 020004.
    A computational methodology called Grossone Infinity Computing introduced with the intention to allow one to work with infinities and infinitesimals numerically has been applied recently to a number of problems in numerical mathematics (optimization, numerical differentiation, numerical algorithms for solving ODEs, etc.). The possibility to use a specially developed computational device called the Infinity Computer (patented in USA and EU) for working with infinite and infinitesimal numbers numerically gives an additional advantage to this approach in comparison with traditional (...)
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  5. Aristotle's Actual Infinities.Jacob Rosen - 2021 - Oxford Studies in Ancient Philosophy 59.
    Aristotle is said to have held that any kind of actual infinity is impossible. I argue that he was a finitist (or "potentialist") about _magnitude_, but not about _plurality_. He did not deny that there are, or can be, infinitely many things in actuality. If this is right, then it has implications for Aristotle's views about the metaphysics of parts and points.
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  6. Absolute Infinity, Knowledge, and Divinity in the Thought of Cusanus and Cantor (ABSTRACT ONLY).Anne Newstead - 2024 - In Mirosław Szatkowski (ed.), Ontology of Divinity. De Gruyter. pp. 561-580.
    Renaissance philosopher, mathematician, and theologian Nicholas of Cusa (1401-1464) said that there is no proportion between the finite mind and the infinite. He is fond of saying reason cannot fully comprehend the infinite. That our best hope for attaining a vision and understanding of infinite things is by mathematics and by the use of contemplating symbols, which help us grasp "the absolute infinite". By the late 19th century, there is a decisive intervention in mathematics and its philosophy: the philosophical mathematician (...)
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  7. An infinity of super-Belnap logics.Umberto Rivieccio - 2012 - Journal of Applied Non-Classical Logics 22 (4):319-335.
    We look at extensions (i.e., stronger logics in the same language) of the Belnap–Dunn four-valued logic. We prove the existence of a countable chain of logics that extend the Belnap–Dunn and do not coincide with any of the known extensions (Kleene’s logics, Priest’s logic of paradox). We characterise the reduced algebraic models of these new logics and prove a completeness result for the first and last element of the chain stating that both logics are determined by a single finite logical (...)
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  8. Infinity in Pascal's Wager.Graham Oppy - 2018 - In Paul F. A. Bartha & Lawrence Pasternack (eds.), Pascal’s Wager. New York: Cambridge University Press. pp. 260-77.
    Bartha (2012) conjectures that, if we meet all of the other objections to Pascal’s wager, then the many-Gods objection is already met. Moreover, he shows that, if all other objections to Pascal’s wager are already met, then, in a choice between a Jealous God, an Indifferent God, a Very Nice God, a Very Perverse God, the full range of Nice Gods, the full range of Perverse Gods, and no God, you should wager on the Jealous God. I argue that his (...)
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  9. Infinity and Metaphysics.Daniel Nolan - 2009 - In Robin Le Poidevin, Simons Peter, McGonigal Andrew & Ross P. Cameron (eds.), The Routledge Companion to Metaphysics. New York: Routledge. pp. 430-439.
    This introduction to the roles infinity plays in metaphysics includes discussion of the nature of infinity itself; infinite space and time, both in extent and in divisibility; infinite regresses; and a list of some other topics in metaphysics where infinity plays a significant role.
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  10. Actualised Infinity: Before-Effect and Nullify-Effect.Steffen Borge - 2003 - Disputatio 1 (14):1 - 17.
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  11. Numerical infinities and infinitesimals: Methodology, applications, and repercussions on two Hilbert problems.Yaroslav Sergeyev - 2017 - EMS Surveys in Mathematical Sciences 4 (2):219–320.
    In this survey, a recent computational methodology paying a special attention to the separation of mathematical objects from numeral systems involved in their representation is described. It has been introduced with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework in all the situations requiring these notions. The methodology does not contradict Cantor’s and non-standard analysis views and is based on the Euclid’s Common Notion no. 5 “The whole is greater than the (...)
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  12. Infinity and givenness: Kant on the intuitive origin of spatial representation.Daniel Smyth - 2014 - Canadian Journal of Philosophy 44 (5-6):551-579.
    I advance a novel interpretation of Kant's argument that our original representation of space must be intuitive, according to which the intuitive status of spatial representation is secured by its infinitary structure. I defend a conception of intuitive representation as what must be given to the mind in order to be thought at all. Discursive representation, as modelled on the specific division of a highest genus into species, cannot account for infinite complexity. Because we represent space as infinitely complex, the (...)
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  13. Immortality, Infinity and the limitations of God.Alexey Prokofyev - manuscript
    I tried to describe Infinity as a major natural conundrum known to man. The booklet also contains answers to some eternal questions, such as the meaning of life, faith, etc. I am especially proud of my Morality section.
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  14. Benign Infinity.Matthias Steup - 2019 - In Cherie Braden, Rodrigo Borges & Branden Fitelson (eds.), Themes From Klein. Springer Verlag. pp. 235-57.
    According to infinitism, all justification comes from an infinite series of reasons. Peter Klein defends infinitism as the correct solution to the regress problem by rejecting two alternative solutions: foundationalism and coherentism. I focus on Klein's argument against foundationalism, which relies on the premise that there is no justification without meta-justification. This premise is incompatible with dogmatic foundationalism as defended by Michael Huemer and Time Pryor. It does not, however, conflict with non-dogmatic foundationalism. Whereas dogmatic foundationalism rejects the need for (...)
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  15. Cantorian Infinity and Philosophical Concepts of God.Joanna Van der Veen & Leon Horsten - 2013 - European Journal for Philosophy of Religion 5 (3):117--138.
    It is often alleged that Cantor’s views about how the set theoretic universe as a whole should be considered are fundamentally unclear. In this article we argue that Cantor’s views on this subject, at least up until around 1896, are relatively clear, coherent, and interesting. We then go on to argue that Cantor’s views about the set theoretic universe as a whole have implications for theology that have hitherto not been sufficiently recognised. However, the theological implications in question, at least (...)
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  16.  34
    An infinity of super-Belnap logics.Umberto Rivieccio - 2012 - Journal of Applied Non-Classical Logics 22 (4):319-335.
    We look at extensions (i.e., stronger logics in the same language) of the Belnap–Dunn four-valued logic. We prove the existence of a countable chain of logics that extend the Belnap–Dunn and do not coincide with any of the known extensions (Kleene’s logics, Priest’s logic of paradox). We characterise the reduced algebraic models of these new log- ics and prove a completeness result for the first and last element of the chain stating that both logics are determined by a single finite (...)
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  17. Infinity and the Sublime.Karin Verelst - 2013 - Journal of Interdisciplinary History of Ideas 2 (4):1-27.
    In their recent work, L. Graham and J.-M. Kantor discuss a remarkable connection between diverging conceptions of the mathematical infinite in Russia and France at the beginning of the twentieth century and the religious convictions of their respective authors. They expand much more on the Russian side of the cultural equation they propose; I do believe, however, that the French (or rather ‘West European’) side is more complex than it seems, and that digging deeper into it is worthwhile. In this (...)
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  18. Infinity and the past.Quentin Smith - 1987 - Philosophy of Science 54 (1):63-75.
    infinite, and offer several arguments in sup port of this thesis. I believe their arguments are unsuccessful and aim to refute six of them in the six sections of the paper. One of my main criticisms concerns their supposition that an infinite series of past events must contain some events separated from the present event by an infinite number of intermediate events, and consequently that from one of these infinitely distant past events the present could never have been reached. I (...)
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  19. Hohfeldian Infinities: Why Not to Worry.Visa A. J. Kurki - 2017 - Res Publica 23 (1):137-146.
    Hillel Steiner has recently attacked the notion of inalienable rights, basing some of his arguments on the Hohfeldian analysis to show that infinite arrays of legal positions would not be associated with any inalienable rights. This essay addresses the nature of the Hohfeldian infinity: the main argument is that what Steiner claims to be an infinite regress is actually a wholly unproblematic form of infinite recursion. First, the nature of the Hohfeldian recursion is demonstrated. It is shown that infinite (...)
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  20. Conceptions of infinity and set in Lorenzen’s operationist system.Carolin Antos - forthcoming - In Logic, Epistemology and the Unity of Science. Springer.
    In the late 1940s and early 1950s Lorenzen developed his operative logic and mathematics, a form of constructive mathematics. Nowadays this is mostly seen as the precursor to the more well-known dialogical logic and one could assumed that the same philosophical motivations were present in both works. However we want to show that this is not always the case. In particular, we claim, that Lorenzen’s well-known rejection of the actual infinite as stated in Lorenzen (1957) was not a major motivation (...)
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  21. Two Strategies to Infinity: Completeness and Incompleteness. The Completeness of Quantum Mechanics.Vasil Penchev - 2020 - High Performance Computing eJournal 12 (11):1-8.
    Two strategies to infinity are equally relevant for it is as universal and thus complete as open and thus incomplete. Quantum mechanics is forced to introduce infinity implicitly by Hilbert space, on which is founded its formalism. One can demonstrate that essential properties of quantum information, entanglement, and quantum computer originate directly from infinity once it is involved in quantum mechanics. Thus, thеse phenomena can be elucidated as both complete and incomplete, after which choice is the border (...)
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  22. "Infinity, Knowledge, and Divinity in the Thought of Cusanus and Cantor" (Manuscript draft of first page of forthcoming book chapter ).Anne Newstead (ed.) - forthcoming - Berlin: De Gruyter.
    Renaissance philosopher, mathematician, and theologian Nicholas of Cusa (1401-1464) said that there is no proportion between the finite mind and the infinite. He is fond of saying reason cannot fully comprehend the infinite. That our best hope for attaining a vision and understanding of infinite things is by mathematics and by the use of contemplating symbols, which help us grasp "the absolute infinite". By the late 19th century, there is a decisive intervention in mathematics and its philosophy: the philosophical mathematician (...)
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  23.  78
    INFINITY LIMITED.James Sirois - 2024 - Online: Self-Publishing.
    (1st draft for review) -/- WARNING: -/- Reading this book comes with certain dangers to be mindful of; Please consider the following suggestions to avoid them: -/- 1: Do not try to perceive infinity; Any kind of success here leads to psychosis. 2: Do not try to resolve the paradoxes; To understand the greater truth of this book, paradoxes must be accepted as true. 3: Do not read this book if your faith is unstable and having it challenged could (...)
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  24. The Absurdity of Infinity and The Beginning of The Universe.Atikur Rahman - manuscript
    One of the common claims of the eternalists is that the "actual" infinite is possible and the universe is eternal. They are trying to refute the Kalam argument. What I wanted to show in this paper is that the "actual" infinite is impossible for logical reasons, and I have shown further that infinity has an effect and application over time, and that there is no way to deny the beginning of the universe for existence. The paper points out the (...)
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  25. Descartes on the Infinity of Space vs. Time.Geoffrey Gorham - 2018 - In Ohad Nachtomy & Reed Winegar (eds.), Infinity in Early Modern Philosophy. Berlin: Brill. pp. 45-61.
    In two rarely discussed passages – from unpublished notes on the Principles of Philosophy and a 1647 letter to Chanut – Descartes argues that the question of the infinite extension of space is importantly different from the infinity of time. In both passages, he is anxious to block the application of his well-known argument for the indefinite extension of space to time, in order to avoid the theologically problematic implication that the world has no beginning. Descartes concedes that we (...)
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  26. Arguing about Infinity: The meaning (and use) of infinity and zero.Paul Mayer - manuscript
    This work deals with problems involving infinities and infinitesimals. It explores the ideas behind zero, its relationship to ontological nothingness, finititude (such as finite numbers and quantities), and the infinite. The idea of infinity and zero are closely related, despite what many perceive as an intuitive inverse relationship. The symbol 0 generally refers to nothingness, whereas the symbol infinity refers to ``so much'' that it cannot be quantified or captured. The notion of finititude rests somewhere between complete nothingness (...)
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  27. To Infinity and Beyond?Trevor Stammers - 2019 - The New Bioethics 25 (4):293-294.
    Volume 25, Issue 4, December 2019, Page 293-294.
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  28. The Nothing from Infinity paradox versus Plenitudinous Indeterminism.Nicholas Shackel - 2022 - European Journal for Philosophy of Science 12 (online early):1-14.
    The Nothing from Infinity paradox arises when the combination of two infinitudes of point particles meet in a supertask and disappear. Corral-Villate claims that my arguments for disappearance fail and concedes that this failure also produces an extreme kind of indeterminism, which I have called plenitudinous. So my supertask at least poses a dilemma of extreme indeterminism within Newtonian point particle mechanics. Plenitudinous indeterminism might be trivial, although easy attempts to prove it so seem to fail in the face (...)
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  29. Infiniti quotidiani.Antonio Chiocchi - 2018 - Biella, Italy: Zigzagando.
    Un'esplorazione tra la storia scritta e la storia dei senza storia, alla ricerca di elementi che possano disfare le trame e le dialettiche del comando/assenso.
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  30. Infiniti quotidiani. Disfare la trama.Antonio Chiocchi - 2018 - Biella, Italia: Zigzagando.
    Un'esplorazione tra la storia scritta e la storia dei senza storia, alla ricerca di elementi che possano disfare le trame e le dialettiche del comando/assenso.
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  31. Infinity and the Problem of Evil.John Leslie - 2019 - European Journal for Philosophy of Religion 11 (2):111-117.
    God seemingly had a duty to create minds each of infinite worth through possessing God-like knowledge. People might object that God’s own infinite worth was all that was needed, or that no mind that God created could have truly infinite worth; however, such objections fail. Yet this does not generate an unsolvable Problem of Evil. We could exist inside an infinite mind that was one among endlessly many, perhaps all created by Platonic Necessity. “God” might be our name for this (...)
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  32. Dispositions, Rule-Following, and Infinity.Robert Allen - manuscript
    The going-on problem (GOP) is the central concern of Wittgenstein's later philosophy. It informs not only his epistemology and philosophy of mind, but also his views on mathematics, universals, and religion. In section I, I frame this issue as a matter of accounting for intentionality. Here I follow Saul Kripke's lead. My departure therefrom follows: first, a criticism of Wittgenstein's “straight” conventionalism and, secondly, a defense of a solution Kripke rejects. I proceed under the assumption, borne out in the end, (...)
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  33. Mathematical Infinity, Its Inventors, Discoverers, Detractors, Defenders, Masters, Victims, Users, and Spectators.Edward G. Belaga - manuscript
    "The definitive clarification of the nature of the infinite has become necessary, not merely for the special interests of the individual sciences, but rather for the honour of the human understanding itself. The infinite has always stirred the emotions of mankind more deeply than any other question; the infinite has stimulated and fertilized reason as few other ideas have ; but also the infinite, more than other notion, is in need of clarification." (David Hilbert 1925).
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  34. Science, Religion, and Infinity.Graham Oppy - 2012 - In J. B. Stump & Alan G. Padgett (eds.), The Blackwell Companion to Science and Christianity. Chichester, UK: Wiley. pp. 430-440.
    This chapter contains sections titled: * Brief History * How We Talk * Science and Infinity * Religion and Infinity * Concluding Remarks * Notes * References * Further Reading.
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  35. Rules to Infinity: The Normative Role of Mathematics in Scientific Explanation.Mark Povich - 2024 - Oxford University Press USA.
    [EDIT: This book will be published open access. Check back around April 2024 to access the entire book.] One central aim of science is to provide explanations of natural phenomena. What role(s) does mathematics play in achieving this aim? How does mathematics contribute to the explanatory power of science? Rules to Infinity defends the thesis, common though perhaps inchoate among many members of the Vienna Circle, that mathematics contributes to the explanatory power of science by expressing conceptual rules, rules (...)
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  36. Dark Imaginarium: Infinity-Curiosity & Dark Consciousness in P-adic Time.Shanna Dobson - manuscript
    We investigate the idea of sleep as the protostate, and posit the idea of dark consciousness where dark is a 2-fold hybrid. We model dark consciousness as a 2-topos in p-adic time, and outline perfectoid and diamond-like versions. We then introduce and illustrate implications of Dark Imaginarium, which is a higher order Curiosity Artificial Intelligence, an Infinity-Curiosity Type, that thinks in infinity categories.
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  37. God and Infinity.Raghavendra Bhat - manuscript
    This article tries to come up with justifications to God and Infinity based on the existence and non-existence of each other.
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  38. Mathematical Platonism and the Nature of Infinity.Gilbert B. Côté - 2013 - Open Journal of Philosophy 3 (3):372-375.
    An analysis of the counter-intuitive properties of infinity as understood differently in mathematics, classical physics and quantum physics allows the consideration of various paradoxes under a new light (e.g. Zeno’s dichotomy, Torricelli’s trumpet, and the weirdness of quantum physics). It provides strong support for the reality of abstractness and mathematical Platonism, and a plausible reason why there is something rather than nothing in the concrete universe. The conclusions are far reaching for science and philosophy.
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  39. Cantor on Infinity in Nature, Number, and the Divine Mind.Anne Newstead - 2009 - American Catholic Philosophical Quarterly 83 (4):533-553.
    The mathematician Georg Cantor strongly believed in the existence of actually infinite numbers and sets. Cantor’s “actualism” went against the Aristotelian tradition in metaphysics and mathematics. Under the pressures to defend his theory, his metaphysics changed from Spinozistic monism to Leibnizian voluntarist dualism. The factor motivating this change was two-fold: the desire to avoid antinomies associated with the notion of a universal collection and the desire to avoid the heresy of necessitarian pantheism. We document the changes in Cantor’s thought with (...)
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  40. The Idea of Infinity in its Physical and Spiritual Meanings.Graham Nicholson - manuscript
    Abstract -/- The concept of infinity is of ancient origins and has puzzled deep thinkers ever since up to the present day. Infinity remains somewhat of a mystery in a physical world in which our comprehension is largely framed around the concept of boundaries. This is partly because we live in a physical world that is governed by certain dimensions or limits – width, breadth, depth, mass, space, age and time. To our ordinary understanding, it is a seemingly (...)
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  41. In search of $$\aleph _{0}$$ ℵ 0 : how infinity can be created.Markus Pantsar - 2015 - Synthese 192 (8):2489-2511.
    In this paper I develop a philosophical account of actual mathematical infinity that does not demand ontologically or epistemologically problematic assumptions. The account is based on a simple metaphor in which we think of indefinitely continuing processes as defining objects. It is shown that such a metaphor is valid in terms of mathematical practice, as well as in line with empirical data on arithmetical cognition.
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  42. The End of Epicurean Infinity: Critical Reflections on the Epicurean Infinite Universe.Frederik Bakker - 2018 - In Carla Palmerino, Delphine Bellis & Frederik Bakker (eds.), Space, Imagination and the Cosmos From Antiquity to the Early Modern Period. Cham: Springer Verlag. pp. 41-67.
    In contrast to other ancient philosophers, Epicurus and his followers famously maintained the infinity of matter, and consequently of worlds. This was inferred from the infinity of space, because they believed that a limited amount of matter would inevitably be scattered through infinite space, and hence be unable to meet and form stable compounds. By contrast, the Stoics claimed that there was only a finite amount of matter in infinite space, which stayed together because of a general centripetal (...)
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  43. Aristotelian Potential Infinity.Anne Newstead - manuscript
    Online philosophy seminar notes, for virtual conference on the Aristotelian philosophy of mathematics, hosted by University of Geneva (organiser Ryan Miller), June 15, 2023.
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  44. Some paradoxes of infinity revisited.Yaroslav Sergeyev - 2022 - Mediterranian Journal of Mathematics 19:143.
    In this article, some classical paradoxes of infinity such as Galileo’s paradox, Hilbert’s paradox of the Grand Hotel, Thomson’s lamp paradox, and the rectangle paradox of Torricelli are considered. In addition, three paradoxes regarding divergent series and a new paradox dealing with multiplication of elements of an infinite set are also described. It is shown that the surprising counting system of an Amazonian tribe, Pirah ̃a, working with only three numerals (one, two, many) can help us to change our (...)
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  45. Life and Infinity.NuyGnues Eel - 2014 - Dissertation,
    Can life be visually represented as a circle? Hegel states that true infinity, when visualized, takes the shape of a circle. The dissertation begins with a hypothesis, "does the progression to the true infinite reflect the notion of life itself?" Then, Hegel's notion of infinity is expanded and applied to the notion of life. This work is trying to explain human evolution and life itself.
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  46. Formalization and infinity.André Porto - 2008 - Manuscrito 31 (1):25-43.
    This article discusses some of Chateaubriand’s views on the connections between the ideas of formalization and infinity, as presented in chapters 19 and 20 of Logical Forms. We basically agree with his criticisms of the standard construal of these connections, a view we named “formal proofs as ultimate provings”, but we suggest an alternative way of picturing that connection based on some ideas of the late Wittgenstein.
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  47. Egoism, Labour, and Possession: A reading of “Interiority and Economy,” Section II of Lévinas' Totality of Infinity.Jacob Blumenfeld - 2014 - Journal of the British Society for Phenomenology 45 (2):107-117.
    Lévinas is the philosopher of the absolutely Other, the thinker of the primacy of the ethical relation, the poet of the face. Against the formalism of Kantian subjectivity, the totality of the Hegelian system, the monism of Husserlian phenomenology and the instrumentalism of Heideggerian ontology, Lévinas develops a phenomenological account of the ethical relation grounded in the idea of infinity, an idea which is concretely produced in the experience with the absolutely other, particularly, in their face. The face of (...)
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  48.  80
    Inconsistency of ℕ and the question of infinity.Enrico Pier Giorgio Cadeddu - manuscript
    In the article ”Inconsistency of N from a not-finitist point of view” we have shown the inconsistency of N, going through a denial. Here we delete this indirect step and essentially repeat the same proof. Contextually we find a contradiction about natural number definition. Then we discuss around the rejection of infinity.
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  49. The axiom of infinity.Bertrand Russell - 1903 - Hibbert Journal 2:809-812.
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  50. Independence of the Grossone-Based Infinity Methodology from Non-standard Analysis and Comments upon Logical Fallacies in Some Texts Asserting the Opposite.Yaroslav D. Sergeyev - 2019 - Foundations of Science 24 (1):153-170.
    This paper considers non-standard analysis and a recently introduced computational methodology based on the notion of ①. The latter approach was developed with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework and in all the situations requiring these notions. Non-standard analysis is a classical purely symbolic technique that works with ultrafilters, external and internal sets, standard and non-standard numbers, etc. In its turn, the ①-based methodology does not use any of these (...)
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