Results for 'Infinity'

972 found
Order:
See also
  1. Approaching Infinity.Michael Huemer - 2016 - New York: Palgrave Macmillan.
    Approaching Infinity addresses seventeen paradoxes of the infinite, most of which have no generally accepted solutions. The book addresses these paradoxes using a new theory of infinity, which entails that an infinite series is uncompletable when it requires something to possess an infinite intensive magnitude. Along the way, the author addresses the nature of numbers, sets, geometric points, and related matters. The book addresses the need for a theory of infinity, and reviews both old and new theories (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   16 citations  
  2.  19
    Introduction: Infinity in Early Modern Philosophy.Ohad Nachtomy & Reed Winegar - 2018 - In Igor Agostini, Richard T. W. Arthur, Geoffrey Gorham, Paul Guyer, Mogens Lærke, Yitzhak Y. Melamed, Ohad Nachtomy, Sanja Särman, Anat Schechtman, Noa Shein & Reed Winegar, Infinity in Early Modern Philosophy. Cham: Springer Verlag. pp. 1-8.
    In his Pensées, Blaise Pascal gives vivid voice to both the wonder and anxiety that many early modern thinkers felt towards infinity. Contemplating our place between the infinite expanse of space and the infinite divisibility of matter, Pascal writes.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  3. Infinity in ontology and mind.Nino B. Cocchiarella - 2008 - Axiomathes 18 (1):1-24.
    Two fundamental categories of any ontology are the category of objects and the category of universals. We discuss the question whether either of these categories can be infinite or not. In the category of objects, the subcategory of physical objects is examined within the context of different cosmological theories regarding the different kinds of fundamental objects in the universe. Abstract objects are discussed in terms of sets and the intensional objects of conceptual realism. The category of universals is discussed in (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  4.  7
    Infinity, what is it?Marnie Luce - 1969 - Minneapolis,: Lerner Publications Co.. Edited by A. B. Lerner & Charles Stenson.
    Explains and gives examples of the mathematical concept of infinity.
    Direct download  
     
    Export citation  
     
    Bookmark  
  5.  85
    Infinity, Causation, and Paradox.Alexander R. Pruss - 2018 - Oxford, England: Oxford University Press.
    Alexander R. Pruss examines a large family of paradoxes to do with infinity - ranging from deterministic supertasks to infinite lotteries and decision theory. Having identified their common structure, Pruss considers at length how these paradoxes can be resolved by embracing causal finitism.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   15 citations  
  6.  55
    Infinity in Early Modern Philosophy.Nachtomy Ohad & Winegar Reed (eds.) - 2018 - Dordrecht, Netherlands: Springer.
    This volume contains essays that examine infinity in early modern philosophy. The essays not only consider the ways that key figures viewed the concept. They also detail how these different beliefs about infinity influenced major philosophical systems throughout the era. These domains include mathematics, metaphysics, epistemology, ethics, science, and theology. Coverage begins with an introduction that outlines the overall importance of infinity to early modern philosophy. It then moves from a general background of infinity up through (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  7.  45
    Infinity in ethics (2nd edition).Peter Vallentyne & Daniel Rubio - 2019 - Routledge Encyclopedia of Philosophy.
    Puzzles can arise in value theory and deontic (permissibility) theory when infinity is involved. These puzzles can arise for ethics, for prudence, or for any normative perspective. For the sake of simplicity, we focus on the ethical versions of these problems. We start by addressing problems that can arise in determining what is permissible, either in a given choice situation when there are an infinite number of options or in infinite sequence of choice situations, each with only finitely many (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  8. Absolute Infinity, Knowledge, and Divinity in the Thought of Cusanus and Cantor (ABSTRACT ONLY).Anne Newstead - 2024 - In Mirosław Szatkowski, Ontology of Divinity. Boston: 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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  9.  93
    (1 other version)Infinity and the mind: the science and philosophy of the infinite.Rudy von Bitter Rucker - 1982 - Princeton, N.J.: Princeton University Press.
    In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Here Rucker acquaints us with Gödel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpretation of quantum mechanics in which billions of parallel worlds are produced every microsecond. It is in the realm of (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   81 citations  
  10. Three Infinities in Early Modern Philosophy.Anat Schechtman - 2019 - Mind 128 (512):1117-1147.
    Many historical and philosophical studies treat infinity as an exclusively quantitative notion, whose proper domain of application is mathematics and physics. The main aim of this paper is to disentangle, by critically examining, three notions of infinity in the early modern period, and to argue that one—but only one—of them is quantitative. One of these non-quantitative notions concerns being or reality, while the other concerns a particular iterative property of an aggregate. These three notions will emerge through examination (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  11.  29
    Infinity.Pablo Bernasconi - 2021 - Oklahoma City & Greensboro: Penny Candy Books.
    What is infinity? It's reading the last line of a book and imagining the rest. No, wait, it's the instruction manual for the machine that operates the sun and the stars. In unexpected observations, captivating images, and even some equations, celebrated Argentinian author-illustrator Pablo Bernasconi, finalist for the 2018 Hans Christian Andersen Award, offers up verses about what infinity could mean to all of us. Winner of the Grand Prize from the Asociación de Literatura Infantil y Juvenil de (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  12.  14
    Badiou, infinity, and subjectivity: reading Hegel and Lacan after Badiou.Reza Naderi - 2024 - Lanham: Lexington Books.
    This book focuses on the three main categories of Badiou's philosophy-being, truth, and subject- which are elaborated according to three encounters: structure, real, and mathematical infinity. It articulates an underlying theory, "discipline," constituted based on these encounters, which reveals the inner logic of Badiou's method.
    Direct download  
     
    Export citation  
     
    Bookmark  
  13. 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. (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  14.  28
    Abstraction and Infinity.Paolo Mancosu - 2016 - Oxford, England: Oxford University Press.
    Paolo Mancosu provides an original investigation of historical and systematic aspects of the notions of abstraction and infinity and their interaction. A familiar way of introducing concepts in mathematics rests on so-called definitions by abstraction. An example of this is Hume's Principle, which introduces the concept of number by stating that two concepts have the same number if and only if the objects falling under each one of them can be put in one-one correspondence. This principle is at the (...)
    No categories
  15.  17
    Infinity: the quest to think the unthinkable.Brian Clegg - 2003 - [Berkeley, Calif.]: Publishers Group West.
    It amazes children, as they try to count themselves out of numbers, only to discover one day that the hundreds, thousands, and zillions go on forever—to something like infinity. And anyone who has advanced beyond the bounds of basic mathematics has soon marveled at that drunken number eight lying on its side in the pages of their work. Infinity fascinates; it takes the mind beyond its everyday concerns—indeed, beyond everything—to something always more. Infinity makes even the infinite (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  16. Actual and Potential Infinity.Øystein Linnebo & Stewart Shapiro - 2017 - Noûs 53 (1):160-191.
    The notion of potential infinity dominated in mathematical thinking about infinity from Aristotle until Cantor. The coherence and philosophical importance of the notion are defended. Particular attention is paid to the question of whether potential infinity is compatible with classical logic or requires a weaker logic, perhaps intuitionistic.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   31 citations  
  17.  25
    Infinity: A Very Short Introduction.Ian Stewart - 2017 - Oxford, United Kingdom: Oxford University Press UK.
    Infinity is an intriguing topic, with connections to religion, philosophy, metaphysics, logic, and physics as well as mathematics. Its history goes back to ancient times, with especially important contributions from Euclid, Aristotle, Eudoxus, and Archimedes. The infinitely large is intimately related to the infinitely small. Cosmologists consider sweeping questions about whether space and time are infinite. Philosophers and mathematicians ranging from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals. Many vital areas of mathematics rest upon (...)
    Direct download  
     
    Export citation  
     
    Bookmark   2 citations  
  18. 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, (...)
    Direct download  
     
    Export citation  
     
    Bookmark   7 citations  
  19.  11
    Infinity and Me.Russell Marcus - 2024 - Infinity Essays.
    Reminiscence of the author's education in infinity and how it turned him toward philosophy.
    Direct download  
     
    Export citation  
     
    Bookmark  
  20.  66
    Divine Infinity in Thomas Aquinas: I. Philosophico‐Theological Background.Robert M. Burns - 1998 - Heythrop Journal 39 (1):57-69.
    A reassessment of Aquinas’s doctrine of divine infinity, particularly in the light of the previous history of the concept within Western philosophy and theology. From the critical perspective provided by this history the central place which has been claimed for it in Aquinas’s thinking is questioned, as are also its originality and coherence. The notion that the doctrine of divine infinity was introduced to Western thought by Judaeo‐Christianity is rejected; from Anaximander onwards it had been a central concept (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  21. Infinity and Metaphysics.Daniel Nolan - 2009 - In Robin Le Poidevin, Simons Peter, McGonigal Andrew & Ross P. Cameron, 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.
    Direct download  
     
    Export citation  
     
    Bookmark  
  22. Philosophical Perspectives on Infinity.Graham Robert Oppy - 2006 - New York: Cambridge University Press.
    This book is an exploration of philosophical questions about infinity. Graham Oppy examines how the infinite lurks everywhere, both in science and in our ordinary thoughts about the world. He also analyses the many puzzles and paradoxes that follow in the train of the infinite. Even simple notions, such as counting, adding and maximising present serious difficulties. Other topics examined include the nature of space and time, infinities in physical science, infinities in theories of probability and decision, the nature (...)
    Direct download  
     
    Export citation  
     
    Bookmark   37 citations  
  23. Infinity and the foundations of linguistics.Ryan M. Nefdt - 2019 - Synthese 196 (5):1671-1711.
    The concept of linguistic infinity has had a central role to play in foundational debates within theoretical linguistics since its more formal inception in the mid-twentieth century. The conceptualist tradition, marshalled in by Chomsky and others, holds that infinity is a core explanandum and a link to the formal sciences. Realism/Platonism takes this further to argue that linguistics is in fact a formal science with an abstract ontology. In this paper, I argue that a central misconstrual of formal (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  24.  4
    Broad Infinity and Generation Principles.Paul Blain Levy - 2025 - Notre Dame Journal of Formal Logic 66 (1):79-141.
    We introduce Broad Infinity, a new set-theoretic axiom scheme based on the slogan “Every time we construct a new element, we gain a new arity.” It says that three-dimensional trees whose growth is controlled by a specified class function form a set. Such trees are called broad numbers. Assuming AC (the axiom of choice) or at least the weak version known as WISC (weakly initial set of covers), we show that Broad Infinity is equivalent to Mahlo’s principle, which (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  25.  43
    Infinity and continuum in the alternative set theory.Kateřina Trlifajová - 2021 - European Journal for Philosophy of Science 12 (1):1-23.
    Alternative set theory was created by the Czech mathematician Petr Vopěnka in 1979 as an alternative to Cantor’s set theory. Vopěnka criticised Cantor’s approach for its loss of correspondence with the real world. Alternative set theory can be partially axiomatised and regarded as a nonstandard theory of natural numbers. However, its intention is much wider. It attempts to retain a correspondence between mathematical notions and phenomena of the natural world. Through infinity, Vopěnka grasps the phenomena of vagueness. Infinite sets (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  26. Infinity: new research frontiers.Michał Heller & W. H. Woodin (eds.) - 2011 - New York: Cambridge University Press.
    'The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite.' David Hilbert (1862-1943). This interdisciplinary study of infinity explores the concept through the prism of mathematics and then offers more expansive investigations in areas beyond mathematical boundaries to reflect the broader, deeper implications of infinity for human intellectual thought. More than (...)
    Direct download  
     
    Export citation  
     
    Bookmark   6 citations  
  27.  18
    Infinity and Transcendence: Husserl, Heidegger and Tengelyi.Mikhail Belousov - 2020 - Studies in Transcendental Philosophy 1 (2-3).
    Laszlo Tengelyi’s phenomenological project, as presented in his book “World and infinity. To the problem of the phenomenological metaphysics”, published posthumously, is founded on the idea of the infinity of the world. In rehabilitating the husserlian thesis of the infinity as constitutive feature of the worldly experience, Tengelyi departs from the phenomenology of the finitude, which goes back to Heidegger. The article analyzes the origins of the infinity/finitude dilemma in transcendental phenomenology of the world in Husserl, (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  28.  26
    Infinity, infinite processes and limit concepts: recovering a neglected background of social and critical theory.Piet Strydom - 2017 - Philosophy and Social Criticism 43 (8):793-811.
    This article seeks to recover a neglected chapter in the historical and theoretical background of social theory in general and critical theory in particular with a view to refining the understanding of the presuppositions of a cognitively enhanced critical social science appropriate to our troubled times. For this purpose, it offers a brief reconstruction of the mathematical-philosophical tradition from ancient to modern times by extrapolating that part of it that is marked by the ideas of infinity, infinite processes and (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  29.  48
    Grasping Infinity by Finite Sets.Ferrante Formato & Giangiacomo Gerla - 1998 - Mathematical Logic Quarterly 44 (3):383-393.
    We show that the existence of an infinite set can be reduced to the existence of finite sets “as big as we will”, provided that a multivalued extension of the relation of equipotence is admitted. In accordance, we modelize the notion of infinite set by a fuzzy subset representing the class of wide sets.
    Direct download  
     
    Export citation  
     
    Bookmark   4 citations  
  30.  23
    Mixed ℋ -Infinity and Passive Synchronization of Markovian Jumping Neutral-Type Complex Dynamical Networks with Randomly Occurring Distributed Coupling Time-Varying Delays and Actuator Faults.N. Boonsatit, R. Sugumar, D. Ajay, G. Rajchakit, C. P. Lim, P. Hammachukiattikul, M. Usha & P. Agarwal - 2021 - Complexity 2021:1-19.
    This article examines mixed ℋ -infinity and passivity synchronization of Markovian jumping neutral-type complex dynamical network models with randomly occurring coupling delays and actuator faults. The randomly occurring coupling delays are considered to design the complex dynamical networks in practice. These delays complied with certain Bernoulli distributed white noise sequences. The relevant data including limits of actuator faults, bounds of the nonlinear terms, and external disturbances are available for designing the controller structure. Novel Lyapunov–Krasovskii functional is constructed to verify (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  31.  15
    Beyond infinity: an expedition to the outer limits of mathematics.Eugenia Cheng - 2017 - New York: Basic Books.
    A mathematician and scientist in residence at the School of the Art Institute of Chicago helps readers explore the concept of infinity through unique concepts including chessboards, a chicken-sandwich sandwich and the creation of infinite cookies from an infinite dough ball.
    Direct download  
     
    Export citation  
     
    Bookmark  
  32.  4
    Towards infinity.Ram Chandra - 1963 - [Shahjahanpur,: Shri Ram Chandra Mission. Edited by Suresh Chandra.
    Towards Infinity is Ram Chandra’s seminal work on the chakras of the human system and the soul’s journey back to the Source. Its implications are far-reaching – for the first time in thousands of years he sheds new light on human spiritual anatomy by going beyond the seven traditional chakras. The author does not discuss the lower chakras, instead, he starts with the heart and its qualities of love, compassion, courage and empathy as the centre of our humanity. He (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  33.  60
    Divine Infinity: 1150-1250.Leo Sweeney - 1957 - Modern Schoolman 35 (1):38-51.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  34.  68
    Infinity in Early Modern Philosophy.Igor Agostini, Richard T. W. Arthur, Geoffrey Gorham, Paul Guyer, Mogens Lærke, Yitzhak Y. Melamed, Ohad Nachtomy, Sanja Särman, Anat Schechtman, Noa Shein & Reed Winegar (eds.) - 2018 - Cham: Springer Verlag.
    This volume contains essays that examine infinity in early modern philosophy. The essays not only consider the ways that key figures viewed the concept. They also detail how these different beliefs about infinity influenced major philosophical systems throughout the era. These domains include mathematics, metaphysics, epistemology, ethics, science, and theology. Coverage begins with an introduction that outlines the overall importance of infinity to early modern philosophy. It then moves from a general background of infinity up through (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  35. 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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  36.  15
    Inclusive infinity and radical particularity: Hegel, Hartshorne and Nishida.Henry Wastila - 2002 - Sophia 41 (1):33-54.
    Three writers who utilize a similar metaphysics to understand the relationship between Ultimate Reality and conventional reality are compared. The metaphysics of what I call an inclusive Infinity is the common thread employed in comparing the thought of Hegel, Hartshorne and Nishida. I contrast the concept of inclusive Infinity with that of radical particularity and argue that people are private centers of conscious awareness who cannot be encompassed within an infinity or totality. Because of the individuality and (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  37.  23
    Infinity in Spinoza’s Therapy of the Passions.Sanja Särman - 2018 - In Igor Agostini, Richard T. W. Arthur, Geoffrey Gorham, Paul Guyer, Mogens Lærke, Yitzhak Y. Melamed, Ohad Nachtomy, Sanja Särman, Anat Schechtman, Noa Shein & Reed Winegar, Infinity in Early Modern Philosophy. Cham: Springer Verlag. pp. 77-95.
    The ontological and epistemological priority of the infinite has been extensively dealt with in Spinoza scholarship. However, Spinoza’s widely debated understanding of the infinite has not figured to the same extent in accounts of his therapy of the passions, the topic which this essay sets out to explore. My reasoning consists of six steps. First, I introduce Spinoza’s cognitive therapy, which claims that we can be healed from our passions by acquiring adequate ideas of them; second, I show that Spinoza’s (...)
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark   2 citations  
  38.  11
    Infinity and the brain: a unified theory of mind, matter, and God.Glenn G. Dudley - 2002 - St. Paul, Minn.: Paragon House.
    Infinity and the Brain proposes a logical and scientific way to resolve the paradox of mind and matter -- by explaining how the perception of a finite image is dependent upon the contrasting infinitude of God. The theory holds that awareness is equal to a tension between existence and nonexistence, such that the self is illuminated to itself (becomes conscious) to the exact measure that it anticipates the infinitude of its own nonexistence. This "anticipation" is actually a "tendency toward" (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  39.  53
    Beyond Infinity: Augustine and Cantor.Adam Drozdek - 1995 - Laval Théologique et Philosophique 51 (1):127-140.
  40. Is infinity merely an idea+ Hilbert, David philosophy.U. Majer - 1993 - Revue Internationale de Philosophie 47 (186):319-341.
  41.  46
    The Infinity in Mathematics.Andrzej Schinzel - 2008 - Dialogue and Universalism 18 (9-10):89-95.
    I shall outline the topic from a historical perspective, placing the main emphasis on the hundred years’ period spanning 1870–1970.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  42.  9
    Infinity in Phenomenology.László Komorjai - 2024 - Phänomenologische Forschungen 2024 (1):144-163.
    The article discusses why the notion of infinity is indispensable in contemporary phenomenology. I will heavily rely on some of L(szl) Tengelyi’s ideas, who in his turn uses Marc Richir’s early works on Cantor and Kant. Although – similarly to Richir and Tengelyi – I also examine some of Cantor’s ideas, I concentrate on a different and more fundamental part of his theory than Tengelyi and Richir.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  43.  64
    Infinity and Newton’s Three Laws of Motion.Chunghyoung Lee - 2011 - Foundations of Physics 41 (12):1810-1828.
    It is shown that the following three common understandings of Newton’s laws of motion do not hold for systems of infinitely many components. First, Newton’s third law, or the law of action and reaction, is universally believed to imply that the total sum of internal forces in a system is always zero. Several examples are presented to show that this belief fails to hold for infinite systems. Second, two of these examples are of an infinitely divisible continuous body with finite (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  44.  84
    Infinity: An Essay in Metaphysics. By Jose A. Bernadette. (Oxford, 1964. Pp. x + 289. Price 45s.).C. W. Kilmister - 1965 - Philosophy 40 (153):262-.
  45.  25
    Infinity and the infinitesimal (concluded): Part III.Winthrop Parkhurst, W. J. Kingsland Jr & William Parkhurst - 1927 - The Monist 37 (1):131 - 149.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  46.  51
    Expressing infinity without foundation.Franco Parlamento & Alberto Policriti - 1991 - Journal of Symbolic Logic 56 (4):1230-1235.
    The axiom of infinity can be expressed by stating the existence of sets satisfying a formula which involves restricted universal quantifiers only, even if the axiom of foundation is not assumed.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  47. 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.
    Direct download  
     
    Export citation  
     
    Bookmark   4 citations  
  48.  26
    Infinity and the Self: Royce on Dedekind.Sébastien Gandon - 2021 - Hopos: The Journal of the International Society for the History of Philosophy of Science 11 (2):354-382.
    In Die Zahlen (1888), Dedekind defines an infinite set as a set that is isomorphic with one of its proper parts. In The World and the Individual (1900), the American philosopher Josiah Royce relates Dedekind’s notion to Fichte’s and Hegel’s concept of Self defined as an entity that reflects itself into itself. The first aim of this article is to explain Royce’s analysis and to put it in its proper context, that of a critique of Bradley’s mystical idealism. The second (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  49. Infinity, Choice, and Hume’s Principle.Stephen Mackereth - 2024 - Journal of Philosophical Logic 53 (5):1413-1439.
    It has long been known that in the context of axiomatic second-order logic (SOL), Hume’s Principle (HP) is mutually interpretable with “the universe is Dedekind infinite” (DI). In this paper, we offer a more fine-grained analysis of the logical strength of HP, measured by deductive implications rather than interpretability. Our main result is that HP is not deductively conservative over SOL + DI. That is, SOL + HP proves additional theorems in the language of pure second-order logic that are not (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  50.  61
    Infinity in Edith Stein’s Endliches und Ewiges sein.Mary Catharine Baseheart - 1981 - Proceedings of the American Catholic Philosophical Association 55:126-134.
1 — 50 / 972