About this topic
Summary The infinite has been an important topic in many branches of philosophy (and neighboring disciplines), including metaphysics, epistemology, the philosophy of physics, the philosophy of religion, and ethics.  But since at least the 19th century, when B. Bolzano, G. Cantor, R. Dedekind, and others made crucial contributions, the most central discussions about the infinite have taken place in the philosophy of mathematics and logic.  For a rich, historically grounded, but also opinionated introduction, see A.W. Moore, The Infinite (2nd edition, Routledge, 2001).  Many classic articles on the topic are contained in A.W. Moore, ed., Infinity (International Research Library of Philosophy, Dartmouth, 1993). For a more basic introduction, see P. Zellini's A Brief History of Infinity (Penguin, 2004), and on the mathematical side, I. Stewart's Infinity. A Very Short Introduction (Oxford University Press, 2017) and E. Cheng's Beyond Infinity (Basic Books, 2017).  Finally, for advanced logico-mathematical aspects, see A. Kanamori, The Higher Infinite (2nd ed., Springer, 1994).
Key works Potential infinity, actual infinity, infinitesimals, paradoxes, the transfinite, set theory, cardinal numbers, ordinal numbers, space, time.
Related

Contents
462 found
Order:
1 — 50 / 462
  1. Strict Finitism's Unrequited Love for Computational Complexity.Noel Arteche - manuscript
    As a philosophy of mathematics, strict finitism has been traditionally concerned with the notion of feasibility, defended mostly by appealing to the physicality of mathematical practice. This has led the strict finitists to influence and be influenced by the field of computational complexity theory, under the widely held belief that this branch of mathematics is concerned with the study of what is “feasible in practice”. In this paper, I survey these ideas and contend that, contrary to popular belief, complexity theory (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  2. Frege's Basic Law V and Cantor's Theorem.Manuel Bremer - manuscript
    The following essay reconsiders the ontological and logical issues around Frege’s Basic Law (V). If focuses less on Russell’s Paradox, as most treatments of Frege’s Grundgesetze der Arithmetik (GGA)1 do, but rather on the relation between Frege’s Basic Law (V) and Cantor’s Theorem (CT). So for the most part the inconsistency of Naïve Comprehension (in the context of standard Second Order Logic) will not concern us, but rather the ontological issues central to the conflict between (BLV) and (CT). These ontological (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  3. Existence Is Evidence of Immortality.Michael Huemer - manuscript
    Time may be infinite in both directions. If it is, then, if persons could live at most once in all of time, the probability that you would be alive now would be zero. But if persons can live more than once, the probability that you would be alive now would be nonzero. Since you are alive now, with certainty, either the past is finite, or persons can live more than once.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   3 citations  
  4. A Secret Ethics of Infinity.Janet Borgerson - forthcoming - Levinas, Business Ethics.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  5. The Infinity of God: Scientific, Theological, and Philosophical Perspectives.Benedikt Paul Goecke (ed.) - forthcoming - Notre Dame University Press.
    Remove from this list  
     
    Export citation  
     
    Bookmark  
  6. Send in the Clowns.Daniel Nolan - forthcoming - In Karen Bennett & Dean Zimmerman (eds.), Oxford Studies in Metaphysics. Oxford: Oxford University Press.
    Thought experiments are common where infinitely many entities acting in concert give rise to strange results. Some of these cases, however, can be generalized to yield almost omnipotent systems from limited materials. This paper discusses one of these cases, bringing out one aspect of what seems so troubling about "New Zeno" cases. -/- This paper is in memory of Josh Parsons.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  7. Cosmic Topology, Underdetermination, and Spatial Infinity.Patrick J. Ryan - forthcoming - European Journal for Philosophy of Science.
    It is well-known that the global structure of every space-time model for relativistic cosmology is observationally underdetermined. In order to alleviate the severity of this underdetermination, it has been proposed that we adopt the Cosmological Principle because the Principle restricts our attention to a distinguished class of space-time models (spatially homogeneous and isotropic models). I argue that, even assuming the Cosmological Principle, the topology of space remains observationally underdetermined. Nonetheless, I argue that we can muster reasons to prefer various topological (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  8. Competing Roles of Aristotle's Account of the Infinite.Robby Finley - 2024 - Apeiron 57 (1):25-54.
    There are two distinct but interrelated questions concerning Aristotle’s account of infinity that have been the subject of recurring debate. The first of these, what I call here the interpretative question, asks for a charitable and internally coherent interpretation of the limited pieces of text where Aristotle outlines his view of the ‘potential’ (and not ‘actual’) infinite. The second, what I call here the philosophical question, asks whether there is a way to make Aristotle’s notion of the potential infinite coherent (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  9. Øystein vs Archimedes: A Note on Linnebo’s Infinite Balance.Daniel Hoek - 2023 - Erkenntnis 88 (4):1791-1796.
    Using Riemann’s Rearrangement Theorem, Øystein Linnebo (2020) argues that, if it were possible to apply an infinite positive weight and an infinite negative weight to a working scale, the resulting net weight could end up being any real number, depending on the procedure by which these weights are applied. Appealing to the First Postulate of Archimedes’ treatise on balance, I argue instead that the scale would always read 0 kg. Along the way, we stop to consider an infinitely jittery flea, (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  10. Lower and Upper Estimates of the Quantity of Algebraic Numbers.Yaroslav Sergeyev - 2023 - Mediterranian Journal of Mathematics 20:12.
    It is well known that the set of algebraic numbers (let us call it A) is countable. In this paper, instead of the usage of the classical terminology of cardinals proposed by Cantor, a recently introduced methodology using ①-based infinite numbers is applied to measure the set A (where the number ① is called grossone). Our interest to this methodology is explained by the fact that in certain cases where cardinals allow one to say only whether a set is countable (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  11. Forever Finite: The Case Against Infinity.Kip Sewell - 2023 - Alexandria, VA: Rond Books.
    Infinity is not what it seems. Infinity is commonly assumed to be a logical concept, reliable for conducting mathematics, describing the Universe, and understanding the divine. Most of us are educated to take for granted that there exist infinite sets of numbers, that lines contain an infinite number of points, that space is infinite in expanse, that time has an infinite succession of events, that possibilities are infinite in quantity, and over half of the world’s population believes in a divine (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   2 citations  
  12. Forever Finite: The Case Against Infinity (Expanded Edition).Kip Sewell - 2023 - Alexandria, VA: Rond Books.
    EXPANDED EDITION (eBook): -/- Infinity Is Not What It Seems...Infinity is commonly assumed to be a logical concept, reliable for conducting mathematics, describing the Universe, and understanding the divine. Most of us are educated to take for granted that there exist infinite sets of numbers, that lines contain an infinite number of points, that space is infinite in expanse, that time has an infinite succession of events, that possibilities are infinite in quantity, and over half of the world’s population believes (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  13. Nothing Infinite: A Summary of Forever Finite.Kip Sewell - 2023 - Rond Media Library.
    In 'Forever Finite: The Case Against Infinity' (Rond Books, 2023), the author argues that, despite its cultural popularity, infinity is not a logical concept and consequently cannot be a property of anything that exists in the real world. This article summarizes the main points in 'Forever Finite', including its overview of what debunking infinity entails for conceptual thought in philosophy, mathematics, science, cosmology, and theology.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  14. The Potential in Frege’s Theorem.Will Stafford - 2023 - Review of Symbolic Logic 16 (2):553-577.
    Is a logicist bound to the claim that as a matter of analytic truth there is an actual infinity of objects? If Hume’s Principle is analytic then in the standard setting the answer appears to be yes. Hodes’s work pointed to a way out by offering a modal picture in which only a potential infinity was posited. However, this project was abandoned due to apparent failures of cross-world predication. We re-explore this idea and discover that in the setting of the (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  15. Divergent Potentialism: A Modal Analysis With an Application to Choice Sequences.Ethan Brauer, Øystein Linnebo & Stewart Shapiro - 2022 - Philosophia Mathematica 30 (2):143-172.
    Modal logic has been used to analyze potential infinity and potentialism more generally. However, the standard analysis breaks down in cases of divergent possibilities, where there are two or more possibilities that can be individually realized but which are jointly incompatible. This paper has three aims. First, using the intuitionistic theory of choice sequences, we motivate the need for a modal analysis of divergent potentialism and explain the challenges this involves. Then, using Beth–Kripke semantics for intuitionistic logic, we overcome those (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  16. L'incommensurable: un concept peut-il changer la vie?François Jullien - 2022 - Paris: Éditions de l'Observatoire.
    Rabattement -- De l'incommensurable -- Évitement -- Il y a de l'incommensurable (la jouissance, l'intime, la mort) -- Dé-commensurabiliser -- Ce qui n'est pas de ce monde, mais qui n'est d'un autre monde -- Un concept peut'il changer la vie? (l'incommensurable déploie l'existence).
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  17. The Price of Mathematical Scepticism.Paul Blain Levy - 2022 - Philosophia Mathematica 30 (3):283-305.
    This paper argues that, insofar as we doubt the bivalence of the Continuum Hypothesis or the truth of the Axiom of Choice, we should also doubt the consistency of third-order arithmetic, both the classical and intuitionistic versions. -/- Underlying this argument is the following philosophical view. Mathematical belief springs from certain intuitions, each of which can be either accepted or doubted in its entirety, but not half-accepted. Therefore, our beliefs about reality, bivalence, choice and consistency should all be aligned.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  18. How can a line segment with extension be composed of extensionless points?Brian Reese, Michael Vazquez & Scott Weinstein - 2022 - Synthese 200 (2):1-28.
    We provide a new interpretation of Zeno’s Paradox of Measure that begins by giving a substantive account, drawn from Aristotle’s text, of the fact that points lack magnitude. The main elements of this account are (1) the Axiom of Archimedes which states that there are no infinitesimal magnitudes, and (2) the principle that all assignments of magnitude, or lack thereof, must be grounded in the magnitude of line segments, the primary objects to which the notion of linear magnitude applies. Armed (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  19. 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 perception (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  20. Numerical infinities and infinitesimals in optimization.Yaroslav D. Sergeyev & Renato De Leone - 2022 - 93413 Cham, Germania: Springer.
    From the Publisher: -/- This book presents a new powerful supercomputing paradigm introduced by Yaroslav D. Sergeyev -/- It gives a friendly introduction to the paradigm and proposes a broad panorama of a successful usage of numerical infinities -/- The volume covers software implementations of the Infinity Computer -/- Abstract -/- This book provides a friendly introduction to the paradigm and proposes a broad panorama of killing applications of the Infinity Computer in optimization: radically new numerical algorithms, great theoretical insights, (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  21. Higher dimensional cardinal characteristics for sets of functions.Corey Bacal Switzer - 2022 - Annals of Pure and Applied Logic 173 (1):103031.
  22. On V.A. Yankov’s Contribution to the History of Foundations of Mathematics.Ioannis M. Vandoulakis - 2022 - In Alex Citkin & Ioannis M. Vandoulakis (eds.), V.A. Yankov on Non-Classical Logics, History and Philosophy of Mathematics. Springer, Outstanding Contributions to Logic (Volume 24). pp. 247-270.
    The paper examines Yankov’s contribution to the history of mathematical logic and the foundations of mathematics. It concerns the public communication of Markov’s critical attitude towards Brouwer’s intuitionistic mathematics from the point of view of his constructive mathematics and the commentary on A.S. Esenin-Vol’pin program of ultra-intuitionistic foundations of mathematics.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  23. Vieri Benci and Mauro Di Nasso. How to Measure the Infinite: Mathematics with Infinite and Infinitesimal Numbers.Sylvia Wenmackers - 2022 - Philosophia Mathematica 30 (1):130-137.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  24. Takeuti's well-ordering proofs revisited.Andrew Arana & Ryota Akiyoshi - 2021 - Mita Philosophy Society 3 (146):83-110.
    Gaisi Takeuti extended Gentzen's work to higher-order case in 1950's–1960's and proved the consistency of impredicative subsystems of analysis. He has been chiefly known as a successor of Hilbert's school, but we pointed out in the previous paper that Takeuti's aimed to investigate the relationships between "minds" by carrying out his proof-theoretic project rather than proving the "reliability" of such impredicative subsystems of analysis. Moreover, as briefly explained there, his philosophical ideas can be traced back to Nishida's philosophy in Kyoto's (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  25. Bolzano’s Mathematical Infinite.Anna Bellomo & Guillaume Massas - 2021 - Review of Symbolic Logic:1-55.
    Bernard Bolzano (1781–1848) is commonly thought to have attempted to develop a theory of size for infinite collections that follows the so-called part–whole principle, according to which the whole is always greater than any of its proper parts. In this paper, we develop a novel interpretation of Bolzano’s mature theory of the infinite and show that, contrary to mainstream interpretations, it is best understood as a theory of infinite sums. Our formal results show that Bolzano’s infinite sums can be equipped (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  26. 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 la Argentina (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  27. Are infinite explanations self-explanatory?Alexandre Billon - 2021 - Erkenntnis 88 (5):1935-1954.
    Consider an infinite series whose items are each explained by their immediate successor. Does such an infinite explanation explain the whole series or does it leave something to be explained? Hume arguably claimed that it does fully explain the whole series. Leibniz, however, designed a very telling objection against this claim, an objection involving an infinite series of book copies. In this paper, I argue that the Humean claim can, in certain cases, be saved from the Leibnizian “infinite book copies” (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  28. On the existence of small antichains for definable quasi-orders.Raphaël Carroy, Benjamin D. Miller & Zoltán Vidnyánszky - 2021 - Journal of Mathematical Logic 21 (2):2150005.
    We generalize Kada’s definable strengthening of Dilworth’s characterization of the class of quasi-orders admitting an antichain of a given finite cardinality.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  29. Existence Is Evidence of Immortality.Michael Huemer - 2021 - Noûs 55 (1):128-151.
    Time may be infinite in both directions. If it is, then, if persons could live at most once in all of time, the probability that you would be alive now would be zero. But if persons can live more than once, the probability that you would be alive now would be nonzero. Since you are alive now, with certainty, either the past is finite, or persons can live more than once.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  30. Can All Things Be Counted?Chris Scambler - 2021 - Journal of Philosophical Logic 50 (5):1079-1106.
    In this paper, I present and motivate a modal set theory consistent with the idea that there is only one size of infinity.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  31. Mirroring Theorems in Free Logic.Ethan Brauer - 2020 - Notre Dame Journal of Formal Logic 61 (4):561-572.
    Linnebo and Shapiro have recently given an analysis of potential infinity using modal logic. A key technical component of their account is to show that under a suitable translation ◊ of nonmodal language into modal language, nonmodal sentences ϕ 1, …, ϕ n entail ψ just in case ϕ 1 ◊, …, ϕ n ◊ entail ψ ◊ in the modal logic S4.2. Linnebo and Shapiro establish this result in nonfree logic. In this note I argue that their analysis of (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  32. Hermann Cohen’s Principle of the Infinitesimal Method: A Defense.Scott Edgar - 2020 - Hopos: The Journal of the International Society for the History of Philosophy of Science 10 (2):440-470.
    In Bertrand Russell's 1903 Principles of Mathematics, he offers an apparently devastating criticism of the neo-Kantian Hermann Cohen's Principle of the Infinitesimal Method and its History (PIM). Russell's criticism is motivated by his concern that Cohen's account of the foundations of calculus saddles mathematics with the paradoxes of the infinitesimal and continuum, and thus threatens the very idea of mathematical truth. This paper defends Cohen against that objection of Russell's, and argues that properly understood, Cohen's views of limits and infinitesimals (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  33. Philosophy of the infinite.Emanuele Gambetta - 2020 - Roma: Gangemi editore SpA international.
  34. Riemann’s Scale: A Puzzle About Infinity.Øystein Linnebo - 2020 - Erkenntnis 88 (1):189-191.
    Ordinarily, the order in which some objects are attached to a scale does not affect the total weight measured by the scale. This principle is shown to fail in certain cases involving infinitely many objects. In these cases, we can produce any desired reading of the scale merely by changing the order in which a fixed collection of objects are attached to the scale. This puzzling phenomenon brings out the metaphysical significance of a theorem about infinite series that is well (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  35. A Philosophical Argument for the Beginning of Time.Laureano Luna & Jacobus Erasmus - 2020 - Prolegomena 19 (2):161-176.
    A common argument in support of a beginning of the universe used by advocates of the kalām cosmological argument (KCA) is the argument against the possibility of an actual infinite, or the “Infinity Argument”. However, it turns out that the Infinity Argument loses some of its force when compared with the achievements of set theory and it brings into question the view that God predetermined an endless future. We therefore defend a new formal argument, based on the nature of time (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   5 citations  
  36. A Philosophical Path from Königsberg to Kyoto: The Science of the Infinite and the Philosophy of Nothingness.Rossella Lupacchini - 2020 - Sophia 60 (4):851-868.
    ‘Mathematics is the science of the infinite, its goal the symbolic comprehension of the infinite with human, that is finite, means.’ Along this line, in The Open World, Hermann Weyl contrasted the desire to make the infinite accessible through finite processes, which underlies any theoretical investigation of reality, with the intuitive feeling for the infinite ‘peculiar to the Orient,’ which remains ‘indifferent to the concrete manifold of reality.’ But a critical analysis may acknowledge a valuable dialectical opposition. Struggling to spell (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  37. The weakness of the pigeonhole principle under hyperarithmetical reductions.Benoit Monin & Ludovic Patey - 2020 - Journal of Mathematical Logic 21 (3):2150013.
    The infinite pigeonhole principle for 2-partitions asserts the existence, for every set A, of an infinite subset of A or of its complement. In this paper, we study the infinite pigeonhole pr...
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  38. L'Univers infini dans le monde des Lumières.Jean Seidengart - 2020 - Paris: Les Belles lettres.
    S'inscrivant dans le prolongement des travaux de P. Duhem et d'A. Koyré, cet ouvrage retrace l'histoire de la cosmologie au XVIIIe siècle en Europe, qui s'accompagne alors d'une conceptualisation de l'infini. Une place centrale est accordée à E. Kant, depuis la période précritique jusqu'aux œuvres posthumes. Ce livre poursuit la réflexion entamée dans Dieu, l'Univers et la sphère infinie.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  39. Infinite Reasoning.Jared Warren - 2020 - Philosophy and Phenomenological Research 103 (2):385-407.
    Our relationship to the infinite is controversial. But it is widely agreed that our powers of reasoning are finite. I disagree with this consensus; I think that we can, and perhaps do, engage in infinite reasoning. Many think it is just obvious that we can't reason infinitely. This is mistaken. Infinite reasoning does not require constructing infinitely long proofs, nor would it gift us with non-recursive mental powers. To reason infinitely we only need an ability to perform infinite inferences. I (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   7 citations  
  40. Anaxagoras, the Thoroughgoing Infinitist: The Relation between his Teachings on Multitude and on Heterogeneity.Miloš Arsenijević, Saša Popović & Miloš Vuletić - 2019 - European Journal of Analytic Philosophy 15 (1):35-70.
    In the analysis of Anaxagoras’ physics in view of the relation between his teachings on multitude and heterogeneity, two central questions emerge: 1) How can the structure of the universe considered purely mereo-topologically help us explain that at the first cosmic stage no qualitative difference is manifest in spite of the fact that the entire qualitative heterogeneity is supposedly already present there? 2) How can heterogeneity become manifest at the second stage, resulting from the noûs intervention, if according to fragment (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  41. The riddle of the infinite or Ananta.Jayant Burde - 2019 - Delhi: Motilal Banarsidass Publishers Private.
    This book explores the bizarre but fascinating world of infinity in different disciplines of knowledge; mathematics, science, philosophy and religion. It projects the views of eastern as well as western scholars. This world is not only mysterious but also treacherous and conceals many conundrums such as a multitude of infinities, the mystic's experience of the infinite, conception of God as absolute infinity. The author also discusses many paradoxes relating to space and time. It is interesting to discover that some eastern (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  42. Ordinal Computability: An Introduction to Infinitary Machines.Merlin Carl - 2019 - Boston: De Gruyter.
    Ordinal Computability discusses models of computation obtained by generalizing classical models, such as Turing machines or register machines, to transfinite working time and space. In particular, recognizability, randomness, and applications to other areas of mathematics, including set theory and model theory, are covered.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  43. Do simple infinitesimal parts solve Zeno’s paradox of measure?Lu Chen - 2019 - Synthese 198 (5):4441-4456.
    In this paper, I develop an original view of the structure of space—called infinitesimal atomism—as a reply to Zeno’s paradox of measure. According to this view, space is composed of ultimate parts with infinitesimal size, where infinitesimals are understood within the framework of Robinson’s nonstandard analysis. Notably, this view satisfies a version of additivity: for every region that has a size, its size is the sum of the sizes of its disjoint parts. In particular, the size of a finite region (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  44. This life: secular faith and spiritual freedom.Martin Hägglund - 2019 - New York: Pantheon Books.
    A profound, original, and accessible book that argues that a faith not in God or eternal life, but in the finite, temporal life we lead here on earth is one that gives that life far greater depth of meaning. A manifesto for a truly secular faith that speaks eloquently to both believers and agnostics alike. The philosopher and critic Martin Hägglund believes that we need a new way of thinking about faith. In contrast to the traditional religious faith in eternity, (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   3 citations  
  45. Apophatic Finitism and Infinitism.Jan Heylen - 2019 - Logique Et Analyse 62 (247):319-337.
    This article is about the ontological dispute between finitists, who claim that only finitely many numbers exist, and infinitists, who claim that infinitely many numbers exist. Van Bendegem set out to solve the 'general problem' for finitism: how can one recast finite fragments of classical mathematics in finitist terms? To solve this problem Van Bendegem comes up with a new brand of finitism, namely so-called 'apophatic finitism'. In this article it will be argued that apophatic finitism is unable to represent (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  46. Rumfitt on the logic of set theory.Øystein Linnebo - 2019 - Inquiry: An Interdisciplinary Journal of Philosophy 62 (7):826-841.
    ABSTRACTAccording to a famous argument by Dummett, the concept of set is indefinitely extensible, and the logic appropriate for reasoning about the instances of any such concept is intuitionistic, not classical. But Dummett's argument is widely regarded as obscure. This note explains how the final chapter of Rumfitt's important new book advances our understanding of Dummett's argument, but it also points out some problems and unanswered questions. Finally, Rumfitt's reconstruction of Dummett's argument is contrasted with my own preferred alternative.
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  47. On the Coherence of Strict Finitism.Auke Alesander Montesano Montessori - 2019 - Kriterion - Journal of Philosophy 33 (2):1-14.
    Strict finitism is the position that only those natural numbers exist that we can represent in practice. Michael Dummett, in a paper called Wang’s Paradox, famously tried to show that strict finitism is an incoherent position. By using the Sorites paradox, he claimed that certain predicates the strict finitist is committed to are incoherent. More recently, Ofra Magidor objected to Dummett’s claims, arguing that Dummett fails to show the incoherence of strict finitism. In this paper, I shall investigate whether Magidor (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  48. 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 apparatus of (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  49. Infinite barbarians.Daniel Nolan - 2019 - Ratio 32 (3):173-181.
    This paper discusses an infinite regress that looms behind a certain kind of historical explanation. The movement of one barbarian group is often explained by the movement of others, but those movements in turn call for an explanation. While their explanation can again be the movement of yet another group of barbarians, if this sort of explanation does not stop somewhere we are left with an infinite regress of barbarians. While that regress would be vicious, it cannot be accommodated by (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  50. 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 of three (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   6 citations  
1 — 50 / 462