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 categories

357 found
Order:
1 — 50 / 357
  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. The Case Against Infinity.Kip Sewell -
    The concept of infinity is argued to contain self-contradictions. To maintain logical consistency, mathematics ought to abandon the notion of infinity. It is proposed that infinity should be replaced with the concept of “indefiniteness”. This further implies that other fields drawing on mathematics, such as physics and cosmology, ought to reject theories that postulate infinities of space and time. It is concluded that however indefinite our calculations of space and time become, the Universe must nevertheless be finite.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  5. Are infinite explanations self-explanatory?Alexandre Billon - forthcoming - Erkenntnis:1-20.
    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 (4 more)  
     
    Export citation  
     
    Bookmark  
  6. A Secret Ethics of Infinity.Janet Borgerson - forthcoming - Levinas, Business Ethics.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  7. Divergent Potentialism: A Modal Analysis With an Application to Choice Sequences.Ethan Brauer, Øystein Linnebo & Stewart Shapiro - forthcoming - Philosophia Mathematica.
    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 (2 more)  
     
    Export citation  
     
    Bookmark  
  8. 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  
  9. Øystein vs Archimedes: A Note on Linnebo’s Infinite Balance.Daniel Hoek - forthcoming - Erkenntnis:1-6.
    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 (4 more)  
     
    Export citation  
     
    Bookmark  
  10. 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  
  11. The Potential in Frege’s Theorem.Will Stafford - forthcoming - Review of Symbolic Logic:1-25.
    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  
  12. Riemann’s Scale: A Puzzle About Infinity.Øystein Linnebo - 2023 - 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  
  13. 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  
  14. 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  
  15. 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  
  16. 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  
  17. 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  
  18. Higher dimensional cardinal characteristics for sets of functions.Corey Bacal Switzer - 2022 - Annals of Pure and Applied Logic 173 (1):103031.
  19. 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  
  20. 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  
  21. 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   1 citation  
  22. 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  
  23. 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  
  24. 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   5 citations  
  25. A Philosophical Path from Königsberg to Kyoto: The Science of the Infinite and the Philosophy of Nothingness.Rossella Lupacchini - 2021 - 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  
  26. 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   1 citation  
  27. Infinite Reasoning.Jared Warren - 2021 - 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   3 citations  
  28. 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  
  29. 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  
  30. 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   1 citation  
  31. 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  
  32. 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  
  33. 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  
  34. The riddle of the infinite or Ananta.Jayant Burde - 2019 - Delhi: Motilal Banarsidass Publishers Private.
    Remove from this list  
     
    Export citation  
     
    Bookmark  
  35. 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  
  36. 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  
  37. 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   7 citations  
  38. 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  
  39. 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   5 citations  
  40. 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 (...)
    Remove from this list   Direct download (6 more)  
     
    Export citation  
     
    Bookmark  
  41. Eight lessons on infinity: a mathematical adventure.Haim Shapira - 2019 - London: Duncan Baird Publishing, an imprint of Watkins Media.
    In this book, best-selling author and mathematician Haim Shapira presents an introduction to mathematical theories which deal with the most beautiful concept ever invented by humankind: infinity. Written in clear, simple language and aimed at a lay audience, this book also offers some strategies that will allow readers to try their ability at solving truly fascinating mathematical problems. Infinity is a deeply counter-intuitive concept that has inspired many great thinkers. In this book we will meet many sages, both familiar and (...)
    Remove from this list  
     
    Export citation  
     
    Bookmark  
  42. Revisão de ' Os Limites Exteriores da Razão ' (The Outer Limits of Reason)por Noson Yanofsky 403p (2013) (revisão revisada 2019).Michael Richard Starks - 2019 - In Delírios Utópicos Suicidas no Século XXI Filosofia, Natureza Humana e o Colapso da Civilization- Artigos e Comentários 2006-2019 5ª edição. Las Vegas, NV USA: Reality Press. pp. 188-202.
    Eu dou uma revisão detalhada de "os limites exteriores da razão" por Noson Yanofsky de uma perspectiva unificada de Wittgenstein e psicologia evolutiva. Eu indico que a dificuldade com tais questões como paradoxo na linguagem e matemática, incompletude, undecidabilidade, computabilidade, o cérebro eo universo como computadores, etc., todos surgem a partir da falta de olhar atentamente para o nosso uso da linguagem no apropriado contexto e, consequentemente, a falta de separar questões de fato científico a partir de questões de como (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  43. Enseignement et apprentissage de l’infini : aspects philosophiques, épistemologiques et didactiques.Pascale Boulais, R. Brouzet, Viviane Durand-Guerrier, Maha Majaj, David Marino, Francoise Monnoyeur & Martine Vergnac - 2018 - In Mathématiques en scène des ponts entre les disciplines. Paris, France: pp. 246-255.
    Résumé – Nous nous intéressons à l’enseignement et l’apprentissage de l’infini en classe de mathématiques en considérant les différences et les relations entre infini potentiel et infini actuel. Nous présentons les principaux éléments de notre étude philosophique, épistémologique et didactique, ainsi que trois situations visant à conduire un travail explicite avec les élèves sur ces questions en début de lycée. ---------------------------------------------------------------------------------------------------- --------------------------------- Abstract – We are interested in the teaching and learning of infinite in mathematics class, taking into account the relations (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  44. Infinite Cardinalities, Measuring Knowledge, and Probabilities in Fine-Tuning Arguments.Isaac Choi - 2018 - In Matthew A. Benton, John Hawthorne & Dani Rabinowitz (eds.), Knowledge, Belief, and God: New Insights in Religious Epistemology. Oxford: Oxford University Press. pp. 103-121.
    This paper deals with two different problems in which infinity plays a central role. I first respond to a claim that infinity renders counting knowledge-level beliefs an infeasible approach to measuring and comparing how much we know. There are two methods of comparing sizes of infinite sets, using the one-to-one correspondence principle or the subset principle, and I argue that we should use the subset principle for measuring knowledge. I then turn to the normalizability and coarse tuning objections to fine-tuning (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  45. A Road Map of Dedekind’s Theorem 66.Ansten Klev - 2018 - Hopos: The Journal of the International Society for the History of Philosophy of Science 8 (2):241-277.
    Richard Dedekind’s theorem 66 states that there exists an infinite set. Its proof invokes such apparently nonmathematical notions as the thought-world and the self. This article discusses the content and context of Dedekind’s proof. It is suggested that Dedekind took the notion of the thought-world from Hermann Lotze. The influence of Kant and Bernard Bolzano on the proof is also discussed, and the reception of the proof in the mathematical and philosophical literature is covered in detail.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  46. Margaret Cavendish on the Order and Infinitude of Nature.Michael Bennett McNulty - 2018 - History of Philosophy Quarterly 35 (3):219-239.
    In this paper, I develop a new interpretation of the order of nature, its function, and its implications in Margaret Cavendish’s philosophy. According to the infinite balance account, the order of nature consists in a balance among the infinite varieties of nature. That is, for Cavendish, nature contains an infinity of different types of matter: infinite species, shapes, and motions. The potential tumult implicated by such a variety, however, is tempered by the counterbalancing of the different kinds and motions of (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  47. The Infinite: Third Edition.A. W. Moore - 2018 - Routledge.
    This third edition of The Infinite includes a new part 'Infinity Superseded' which contains two new chapters refining Moore's ideas through a re-examination of the ideas of Spinoza, Hegel, and Nietzsche. Much of this is heavily influenced by the work of Deleuze. There is also a new technical appendix on still unresolved issues about different infinite sizes.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   2 citations  
  48. The end of infinity.Anthony C. Patton - 2018 - New York: Algora Publishing.
    Remove from this list  
     
    Export citation  
     
    Bookmark  
  49. 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.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  50. Discrete and continuous: a fundamental dichotomy in mathematics.James Franklin - 2017 - Journal of Humanistic Mathematics 7 (2):355-378.
    The distinction between the discrete and the continuous lies at the heart of mathematics. Discrete mathematics (arithmetic, algebra, combinatorics, graph theory, cryptography, logic) has a set of concepts, techniques, and application areas largely distinct from continuous mathematics (traditional geometry, calculus, most of functional analysis, differential equations, topology). The interaction between the two – for example in computer models of continuous systems such as fluid flow – is a central issue in the applicable mathematics of the last hundred years. This article (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
1 — 50 / 357