Switch to: Citations

References in:

Three Infinities in Early Modern Philosophy

Mind 128 (512):1117-1147 (2019)

Add references

You must login to add references.
  1. On Infinite Size.Bruno Whittle - 2015 - In Oxford Studies in Metaphysics: Volume 9. Oxford University Press. pp. 3-19.
    Cantor showed that there are infinite sets that do not have one-to-one correspondences between them. The standard understanding of this result is that it shows that there are different sizes of infinity. This paper challenges this standard understanding, and argues, more generally, that we do not have any reason to think that there are different sizes of infinity. Two arguments are given against the claim that Cantor established that there are different such sizes: one involves an analogy between Cantor’s result (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • The Principles of Mathematics.Bertrand Russell - 1903 - Revue de Métaphysique et de Morale 11 (4):11-12.
    Download  
     
    Export citation  
     
    Bookmark   751 citations  
  • Locke and the Scholastics on Theological Discourse.Walter Ott - 1997 - Locke Studies 28 (1):51-66.
    On the face of it, Locke rejects the scholastics' main tool for making sense of talk of God, namely, analogy. Instead, Locke claims that we generate an idea of God by 'enlarging' our ideas of some attributes (such as knowledge) with the idea of infinity. Through an analysis of Locke's idea of infinity, I argue that he is in fact not so distant from the scholastics and in particular must rely on analogy of inequality.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • An Essay Concerning Human Understanding.John Locke - 1979 - Revue Philosophique de la France Et de l'Etranger 169 (2):221-222.
    Download  
     
    Export citation  
     
    Bookmark   631 citations  
  • The Principles of Mathematics.Bertrand Russell - 1903 - Cambridge, England: Allen & Unwin.
    Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...)
    Download  
     
    Export citation  
     
    Bookmark   467 citations  
  • Measuring the Size of Infinite Collections of Natural Numbers: Was Cantor’s Theory of Infinite Number Inevitable?Paolo Mancosu - 2009 - Review of Symbolic Logic 2 (4):612-646.
    Cantor’s theory of cardinal numbers offers a way to generalize arithmetic from finite sets to infinite sets using the notion of one-to-one association between two sets. As is well known, all countable infinite sets have the same ‘size’ in this account, namely that of the cardinality of the natural numbers. However, throughout the history of reflections on infinity another powerful intuition has played a major role: if a collectionAis properly included in a collectionBthen the ‘size’ ofAshould be less than the (...)
    Download  
     
    Export citation  
     
    Bookmark   38 citations  
  • Leibniz on Wholes, Unities, and Infinite Number.Gregory Brown - 2000 - The Leibniz Review 10:21-51.
    One argument that Leibniz employed to rule out the possibility of a world soul appears to turn on the assumption that the very notion of an infinite number or of an infinite whole is inconsistent. This argument was considered in a series of three papers published in The Leibniz Review: in the first, by Laurence Carlin, the argument was delineated and analyzed; in the second, by myself, the argument was criticized and rejected; in the third, by Richard Arthur, an attempt (...)
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  • Archimedes, Infinitesimals and the Law of Continuity: On Leibniz’s Fictionalism.Samuel Levey - 2008 - In Douglas Jesseph & Ursula Goldenbaum (eds.), Infinitesimal Differences: Controversies Between Leibniz and His Contemporaries. Walter de Gruyter.
    Download  
     
    Export citation  
     
    Bookmark   10 citations  
  • Locke on measurement.Peter R. Anstey - 2016 - Studies in History and Philosophy of Science Part A 60:70-81.
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Substance and Independence in Descartes.Anat Schechtman - 2016 - Philosophical Review 125 (2):155-204.
    Descartes notoriously characterizes substance in two ways: first, as an ultimate subject of properties ; second, as an independent entity. The characterizations have appeared to many to diverge on the definition as well as the scope of the notion of substance. For it is often thought that the ultimate subject of properties need not—and, in some cases, cannot—be independent. Drawing on a suite of historical, textual, and philosophical considerations, this essay argues for an interpretation that reconciles Descartes's two characterizations. It (...)
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  • The Hypercategorematic Infinite.Maria Rosa Antognazza - 2015 - The Leibniz Review 25:5-30.
    This paper aims to show that a proper understanding of what Leibniz meant by “hypercategorematic infinite” sheds light on some fundamental aspects of his conceptions of God and of the relationship between God and created simple substances or monads. After revisiting Leibniz’s distinction between (i) syncategorematic infinite, (ii) categorematic infinite, and (iii) actual infinite, I examine his claim that the hypercategorematic infinite is “God himself” in conjunction with other key statements about God. I then discuss the issue of whether the (...)
    Download  
     
    Export citation  
     
    Bookmark   12 citations  
  • Confessions.R. S. Augustine & Pine-Coffin - 2019 - Hackett Publishing Company.
    "Williams's masterful translation satisfies (at last!) a long-standing need. There are lots of good translations of Augustine's great work, but until now we have been forced to choose between those that strive to replicate in English something of the majesty and beauty of Augustine's Latin style and those that opt instead to convey the careful precision of his philosophical terminology and argumentation. Finally, Williams has succeeded in capturing both sides of Augustine's mind in a richly evocative, impeccably reliable, elegantly readable (...)
    Download  
     
    Export citation  
     
    Bookmark   168 citations  
  • Leibniz's Philosophy of Logic and Language.Hideko Ishiguro - 1974 - Philosophy East and West 24 (3):376-378.
    Download  
     
    Export citation  
     
    Bookmark   65 citations  
  • To a reader voyaging through the Meditations for the first time, Descartes' proofs for the existence of God can seem daunting, especially the argument of Meditation III, with its appeal to causal principles that seem arcane, and to medieval doctrines about different modes of being and degrees of reality. First-time readers are not alone in feeling bewildered. Many commentators have had the same reaction. In an attempt at charity, some of them have tried to tame the complexity of Descartes' discussion by .. [REVIEW]Lawrence Nolan & Alan Nelson - 2006 - In Stephen Gaukroger (ed.), The Blackwell Guide to Descartes' Meditations. Wiley-Blackwell. pp. 2--104.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Locke’s Newtonianism and Lockean Newtonianism.Lisa J. Downing - 1997 - Perspectives on Science 5 (3):285-310.
    I explore Locke’s complex attitude toward the natural philosophy of his day by focusing on Locke’s own treatment of Newton’s theory of gravity and the presence of Lockean themes in defenses of Newtonian attraction/gravity by Maupertuis and other early Newtonians. In doing so, I highlight the inadequacy of an unqualified labeling of Locke as “mechanist” or “Newtonian.”.
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  • Proofs for the Existence of God.Lawrence Nolan & Alan Nelson - 2006 - In Lawrence Nolan & Alan Nelson (eds.), Proofs for the Existence of God. Blackwell. pp. 104--121.
    We argue that Descartes’s theistic proofs in the ’Meditations’ are much simpler and straightforward than they are traditionally taken to be. In particular, we show how the causal argument of the "Third Meditation" depends on the intuitively innocent principle that nothing comes from nothing, and not on the more controversial principle that the objective reality of an idea must have a cause with at least as much formal reality. We also demonstrate that the so-called ontological "argument" of the "Fifth Meditation" (...)
    Download  
     
    Export citation  
     
    Bookmark   11 citations  
  • Leibniz on Infinite Number, Infinite Wholes, and the Whole World.Richard Arthur - 2001 - The Leibniz Review 11:103-116.
    Reductio arguments are notoriously inconclusive, a fact which no doubt contributes to their great fecundity. For once a contradiction has been proved, it is open to interpretation which premise should be given up. Indeed, it is often a matter of great creativity to identify what can be consistently given up. A case in point is a traditional paradox of the infinite provided by Galileo Galilei in his Two New Sciences, which has since come to be known as Galileo’s Paradox. It (...)
    Download  
     
    Export citation  
     
    Bookmark   12 citations  
  • A Tale of Two Thinkers, One Meeting, and Three Degrees of Infinity: Leibniz and Spinoza (1675–8).Ohad Nachtomy - 2011 - British Journal for the History of Philosophy 19 (5):935-961.
    The article presents Leibniz's preoccupation (in 1675?6) with the difference between the notion of infinite number, which he regards as impossible, and that of the infinite being, which he regards as possible. I call this issue ?Leibniz's Problem? and examine Spinoza's solution to a similar problem that arises in the context of his philosophy. ?Spinoza's solution? is expounded in his letter on the infinite (Ep.12), which Leibniz read and annotated in April 1676. The gist of Spinoza's solution is to distinguish (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • John Locke and natural philosophy.Peter R. Anstey - 2011 - New York: Oxford University Press.
    Peter Anstey presents a thorough and innovative study of John Locke's views on the method and content of natural philosophy. Focusing on Locke's Essay concerning Human Understanding, but also drawing extensively from his other writings and manuscript remains, Anstey argues that Locke was an advocate of the Experimental Philosophy: the new approach to natural philosophy championed by Robert Boyle and the early Royal Society who were opposed to speculative philosophy. On the question of method, Anstey shows how Locke's pessimism about (...)
    Download  
     
    Export citation  
     
    Bookmark   22 citations  
  • Locke and the Intuitionist Theory of Number.Richard Aaron & Philip Walters - 1965 - Philosophy 40 (153):197 - 206.
    The Purpose of this paper is to ask how far Locke can be said to have anticipated modern theories of number, particularly the intuitionist theory of Brouwer and Heyting. It has in mind Mr Edward E. Dawson's statement that Locke's account of number was not merely ‘a good effort in his own day’ but that ‘what Locke had to say really was quite fundamental, and a good deal of modern mathematics assumes his position, either explicitly or implicitly’. Mr Dawson thinks (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • The Principia: Mathematical Principles of Natural Philosophy.Isaac Newton - 1999 - University of California Press.
    Presents Newton's unifying idea of gravitation and explains how he converted physics from a science of explanation into a general mathematical system.
    Download  
     
    Export citation  
     
    Bookmark   198 citations  
  • General scholium.Isaac Newton - 1999 - In The Principia: Mathematical Principles of Natural Philosophy. University of California Press. pp. 939-944.
    Download  
     
    Export citation  
     
    Bookmark   129 citations  
  • Totality and infinity: an essay on exteriority.Emmanuel Levinas - 1961 - Hingham, MA: distribution for the U.S. and Canada, Kluwer Boston.
    INTRODUCTION Ever since the beginning of the modern phenomenological movement disciplined attention has been paid to various patterns of human experience as ...
    Download  
     
    Export citation  
     
    Bookmark   439 citations  
  • Philosophy of mathematics and mathematical practice in the seventeenth century.Paolo Mancosu (ed.) - 1996 - New York: Oxford University Press.
    The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmatic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting with (...)
    Download  
     
    Export citation  
     
    Bookmark   94 citations  
  • The philosophical writings of Descartes.René Descartes - 1984 - New York: Cambridge University Press.
    Volumes I and II provided a completely new translation of the philosophical works of Descartes, based on the best available Latin and French texts. Volume III contains 207 of Descartes' letters, over half of which have previously not been translated into English. It incorporates, in its entirety, Anthony Kenny's celebrated translation of selected philosophical letters, first published in 1970. In conjunction with Volumes I and II it is designed to meet the widespread demand for a comprehensive, authoritative and accurate edition (...)
    Download  
     
    Export citation  
     
    Bookmark   435 citations  
  • Leibniz on mathematics and the actually infinite division of matter.Samuel Levey - 1998 - Philosophical Review 107 (1):49-96.
    Mathematician and philosopher Hermann Weyl had our subject dead to rights.
    Download  
     
    Export citation  
     
    Bookmark   38 citations  
  • Locke and Descartes.Lisa Downing - 2015 - In Matthew Stuart (ed.), A Companion to Locke. Chichester, West Sussex, UK: Blackwell. pp. 100–120.
    In this chapter, John Locke's anti‐Cartesian stances on the difference between body and space, on whether the soul always thinks, on the possibility of thinking matter, all connect back to the basic opposition to Cartesian overreaching in regard to essences. The chapter presents a summary of Locke's anti‐Cartesianism, which seems to fit with his own representation of his Cartesian inheritance, which, notoriously, is that it is minimal, consisting only in anti‐scholasticism. The only acknowledgment that Locke wishes to give Descartes is (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Cavalieri's method of indivisibles.Kirsti Andersen - 1985 - Archive for History of Exact Sciences 31 (4):291-367.
    Download  
     
    Export citation  
     
    Bookmark   13 citations  
  • The Ontic and the Iterative: Descartes on the Infinite and the Indefinite.Anat Schechtman - 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 (eds.), Infinity in Early Modern Philosophy. Cham: Springer Verlag. pp. 27-44.
    Descartes’s metaphysics posits a sharp distinction between two types of non-finitude, or unlimitedness: whereas God alone is infinite, numbers, space, and time are indefinite. The distinction has proven difficult to interpret in a way that abides by the textual evidence and conserves the theoretical roles that the distinction plays in Descartes’s philosophy—in particular, the important role it plays in the causal proof for God’s existence in the Meditations. After formulating the interpretive task, I criticize extant interpretations of the distinction. I (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Locke and Newton on Space and Time and Their Sensible Measures.Edward Slowik & Geoffrey Gorham - 2014 - In Zvi Biener Eric Schliesser (ed.), Newton and Empiricism. New York: Oxford University Press USA. pp. 119-137.
    It is well-known that Isaac Newton’s conception of space and time as absolute -- “without reference to anything external” (Principia, 408) -- was anticipated, and probably influenced, by a number of figures among the earlier generation of seventeenth century natural philosophers, including Pierre Gassendi, Henry More, and Newton’s own teacher Isaac Barrow. The absolutism of Newton’s contemporary and friend, John Locke, has received much less attention, which is unfortunate for several reasons. First, Locke’s views of space and time undergo a (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • On infinite size.Bruno Whittle - 2015 - Oxford Studies in Metaphysics 9:3-19.
    This chapter challenges Cantor’s notion of the ‘power’, or ‘cardinality’, of an infinite set. According to Cantor, two infinite sets have the same cardinality if and only if there is a one-to-one correspondence between them. Cantor showed that there are infinite sets that do not have the same cardinality in this sense. Further, he took this result to show that there are infinite sets of different sizes. This has become the standard understanding of the result. The chapter challenges this, arguing (...)
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  • Galileo and Leibniz: Different Approaches to Infinity.Eberhard Knobloch - 1999 - Archive for History of Exact Sciences 54 (2):87-99.
    Download  
     
    Export citation  
     
    Bookmark   10 citations  
  • All or Nothing. Systematicity, Transcendental Arguments, and Scepticism in German Idealism.Paul W. Franks - 2006 - Tijdschrift Voor Filosofie 68 (3):616-619.
    Download  
     
    Export citation  
     
    Bookmark   70 citations  
  • New Essays on Human Understanding.G. W. Leibniz - 1981 - Tijdschrift Voor Filosofie 45 (3):489-490.
    Download  
     
    Export citation  
     
    Bookmark   168 citations  
  • Mind-Body Interaction and Metaphysical Consistency: A Defense of Descartes.Eileen O' Neill - 1987 - Journal of the History of Philosophy 25 (2):227.
    Download  
     
    Export citation  
     
    Bookmark   16 citations  
  • From the closed world to the infinite universe.A. Koyré - 1957 - Revue Philosophique de la France Et de l'Etranger 148:101-102.
    Download  
     
    Export citation  
     
    Bookmark   116 citations  
  • The Infinite.A. W. MOORE - 1990 - Revue Philosophique de la France Et de l'Etranger 182 (3):355-357.
    Download  
     
    Export citation  
     
    Bookmark   48 citations  
  • Infinity, an essay in metaphysics. [REVIEW]R. Blanché - 1964 - Revue Philosophique de la France Et de l'Etranger 156:502-503.
    Download  
     
    Export citation  
     
    Bookmark   29 citations  
  • From the Closed World to the Infinite Universe.[author unknown] - 1958 - British Journal for the Philosophy of Science 9 (35):234-245.
    Download  
     
    Export citation  
     
    Bookmark   34 citations  
  • Leibniz's Philosophy of Logic and Language.L. E. Loemker - 1974 - Philosophical Quarterly 24 (95):170-172.
    Download  
     
    Export citation  
     
    Bookmark   13 citations  
  • The Leibniz-Des Bosses Correspondence. [REVIEW]Philip Beeley - 2008 - The Leibniz Review 18:193-204.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Who’s Afraid of Infinite Numbers?Gregory Brown - 1998 - The Leibniz Review 8:113-125.
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  • Leibniz on Infinite Number, Infinite Wholes, and the Whole World.Richard Arthur - 2001 - The Leibniz Review 11:103-116.
    Reductio arguments are notoriously inconclusive, a fact which no doubt contributes to their great fecundity. For once a contradiction has been proved, it is open to interpretation which premise should be given up. Indeed, it is often a matter of great creativity to identify what can be consistently given up. A case in point is a traditional paradox of the infinite provided by Galileo Galilei in his Two New Sciences, which has since come to be known as Galileo’s Paradox. It (...)
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  • The Labyrinth of the Continuum: Writings on the Continuum Problem, 1672-1686.G. W. Leibniz - 2001
    Download  
     
    Export citation  
     
    Bookmark   19 citations  
  • Infinity and Continuity in Ancient and Medieval Thought.John Longeway - 1985 - Philosophical Review 94 (2):263.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • New Essays on Human Understanding.R. M. Mattern - 1984 - Philosophical Review 93 (2):315.
    Download  
     
    Export citation  
     
    Bookmark   119 citations  
  • Leibniz's Philosophy of Logic and Language.Fabrizio Mondadori & Hide Ishiguro - 1975 - Philosophical Review 84 (1):140.
    Download  
     
    Export citation  
     
    Bookmark   20 citations  
  • An Essay Concerning Human Understanding.H. R. Smart - 1925 - Philosophical Review 34 (4):413.
    Download  
     
    Export citation  
     
    Bookmark   78 citations  
  • The Leibniz-Des Bosses Correspondence.Philip Beeley - 2008 - The Leibniz Review 18:193-204.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Leibniz on Wholes, Unities, and Infinite Number.Gregory Brown - 2000 - The Leibniz Review 10:21-51.
    One argument that Leibniz employed to rule out the possibility of a world soul appears to turn on the assumption that the very notion of an infinite number or of an infinite whole is inconsistent. This argument was considered in a series of three papers published in The Leibniz Review: in the first, by Laurence Carlin, the argument was delineated and analyzed; in the second, by myself, the argument was criticized and rejected; in the third, by Richard Arthur, an attempt (...)
    Download  
     
    Export citation  
     
    Bookmark   11 citations