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Propositions as Intentions

Husserl Studies 39 (2):143-160 (2023)

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  1. Die intuitionistische grundlegung der mathematik.Arend Heyting - 1931 - Erkenntnis 2 (1):106-115.
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  • La conception intuitionniste de la logique.A. Heyting - 1956 - Les Etudes Philosophiques 11 (2):226 - 233.
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  • Intuitionism and Formalism.L. E. J. Brouwer - 1913 - Bulletin of the American Mathematical Society 20:81-96.
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  • On the meanings of the logical constants and the justifications of the logical laws.Per Martin-Löf - 1996 - Nordic Journal of Philosophical Logic 1 (1):11-60.
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  • The Philosophical Basis of Intuitionistic Logic.Michael Dummett - 1978 - In Truth and other enigmas. Cambridge: Harvard University Press. pp. 215--247.
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  • Experience and judgment: investigations in a genealogy of logic.Edmund Husserl - 1973 - London: Routledge and Kegan Paul. Edited by Ludwig Landgrebe.
    This volume provides an articulate restatement of many of the themes of Husserlian phenomenology.
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  • Logical Investigations.Edmund Husserl - 1970 - London, England: Routledge. Edited by Dermot Moran.
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  • Construction and Constitution in Mathematics.Mark van Atten - 2010 - New Yearbook for Phenomenology and Phenomenological Philosophy 10 (1):43-90.
    In the following, I argue that L. E. J. Brouwer's notion of the construction of purely mathematical objects and Edmund Husserl's notion of their constitution coincide.
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  • Mathematical intuition and Husserl's phenomenology.Richard Tieszen - 1984 - Noûs 18 (3):395-421.
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  • Constructions, proofs and the meaning of logical constants.Göran Sundholm - 1983 - Journal of Philosophical Logic 12 (2):151 - 172.
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  • The cognitive act and the first-person perspective: an epistemology for constructive type theory.Maria van der Schaar - 2011 - Synthese 180 (3):391 - 417.
    The notion of cognitive act is of importance for an epistemology that is apt for constructive type theory, and for epistemology in general. Instead of taking knowledge attributions as the primary use of the verb 'to know' that needs to be given an account of, and understanding a first-person knowledge claim as a special case of knowledge attribution, the account of knowledge that is given here understands first-person knowledge claims as the primary use of the verb 'to know'. This means (...)
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  • Logical Investigations.Edmund Husserl & J. N. Findlay - 1972 - Journal of Philosophy 69 (13):384-398.
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  • Logical investigations.Edmund Husserl - 2000 - New York: Routledge. Edited by Dermot Moran.
    Edmund Husserl is the founder of phenomenology. The Logical Investigations is Edmund Husserl's most famous work and has had a decisive impact on the direction of twentieth century philosophy. This is the first time both volumes of this classic work, translated by J.N. Findlay, have been available in paperback. They include a new introduction by Dermot Moran, placing the Logical Investigations in historical context and bringing out its importance for contemporary philosophy.
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  • Formal and transcendental logic.Edmund Husserl - 1969 - The Hague,: Martinus Nijhoff.
    Science in a new sense arises in the first instance from Plato's establishing of logic, as a place for exploring the essential requirements of "genuine" ...
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  • Formal and Transcendental Logic.Edmund Husserl, Dorion Cairns, Suzanne Bachelard & Lester E. Embree - 1971 - Philosophical Review 80 (2):267-273.
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  • Brouwer's Cambridge lectures on intuitionism.Luitzen Egbertus Jan Brouwer - 1981 - New York: Cambridge University Press. Edited by D. van Dalen.
    Luitzen Egburtus Jan Brouwer founded a school of thought whose aim was to include mathematics within the framework of intuitionistic philosophy; mathematics was to be regarded as an essentially free development of the human mind. What emerged diverged considerably at some points from tradition, but intuitionism has survived well the struggle between contending schools in the foundations of mathematics and exact philosophy. Originally published in 1981, this monograph contains a series of lectures dealing with most of the fundamental topics such (...)
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  • Intuitionism in the Philosophy of Mathematics: Introducing a Phenomenological Account.Philipp Berghofer - 2020 - Philosophia Mathematica 28 (2):204-235.
    The aim of this paper is to establish a phenomenological mathematical intuitionism that is based on fundamental phenomenological-epistemological principles. According to this intuitionism, mathematical intuitions are sui generis mental states, namely experiences that exhibit a distinctive phenomenal character. The focus is on two questions: what does it mean to undergo a mathematical intuition and what role do mathematical intuitions play in mathematical reasoning? While I crucially draw on Husserlian principles and adopt ideas we find in phenomenologically minded mathematicians such as (...)
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  • Construction and Constitution in Mathematics.Mark Atten - 2017 - In Stefania Centrone (ed.), Essays on Husserl’s Logic and Philosophy of Mathematics. Dordrecht, Netherland: Springer Verlag.
    I argue that Brouwer’s notion of the construction of purely mathematical objects and Husserl’s notion of their constitution by the transcendental subject coincide. Various objections to Brouwer’s intuitionism that have been raised in recent phenomenological literature are addressed. Then I present objections to Gödel’s project of founding classical mathematics on transcendental phenomenology. The problem for that project lies not so much in Husserl’s insistence on the spontaneous character of the constitution of mathematical objects, or in his refusal to allow an (...)
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  • Constructivism in mathematics: an introduction.A. S. Troelstra - 1988 - New York, N.Y.: Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.. Edited by D. van Dalen.
    Provability, Computability and Reflection.
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  • Husserl on axiomatization and arithmetic.Claire Ortiz Hill - 2010 - In Mirja Hartimo (ed.), Phenomenology and mathematics. London: Springer.
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  • The proper explanation of intuitionistic logic: on Brouwer's demonstration of the Bar Theorem.Mark Van Atten & Göran Sundholm - unknown
    Brouwer's demonstration of his Bar Theorem gives rise to provocative questions regarding the proper explanation of the logical connectives within intuitionistic and constructivist frameworks, respectively, and, more generally, regarding the role of logic within intuitionism. It is the purpose of the present note to discuss a number of these issues, both from an historical, as well as a systematic point of view.
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  • Mathematics and Its Applications, A Transcendental-Idealist Perspective.Jairo José da Silva - 2017 - Cham: Springer.
    This monograph offers a fresh perspective on the applicability of mathematics in science. It explores what mathematics must be so that its applications to the empirical world do not constitute a mystery. In the process, readers are presented with a new version of mathematical structuralism. The author details a philosophy of mathematics in which the problem of its applicability, particularly in physics, in all its forms can be explained and justified. Chapters cover: mathematics as a formal science, mathematical ontology: what (...)
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  • The correspondence between Oskar Becker and Arend Heyting.Mark van Atten - 2005 - In Volker Peckhaus (ed.), Oskar Becker und die Philosophie der Mathematik. Wilhelm Fink Verlag. pp. 119-142.
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  • Brouwer meets Husserl. On the Phenomenology of Choice Sequences.Mark van Atten (ed.) - 2006 - Springer.
    Can the straight line be analysed mathematically such that it does not fall apart into a set of discrete points, as is usually done but through which its fundamental continuity is lost? And are there objects of pure mathematics that can change through time? The mathematician and philosopher L.E.J. Brouwer argued that the two questions are closely related and that the answer to both is "yes''. To this end he introduced a new kind of object into mathematics, the choice sequence. (...)
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  • Ideas: General Introduction to Pure Phenomenology.Edmund Husserl - 1931 - New York: Routledge. Edited by William Ralph Boyce Gibson.
    First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.
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  • Philosophy of Arithmetic: Psychological and Logical Investigations - with Supplementary Texts from 1887-1901.Edmund Husserl - 2003 - Springer Verlag.
    This volume is a window on a period of rich and illuminating philosophical activity that has been rendered generally inaccessible by the supposed "revolution" attributed to "Analytic Philosophy" so-called. Careful exposition and critique is given to every serious alternative account of number and number relations available at the time.
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  • Mathematical Intuition: Phenomenology and Mathematical Knowledge.Richard L. Tieszen - 1989 - Dordrecht/Boston/London: Kluwer Academic Publishers.
    "Intuition" has perhaps been the least understood and the most abused term in philosophy. It is often the term used when one has no plausible explanation for the source of a given belief or opinion. According to some sceptics, it is understood only in terms of what it is not, and it is not any of the better understood means for acquiring knowledge. In mathematics the term has also unfortunately been used in this way. Thus, intuition is sometimes portrayed as (...)
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  • General introduction to a pure phenomenology.Edmund Husserl - 1982 - Hingham, MA, USA: Distributors for the U.S. and Canada, Kluwer Boston.
    the Logische Untersuchungen,l phenomenology has been conceived as a substratum of empirical psychology, as a sphere comprising "imma nental" descriptions of psychical mental processes, a sphere compris ing descriptions that - so the immanence in question is understood - are strictly confined within the bounds of internal experience. It 2 would seem that my protest against this conception has been oflittle avail; and the added explanations, which sharply pinpointed at least some chief points of difference, either have not been understood (...)
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  • On Brouwer.Mark van Atten - 2004 - Wadsworth Publishing Company.
    ON BROUWER, like other titles in the Wadsworth Philosopher's Series, offers a concise, yet comprehensive, introduction to this philosopher's most important ideas. Presenting the most important insights of well over a hundred seminal philosophers in both the Eastern and Western traditions, the Wadsworth Philosophers Series contains volumes written by scholars noted for their excellence in teaching and for their well-versed comprehension of each featured philosopher's major works and contributions. These titles have proven valuable in a number of ways. Serving as (...)
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  • Mathematical Intuition: Phenomenology and Mathematical Knowledge.Richard L. TIESZEN - 1993 - Studia Logica 52 (3):484-486.
    The thesis is a study of the notion of intuition in the foundations of mathematics which focuses on the case of natural numbers and hereditarily finite sets. Phenomenological considerations are brought to bear on some of the main objections that have been raised to this notion. ;Suppose that a person P knows that S only if S is true, P believes that S, and P's belief that S is produced by a process that gives evidence for it. On a phenomenological (...)
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  • Historical introduction and fundamental notions.L. E. J. Brouwer - 1981 - In D. van Dalen (ed.), Brouwer’s Cambridge Lectures on Intuitionism. Cambridge University Press. pp. 1–20.
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  • Consciousness, philosophy and mathematics.L. E. J. Brouwer - 1975 - In A. Heyting (ed.), L. E. J. Brouwer Collected Works Vol. I: Philosophy and Foundations of Mathematics. North-Holland Publishing. pp. 480–494.
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  • Arend Heyting and Phenomenology: Is the Meeting Feasible?Miriam Franchella - 2007 - Bulletin d'Analyse Phénoménologique (2).
    La littérature témoigne d’une tendance croissante à soutenir l’intuitionisme par la phénoménologie. Le disciple de Brouwer Arend Heyting est considéré comme un précurseur de cette tendance, parce qu’il usait d’une terminologie phénoménologique en vue de définir la négation intuitioniste, en élaborant la première logique intuitioniste. Dans cet article, l’auteur tente d’explorer — en référence aux matériaux inédits conservés aux Archives Heyting — ce qui, dans la pensée de Heyting, est compatible avec la phénoménologie. Dans la conclusion, l’auteur suggère que Heyting (...)
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  • Experience and Judgment.Edmund Husserl, L. Landgrebe, J. S. Churchill & K. Ameriks - 1973 - Tijdschrift Voor Filosofie 39 (4):712-713.
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  • Experience and Judgment: Investigations in a Genealogy of Logic.Edmund Husserl, James S. Churchill & Karl Ameriks - 1981 - Human Studies 4 (3):279-297.
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  • Consciousness, Philosophy, and Mathematics.L. E. J. Brouwer - 1949 - Proceedings of the Tenth International Congress of Philosophy 2:1235-1249.
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