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After Thirty Years

Journal of Symbolic Logic 36 (4):674-674 (1971)

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  1. Shaping the Enemy: Foundational Labelling by L.E.J. Brouwer and A. Heyting.Miriam Franchella - 2018 - History and Philosophy of Logic 40 (2):152-181.
    The use of the three labels to denote the three foundational schools of the early twentieth century are now part of literature. Yet, neither their number nor the...
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  • Intuition in Mathematics: from Racism to Pluralism.Miriam Franchella - 2022 - Philosophia 50 (3):1055-1091.
    In the nineteenth and twentieth centuries many mathematicians referred to intuition as the indispensable research tool for obtaining new results. In this essay we will analyse a group of mathematicians who interacted with Luitzen Egbertus Jan Brouwer in order to compare their conceptions of intuition. We will see how to the same word “intuition” very different meanings corresponded: they varied from geometrical vision, to a unitary view of a demonstration, to the perception of time, to the faculty of considering concepts (...)
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  • Constructivity and Computability in Historical and Philosophical Perspective.Jacques Dubucs & Michel Bourdeau (eds.) - 2014 - Dordrecht, Netherland: Springer.
    Ranging from Alan Turing’s seminal 1936 paper to the latest work on Kolmogorov complexity and linear logic, this comprehensive new work clarifies the relationship between computability on the one hand and constructivity on the other. The authors argue that even though constructivists have largely shed Brouwer’s solipsistic attitude to logic, there remain points of disagreement to this day. Focusing on the growing pains computability experienced as it was forced to address the demands of rapidly expanding applications, the content maps the (...)
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  • Péter on Church's Thesis, Constructivity and Computers.Mate Szabo - 2021 - In Liesbeth De Mol, Andreas Weiermann, Florin Manea & David Fernández-Duque (eds.), Connecting with Computability. Proceedings of Computability in Europe. pp. 434-445.
    Abstract The aim of this paper is to take a look at Péter's talk "Rekursivität und Konstruktivität" delivered at the Constructivity in Mathematics Colloquium in 1957, where she challenged Church's Thesis from a constructive point of view. The discussion of her argument and motivations is then connected to her earlier work on recursion theory as well as her later work on theoretical computer science.
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  • Intuitionism, Meaning Theory and Cognition.Richard Tieszen - 2000 - History and Philosophy of Logic 21 (3):179-194.
    Michael Dummett has interpreted and expounded upon intuitionism under the influence of Wittgensteinian views on language, meaning and cognition. I argue against the application of some of these views to intuitionism and point to shortcomings in Dummett's approach. The alternative I propose makes use of recent, post-Wittgensteinian views in the philosophy of mind, meaning and language. These views are associated with the claim that human cognition exhibits intentionality and with related ideas in philosophical psychology. Intuitionism holds that mathematical constructions are (...)
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  • Concepts of Solution and the Finite Element Method: a Philosophical Take on Variational Crimes.Nicolas Fillion & Robert M. Corless - 2019 - Philosophy and Technology 34 (1):129-148.
    Despite being one of the most dependable methods used by applied mathematicians and engineers in handling complex systems, the finite element method commits variational crimes. This paper contextualizes the concept of variational crime within a broader account of mathematical practice by explaining the tradeoff between complexity and accuracy involved in the construction of numerical methods. We articulate two standards of accuracy used to determine whether inexact solutions are good enough and show that, despite violating the justificatory principles of one, the (...)
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