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  1. Intuitionistic logic versus paraconsistent logic. Categorical approach.Mariusz Kajetan Stopa - 2023 - Dissertation, Jagiellonian University
    The main research goal of the work is to study the notion of co-topos, its correctness, properties and relations with toposes. In particular, the dualization process proposed by proponents of co-toposes has been analyzed, which transforms certain Heyting algebras of toposes into co-Heyting ones, by which a kind of paraconsistent logic may appear in place of intuitionistic logic. It has been shown that if certain two definitions of topos are to be equivalent, then in one of them, in the context (...)
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  • Esbozo de una concepción particularista de las Leyes Lógicas.Miguel Agustín Álvarez Lisboa - 2021 - Culturas Cientificas 2 (1):04-22.
    El Anti-Excepcionalismo Lógico afirma que la Lógica es como cualquier otra ciencia. Si esta afirmación es cierta, entonces ella no sólo es revisable, sino que además todo lo que se puede decir sobre las ciencias aplica, mutatis mutandis, para la misma. El propósito de este artículo es explorar esta consecuencia del Anti-Excepcionalismo Lógico, acercando a la Filosofía de la Lógica el marco teórico de las Máquinas Nomológicas de Nancy Cartwright. De acuerdo con esta visión, lo que hay de verdadero en (...)
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  • Connecting the revolutionary with the conventional: Rethinking the differences between the works of Brouwer, Heyting, and Weyl.Kati Kish Bar-On - 2023 - Philosophy of Science 90 (3):580–602.
    Brouwer’s intuitionism was a far-reaching attempt to reform the foundations of mathematics. While the mathematical community was reluctant to accept Brouwer’s work, its response to later-developed brands of intuitionism, such as those presented by Hermann Weyl and Arend Heyting, was different. The paper accounts for this difference by analyzing the intuitionistic versions of Brouwer, Weyl, and Heyting in light of a two-tiered model of the body and image of mathematical knowledge. Such a perspective provides a richer account of each story (...)
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  • The Methodological Roles of Tolerance and Conventionalism in the Philosophy of Mathematics: Reconsidering Carnap's Logic of Science.Emerson P. Doyle - 2014 - Dissertation, University of Western Ontario
    This dissertation makes two primary contributions. The first three chapters develop an interpretation of Carnap's Meta-Philosophical Program which places stress upon his methodological analysis of the sciences over and above the Principle of Tolerance. Most importantly, I suggest, is that Carnap sees philosophy as contiguous with science—as a part of the scientific enterprise—so utilizing the very same methods and subject to the same limitations. I argue that the methodological reforms he suggests for philosophy amount to philosophy as the explication of (...)
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  • Logic, Logicism, and Intuitions in Mathematics.Besim Karakadılar - 2001 - Dissertation, Middle East Technical University
    In this work I study the main tenets of the logicist philosophy of mathematics. I deal, basically, with two problems: (1) To what extent can one dispense with intuition in mathematics? (2) What is the appropriate logic for the purposes of logicism? By means of my considerations I try to determine the pros and cons of logicism. My standpoint favors the logicist line of thought. -/- .
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  • Brouwer, as never read by Husserl.Mark van Atten - 2003 - Synthese 137 (1-2):3-19.
    Even though Husserl and Brouwer have never discussed each other's work, ideas from Husserl have been used to justify Brouwer's intuitionistic logic. I claim that a Husserlian reading of Brouwer can also serve to justify the existence of choice sequences as objects of pure mathematics. An outline of such a reading is given, and some objections are discussed.
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  • An intuitionistic interpretation of Bishop’s philosophy.Bruno Bentzen - 2024 - Philosophia Mathematica 32 (3):307-331.
    The constructive mathematics developed by Bishop in Foundations of Constructive Analysis succeeded in gaining the attention of mathematicians, but discussions of its underlying philosophy are still rare in the literature. Commentators seem to conclude, from Bishop’s rejection of choice sequences and his severe criticism of Brouwerian intuitionism, that he is not an intuitionist–broadly understood as someone who maintains that mathematics is a mental creation, mathematics is meaningful and eludes formalization, mathematical objects are mind-dependent constructions given in intuition, and mathematical truths (...)
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  • What is Intuitionistic Arithmetic?V. Alexis Peluce - 2024 - Erkenntnis 89 (8):3351-3376.
    L.E.J. Brouwer famously took the subject’s intuition of time to be foundational and from there ventured to build up mathematics. Despite being largely critical of formal methods, Brouwer valued axiomatic systems for their use in both communication and memory. Through the Dutch Mathematical Society, Gerrit Mannoury posed a challenge in 1927 to provide an axiomatization of intuitionistic arithmetic. Arend Heyting’s 1928 axiomatization was chosen as the winner and has since enjoyed the status of being the _de facto_ formalization of intuitionistic (...)
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  • Anti-exceptionalism and methodological pluralism in logic.Diego Tajer - 2022 - Synthese 200 (3):1-21.
    According to methodological anti-exceptionalism, logic follows a scientific methodology. There has been some discussion about which methodology logic has. Authors such as Priest, Hjortland and Williamson have argued that logic can be characterized by an abductive methodology. We choose the logical theory that behaves better under a set of epistemic criteria. In this paper, I analyze some important discussions in the philosophy of logic, and I show that they presuppose different methodologies, involving different notions of evidence and different epistemic values. (...)
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  • Logics and Falsifications: A New Perspective on Constructivist Semantics.Andreas Kapsner - 2014 - Cham, Switzerland: Springer.
    This volume examines the concept of falsification as a central notion of semantic theories and its effects on logical laws. The point of departure is the general constructivist line of argument that Michael Dummett has offered over the last decades. From there, the author examines the ways in which falsifications can enter into a constructivist semantics, displays the full spectrum of options, and discusses the logical systems most suitable to each one of them. While the idea of introducing falsifications into (...)
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  • Brouwer’s Notion of ‘Egoicity’.Ivan Restović - 2022 - Axiomathes 32 (1):83-100.
    According to Brouwer’s ‘theory of the exodus of consciousness’, our experience includes ‘egoicity’, a distinct kind of feeling. In this paper, we describe his phenomenology in order to explore and elaborate on the notion of egoic sensations. In the world of perception formed from sensations, some of them are, Brouwer claims, not completely separated or ‘estranged’ from the subject, which is to say they have a certain degree of egoicity. We claim this phenomenon can be explained in terms of the (...)
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  • The proper explanation of intuitionistic logic: on Brouwer's demonstration of the Bar Theorem.Mark van Atten & Göran Sundholm - 2008 - In Mark van Atten, Pascal Boldini, Michel Bourdeau & Gerhard Heinzmann (eds.), One Hundred Years of Intuitionism : The Cerisy Conference. Birkhäuser Basel. pp. 60-77.
    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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  • Pidiendo un Harry en su contexto.Miguel Alvarez Lisboa & Carlo Apablaza Ávila - 2022 - Análisis Filosófico 42 (1):145-169.
    El Problema de la Adopción afirma que ciertas leyes lógicas no pueden ser adoptadas. El argumento constituye un desafío al antiexcepcionalismo lógico, en la medida en que este último debe poder justificar su afirmación de que la teoría lógica en ejercicio puede revisarse. El propósito de este artículo es responder al desafío, utilizando como unidad de análisis el concepto de Taxonomía Lexical propuesto por Kuhn. Como mostraremos, una visión sociológicamente enriquecida de las teorías científicas y la naturaleza de sus cambios (...)
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  • Dummett's objection to the ontological route to intuitionistic logic: a rejoinder.Mark van Atten - 2022 - Inquiry: An Interdisciplinary Journal of Philosophy 65 (6):725-742.
    ABSTRACT In ‘The philosophical basis of intuitionistic logic’, Michael Dummett discusses two routes towards accepting intuitionistic rather than classical logic in number theory, one meaning-theoretical and the other ontological. He concludes that the former route is open, but the latter is closed. I reconstruct Dummett's argument against the ontological route and argue that it fails. Call a procedure ‘investigative’ if that in virtue of which a true proposition stating its outcome is true exists prior to the execution of that procedure; (...)
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  • Luitzen egbertus Jan Brouwer.Mark van Atten - 2008 - Stanford Encyclopedia of Philosophy.
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  • Does Science Progress Towards Ever Higher Solvability Through Feedbacks Between Insights and Routines?Witold Marciszewski - 2018 - Studia Semiotyczne 32 (2):153-185.
    The affirmative answer to the title question is justified in two ways: logical and empirical. The logical justification is due to Gödel’s discovery that in any axiomatic formalized theory, having at least the expressive power of PA, at any stage of development there must appear unsolvable problems. However, some of them become solvable in a further development of the theory in question, owing to subsequent investigations. These lead to new concepts, expressed with additional axioms or rules. Owing to the so-amplified (...)
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  • L. E. J. Brouwer and Karl Popper: Two Perspectives on Mathematics.Alexander John Naraniecki - 2015 - Cosmos and History 11 (1):239-255.
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  • The irreflexivity of Brouwer's philosophy.Mark van Atten - 2002 - Axiomathes 13 (1):65-77.
    I argue that Brouwer''s general philosophy cannot accountfor itself, and, a fortiori, cannot lend justification tomathematical principles derived from it. Thus it cannot groundintuitionism, the jobBrouwer had intended it to do. The strategy is to ask whetherthat philosophy actually allows for the kind of knowledge thatsuch an account of itself would amount to.
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  • Semiotic Anthropology in Poland.Marcin Brocki - 2007 - Studia Semiotyczne—English Supplement 26:168-183.
    In British and American anthropological literature, the ethnology of Central and Eastern European countries has shared in the plight of descriptions of this part of the world: it was seen as exotic, foreign, remote, a backwater, focused on sideline problems and situated on the periphery of this field of science. This state of affairs has been the case since at least the beginning of the Cold War as the descriptions of the national characters of Eastern Bloc communities, drafted by American (...)
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