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Mathematical realism and transcendental phenomenological realism

In Mirja Hartimo (ed.), Phenomenology and mathematics. London: Springer. pp. 1--22 (2010)

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  1. Mathematical Objectivity and Husserl’s “Community of Monads”.Noam Cohen - 2022 - Axiomathes 32 (3):971-991.
    This paper argues that the shared intersubjective accessibility of mathematical objects has its roots in a stratum of experience prior to language or any other form of concrete social interaction. On the basis of Husserl’s phenomenology, I demonstrate that intersubjectivity is an essential stratum of the objects of mathematical experience, i.e., an integral part of the peculiar sense of a mathematical object is its common accessibility to any consciousness whatsoever. For Husserl, any experience of an objective nature has as its (...)
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  • Eidetic results in transcendental phenomenology: Against naturalization.Richard Tieszen - 2016 - Phenomenology and the Cognitive Sciences 15 (4):489-515.
    In this paper I contrast Husserlian transcendental eidetic phenomenology with some other views of what phenomenology is supposed to be and argue that, as eidetic, it does not admit of being ‘naturalized’ in accordance with standard accounts of naturalization. The paper indicates what some of the eidetic results in phenomenology are and it links these to the employment of reason in philosophical investigation, as distinct from introspection, emotion or empirical observation. Eidetic phenomenology, unlike cognitive science, should issue in a ‘logic’ (...)
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  • Modalization and demodalization: On the phenomenology of negation.Kyle Banick - forthcoming - European Journal of Philosophy.
    Negation is widely thought to be uniquely captured by the usual extensional Boolean connective in the setting of classical logic. However, there has been recent interest in a modal approach to negation. This essay examines the problem of modal negation with an Husserlian phenomenological lens. I argue that the Husserlian approach to negation contains an ambiguity which points to a pluralism about negation. On this view, negation begins its life as a modal notion with nonclassical properties, and the question of (...)
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  • (1 other version)Toward a Phenomenological Epistemology of Mathematical Logic.Manuel Gustavo Isaac - 2018 - Synthèse: An International Journal for Epistemology, Methodology and Philosophy of Science 195 (2):863-874.
    This paper deals with Husserl’s idea of pure logic as it is coined in the Logical Investigations. First, it exposes the formation of pure logic around a conception of completeness ; then, it presents intentionality as the keystone of such a structuring ; and finally, it provides a systematic reconstruction of pure logic from the semiotic standpoint of intentionality. In this way, it establishes Husserlian pure logic as a phenomenological epistemology of mathematical logic.
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  • (1 other version)Husserl and the Problem of Abstract Objects.George Duke & Peter Woelert - 2015 - Pacific Philosophical Quarterly 97 (1):27-47.
    One major difficulty confronting attempts to clarify the epistemological and ontological status of abstract objects is determining the sense, if any, in which such entities may be characterised as mind and language independent. Our contention is that the tolerant reductionist position of Michael Dummett can be strengthened by drawing on Husserl's mature account of the constitution of ideal objects and mathematical objectivity. According to the Husserlian position we advocate, abstract singular terms pick out weakly mind-independent sedimented meaning-contents. These meaning-contents serve (...)
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  • (1 other version)Exploring conceptual thinking and pure concepts from a first person perspective.Renatus Ziegler & Ulrich Weger - 2018 - Phenomenology and the Cognitive Sciences 2019 (5):947-972.
    Traditionally, conceptual thinking is explored via philosophical analysis or psychological experimentation. We seek to complement these mainstream approaches with the perspective of a first person exploration into pure thinking. To begin with, pure thinking is defined as a process and differentiated from its content, the concepts itself. Pure thinking is an active process and not a series of associative thought-events; we participate in it, we immerse ourselves within its active performance. On the other hand, concepts are also of an experiential (...)
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  • (1 other version)Exploring conceptual thinking and pure concepts from a first person perspective.Renatus Ziegler & Ulrich Weger - 2019 - Phenomenology and the Cognitive Sciences 18 (5):947-972.
    Traditionally, conceptual thinking is explored via philosophical analysis or psychological experimentation. We seek to complement these mainstream approaches with the perspective of a first person exploration into pure thinking. To begin with, pure thinking is defined as a process and differentiated from its content, the concepts itself. Pure thinking is an active process and not a series of associative thought-events; we participate in it, we immerse ourselves within its active performance. On the other hand, concepts are also of an experiential (...)
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  • Husserl on symbolic technologies and meaning-constitution: A critical inquiry.Peter Woelert - 2017 - Continental Philosophy Review 50 (3):289-310.
    This paper reconstructs and critically analyzes Husserl’s philosophical engagement with symbolic technologies—those material artifacts and cultural devices that serve to aid, structure and guide processes of thinking. Identifying and exploring a range of tensions in Husserl’s conception of symbolic technologies, I argue that this conception is limited in several ways, and particularly with regard to the task of accounting for the more constructive role these technologies play in processes of meaning-constitution. At the same time, this paper shows that a critical (...)
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  • Mathematical Problem-Solving and Ontology: An Exercise. [REVIEW]Richard Tieszen - 2010 - Axiomathes 20 (2-3):295-312.
    In this paper the reader is asked to engage in some simple problem-solving in classical pure number theory and to then describe, on the basis of a series of questions, what it is like to solve the problems. In the recent philosophy of mind this “what is it like” question is one way of signaling a turn to phenomenological description. The description of what it is like to solve the problems in this paper, it is argued, leads to several morals (...)
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  • Monads and Mathematics: Gödel and Husserl.Richard Tieszen - 2012 - Axiomathes 22 (1):31-52.
    In 1928 Edmund Husserl wrote that “The ideal of the future is essentially that of phenomenologically based (“philosophical”) sciences, in unitary relation to an absolute theory of monads” (“Phenomenology”, Encyclopedia Britannica draft) There are references to phenomenological monadology in various writings of Husserl. Kurt Gödel began to study Husserl’s work in 1959. On the basis of his later discussions with Gödel, Hao Wang tells us that “Gödel’s own main aim in philosophy was to develop metaphysics—specifically, something like the monadology of (...)
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