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  1. Frameworks, models, and case studies: a new methodology for studying conceptual change in science and philosophy.Matteo De Benedetto - 2022 - Dissertation, Ludwig Maximilians Universität, München
    This thesis focuses on models of conceptual change in science and philosophy. In particular, I developed a new bootstrapping methodology for studying conceptual change, centered around the formalization of several popular models of conceptual change and the collective assessment of their improved formal versions via nine evaluative dimensions. Among the models of conceptual change treated in the thesis are Carnap’s explication, Lakatos’ concept-stretching, Toulmin’s conceptual populations, Waismann’s open texture, Mark Wilson’s patches and facades, Sneed’s structuralism, and Paul Thagard’s conceptual revolutions. (...)
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  • Implicit and Explicit Examples of the Phenomenon of Deviant Encodings.Paula Quinon - 2020 - Studies in Logic, Grammar and Rhetoric 63 (1):53-67.
    The core of the problem discussed in this paper is the following: the Church-Turing Thesis states that Turing Machines formally explicate the intuitive concept of computability. The description of Turing Machines requires description of the notation used for the input and for the output. Providing a general definition of notations acceptable in the process of computations causes problems. This is because a notation, or an encoding suitable for a computation, has to be computable. Yet, using the concept of computation, in (...)
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  • The Anti-Mechanist Argument Based on Gödel’s Incompleteness Theorems, Indescribability of the Concept of Natural Number and Deviant Encodings.Paula Quinon - 2020 - Studia Semiotyczne 34 (1):243-266.
    This paper reassesses the criticism of the Lucas-Penrose anti-mechanist argument, based on Gödel’s incompleteness theorems, as formulated by Krajewski : this argument only works with the additional extra-formal assumption that “the human mind is consistent”. Krajewski argues that this assumption cannot be formalized, and therefore that the anti-mechanist argument – which requires the formalization of the whole reasoning process – fails to establish that the human mind is not mechanistic. A similar situation occurs with a corollary to the argument, that (...)
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  • On Algorithms, Effective Procedures, and Their Definitions.Philippos Papayannopoulos - 2023 - Philosophia Mathematica 31 (3):291-329.
    I examine the classical idea of ‘algorithm’ as a sequential, step-by-step, deterministic procedure (i.e., the idea of ‘algorithm’ that was already in use by the 1930s), with respect to three themes, its relation to the notion of an ‘effective procedure’, its different roles and uses in logic, computer science, and mathematics (focused on numerical analysis), and its different formal definitions proposed by practitioners in these areas. I argue that ‘algorithm’ has been conceptualized and used in contrasting ways in the above (...)
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  • Vienna circle.Thomas Uebel - 2008 - Stanford Encyclopedia of Philosophy.
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  • Cognitive Structuralism: Explaining the Regularity of the Natural Numbers Progression.Paula Quinon - 2022 - Review of Philosophy and Psychology 13 (1):127-149.
    According to one of the most powerful paradigms explaining the meaning of the concept of natural number, natural numbers get a large part of their conceptual content from core cognitive abilities. Carey’s bootstrapping provides a model of the role of core cognition in the creation of mature mathematical concepts. In this paper, I conduct conceptual analyses of various theories within this paradigm, concluding that the theories based on the ability to subitize (i.e., to assess anexactquantity of the elements in a (...)
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