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  1. The Representational Foundations of Computation.Michael Rescorla - 2015 - Philosophia Mathematica 23 (3):338-366.
    Turing computation over a non-linguistic domain presupposes a notation for the domain. Accordingly, computability theory studies notations for various non-linguistic domains. It illuminates how different ways of representing a domain support different finite mechanical procedures over that domain. Formal definitions and theorems yield a principled classification of notations based upon their computational properties. To understand computability theory, we must recognize that representation is a key target of mathematical inquiry. We must also recognize that computability theory is an intensional enterprise: it (...)
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  • Posséder un concept selon Peacocke.Martin Montminy - 2001 - Dialogue 40 (2):219-.
    ABSTRACT: Christopher Peacocke defends a sophisticated version of Conceptual Role Theory. For him, the nature of a concept is completely determined by an account of what it is to possess that concept. The possession conditions he puts forward rest on the notion of primitively compelling transitions or, more recently, on the idea of implicit conceptions. I show that his account is circular and appeals to a dubious distinction between constitutive transitions and transitions that depend on factual beliefs. I also point (...)
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  • Incomplete understanding of complex numbers Girolamo Cardano: a case study in the acquisition of mathematical concepts.Denis Buehler - 2014 - Synthese 191 (17):4231-4252.
    In this paper, I present the case of the discovery of complex numbers by Girolamo Cardano. Cardano acquires the concepts of (specific) complex numbers, complex addition, and complex multiplication. His understanding of these concepts is incomplete. I show that his acquisition of these concepts cannot be explained on the basis of Christopher Peacocke’s Conceptual Role Theory of concept possession. I argue that Strong Conceptual Role Theories that are committed to specifying a set of transitions that is both necessary and sufficient (...)
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  • Posséder un concept selon Peacocke.Martin Montminy - 2001 - Dialogue 40 (2):219-240.
    ABSTRACT: Christopher Peacocke defends a sophisticated version of Conceptual Role Theory. For him, the nature of a concept is completely determined by an account of what it is to possess that concept. The possession conditions he puts forward rest on the notion of primitively compelling transitions or, more recently, on the idea of implicit conceptions. I show that his account is circular and appeals to a dubious distinction between constitutive transitions and transitions that depend on factual beliefs. I also point (...)
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