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  1. Ancient Greek Mathematical Proofs and Metareasoning.Mario Bacelar Valente - 2024 - In Maria Zack (ed.), Research in History and Philosophy of Mathematics. Annals of the Canadian Society for History and Philosophy of Mathematics. pp. 15-33.
    We present an approach in which ancient Greek mathematical proofs by Hippocrates of Chios and Euclid are addressed as a form of (guided) intentional reasoning. Schematically, in a proof, we start with a sentence that works as a premise; this sentence is followed by another, the conclusion of what we might take to be an inferential step. That goes on until the last conclusion is reached. Guided by the text, we go through small inferential steps; in each one, we go (...)
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  • Degrees of Objectivity? Mathemata and Social Objects.José Ferreirós - 2022 - Topoi 42 (1):199-209.
    A down-to-earth admission of abstract objects can be based on detailed explanation of where the objectivity of mathematics comes from, and how a ‘thin’ notion of object emerges from objective mathematical discourse or practices. We offer a sketch of arguments concerning both points, as a basis for critical scrutiny of the idea that mathematical and social objects are essentially of the same kind—which is criticized. Some authors have proposed that mathematical entities are indeed institutional objects, a product of our collective (...)
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  • Naturalising Mathematics? A Wittgensteinian Perspective.Jan Stam, Martin Stokhof & Michiel Van Lambalgen - 2022 - Philosophies 7 (4):85.
    There is a noticeable gap between results of cognitive neuroscientific research into basic mathematical abilities and philosophical and empirical investigations of mathematics as a distinct intellectual activity. The paper explores the relevance of a Wittgensteinian framework for dealing with this discrepancy.
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  • On the development of geometric cognition: Beyond nature vs. nurture.Markus Pantsar - 2022 - Philosophical Psychology 35 (4):595-616.
    How is knowledge of geometry developed and acquired? This central question in the philosophy of mathematics has received very different answers. Spelke and colleagues argue for a “core cognitivist”, nativist, view according to which geometric cognition is in an important way shaped by genetically determined abilities for shape recognition and orientation. Against the nativist position, Ferreirós and García-Pérez have argued for a “culturalist” account that takes geometric cognition to be fundamentally a culturally developed phenomenon. In this paper, I argue that (...)
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  • (1 other version)Ecological-enactive scientific cognition: modeling and material engagement.Giovanni Rolla & Felipe Novaes - 2020 - Phenomenology and the Cognitive Sciences 1:1-19.
    Ecological-enactive approaches to cognition aim to explain cognition in terms of the dynamic coupling between agent and environment. Accordingly, cognition of one’s immediate environment (which is sometimes labeled “basic” cognition) depends on enaction and the picking up of affordances. However, ecological-enactive views supposedly fail to account for what is sometimes called “higher” cognition, i.e., cognition about potentially absent targets, which therefore can only be explained by postulating representational content. This challenge levelled against ecological-enactive approaches highlights a putative explanatory gap between (...)
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  • (1 other version)Ecological-enactive scientific cognition: modeling and material engagement.Giovanni Rolla & Felipe Novaes - 2022 - Phenomenology and the Cognitive Sciences 21 (3):625-643.
    Ecological-enactive approaches to cognition aim to explain cognition in terms of the dynamic coupling between agent and environment. Accordingly, cognition of one’s immediate environment depends on enaction and the picking up of affordances. However, ecological-enactive views supposedly fail to account for what is sometimes called “higher” cognition, i.e., cognition about potentially absent targets, which therefore can only be explained by postulating representational content. This challenge levelled against ecological-enactive approaches highlights a putative explanatory gap between basic and higher cognition. In this (...)
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  • Conceptual Structuralism.José Ferreirós - 2023 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 54 (1):125-148.
    This paper defends a conceptualistic version of structuralism as the most convincing way of elaborating a philosophical understanding of structuralism in line with the classical tradition. The argument begins with a revision of the tradition of “conceptual mathematics”, incarnated in key figures of the period 1850 to 1940 like Riemann, Dedekind, Hilbert or Noether, showing how it led to a structuralist methodology. Then the tension between the ‘presuppositionless’ approach of those authors, and the platonism of some recent versions of philosophical (...)
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  • What Proto-logic Could not be.Woosuk Park - 2022 - Axiomathes 32 (6):1451-1482.
    Inspired by Bermúdez’s notion of proto-logic, I would like to fathom what the true proto-logic could be like. But this will be approached only in a negative way of figuring out what it could not be. I shall argue that it could not be purely deductive by exploiting the recent researches in logic of maps. This will allow us to reorient the search for proto-logic, starting with animal abduction. I will also suggest that proto-logic won’t get off the ground without (...)
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  • Graded human sensitivity to geometric and topological concepts.Vijay Marupudi & Sashank Varma - 2023 - Cognition 232 (C):105331.
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