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  1. Social Construction, Mathematics, and the Collective Imposition of Function onto Reality.Julian C. Cole - 2015 - Erkenntnis 80 (6):1101-1124.
    Stereotypes of social construction suggest that the existence of social constructs is accidental and that such constructs have arbitrary and subjective features. In this paper, I explore a conception of social construction according to which it consists in the collective imposition of function onto reality and show that, according to this conception, these stereotypes are incorrect. In particular, I argue that the collective imposition of function onto reality is typically non-accidental and that the products of such imposition frequently have non-arbitrary (...)
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  • On a New Approach to Peirce’s Three-Value Propositional Logic.José Renato Salatiel - 2022 - Manuscrito 45 (4):79-106.
    In 1909, Peirce recorded in a few pages of his logic notebook some experiments with matrices for three-valued propositional logic. These notes are today recognized as one of the first attempts to create non-classical formal systems. However, besides the articles published by Turquette in the 1970s and 1980s, very little progress has been made toward a comprehensive understanding of the formal aspects of Peirce's triadic logic (as he called it). This paper aims to propose a new approach to Peirce's matrices (...)
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  • Some Preliminary Notes on the Objectivity of Mathematics.Julian C. Cole - 2022 - Topoi 42 (1):235-245.
    I respond to a challenge by Dieterle (Philos Math 18:311–328, 2010) that requires mathematical social constructivists to complete two tasks: (i) counter the myth that socially constructed contents lack objectivity and (ii) provide a plausible social constructivist account of the objectivity of mathematical contents. I defend three theses: (a) the collective agreements responsible for there being socially constructed contents differ in ways that account for such contents possessing varying levels of objectivity, (b) to varying extents, the truth values of objective, (...)
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  • From Maximal Intersubjectivity to Objectivity: An Argument from the Development of Arithmetical Cognition.Markus Pantsar - 2022 - Topoi 42 (1):271-281.
    One main challenge of non-platonist philosophy of mathematics is to account for the apparent objectivity of mathematical knowledge. Cole and Feferman have proposed accounts that aim to explain objectivity through the intersubjectivity of mathematical knowledge. In this paper, focusing on arithmetic, I will argue that these accounts as such cannot explain the apparent objectivity of mathematical knowledge. However, with support from recent progress in the empirical study of the development of arithmetical cognition, a stronger argument can be provided. I will (...)
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  • The semantics of social constructivism.Shay Allen Logan - 2015 - Synthese 192 (8):2577-2598.
    This essay will examine some rather serious trouble confronting claims that mathematicalia might be social constructs. Because of the clarity with which he makes the case and the philosophical rigor he applies to his analysis, our exemplar of a social constructivist in this sense is Julian Cole, especially the work in his 2009 and 2013 papers on the topic. In a 2010 paper, Jill Dieterle criticized the view in Cole’s 2009 paper for being unable to account for the atemporality of (...)
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  • Towards an Institutional Account of the Objectivity, Necessity, and Atemporality of Mathematics.Julian C. Cole - 2013 - Philosophia Mathematica 21 (1):9-36.
    I contend that mathematical domains are freestanding institutional entities that, at least typically, are introduced to serve representational functions. In this paper, I outline an account of institutional reality and a supporting metaontological perspective that clarify the content of this thesis. I also argue that a philosophy of mathematics that has this thesis as its central tenet can account for the objectivity, necessity, and atemporality of mathematics.
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