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Julian Cole
Buffalo State College
  1. 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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  2. 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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    Creativity, Freedom, and Authority: A New Perspective On the Metaphysics of Mathematics.Julian C. Cole - 2009 - Australasian Journal of Philosophy 87 (4):589-608.
    I discuss a puzzle that shows there is a need to develop a new metaphysical interpretation of mathematical theories, because all well-known interpretations conflict with important aspects of mathematical activities. The new interpretation, I argue, must authenticate the ontological commitments of mathematical theories without curtailing mathematicians' freedom and authority to creatively introduce mathematical ontology during mathematical problem-solving. Further, I argue that these two constraints are best met by a metaphysical interpretation of mathematics that takes mathematical entities to be constitutively constructed (...)
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    An Abstract Status Function Account of Corporations.Julian C. Cole - 2012 - Philosophy of the Social Sciences (1):0048393112455106.
    In this article, I articulate and defend an account of corporations motivated by John Searle’s discussion of them in his Making the Social World. According to this account, corporations are abstract entities that are the products of status function Declarations. They are also connected with, though not reducible to, various people and certain of the power relations among them. Moreover, these connections are responsible for corporations having features that stereotypical abstract entities lack (e.g., the abilities to take actions and make (...)
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  5.  47
    Mathematical Domains: Social Constructs?Julian C. Cole - 2008 - In Bonnie Gold & Roger Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematics Association of America. pp. 109--128.
    I discuss social constructivism in the philosophy of mathematics and argue for a novel variety of social constructivism that I call Practice-Dependent Realism.
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  6. Mathematical structuralism today.Julian C. Cole - 2010 - Philosophy Compass 5 (8):689-699.
    Two topics figure prominently in recent discussions of mathematical structuralism: challenges to the purported metaphysical insight provided by sui generis structuralism and the significance of category theory for understanding and articulating mathematical structuralism. This article presents an overview of central themes related to these topics.
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    Jens Erik Fenstad.*Structures and Algorithms: Mathematics and the Nature of Knowledge.Julian C. Cole - 2023 - Philosophia Mathematica 31 (1):125-131.
    This book collects eight essays — written over multiple decades, for a general audience — that address Fenstad’s thoughts on the topics of what there is and how.
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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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    Gila Sher. Epistemic Friction: An Essay on Knowledge, Truth, and Logic.Julian C. Cole - 2018 - Philosophia Mathematica 26 (1):136-148.
    © The Authors [2017]. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected] Sher believes that our basic epistemic situation — that we aim to gain knowledge of a highly complex world using our severely limited, yet highly resourceful, cognitive capacities — demands that all epistemic projects be undertaken within two broad constraints: epistemic freedom and epistemic friction. The former permits us to employ our cognitive resourcefulness fully while undertaking epistemic projects, while the latter requires that (...)
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    Giovanni Sommaruga (ed.), Foundational Theories of Classical and Constructive Mathematics, Springer, The Western Ontario Series in Philosophy of Science, Vol. 76, 2011, pp. xi+314. ISBN 978-94-007-0430-5 (hardcover) US $139.00. [REVIEW]Julian C. Cole - 2012 - Studia Logica 100 (5):1047-1050.
  11. Mathematical Platonism.Julian C. Cole - 2010 - Internet Encyclopedia of Philosophy.
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    Gianluigi Oliveri. A realist philosophy of mathematics. Texts in philosophy;.Julian C. Cole - 2008 - Philosophia Mathematica 16 (3):409-420.
    1.1 ContextIn the period following the demise of logicism, formalism, and intuitionism, contributors to the philosophy of mathematics have been divided. On the one hand, there are those who tend to focus on such issues as: Do mathematical entities exist? If so, what type of entities are they and how do we know about them? If not, how can we account for the role that mathematics plays in our everyday and scientific lives? Contributors to this school—let us call it the (...)
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    Alan Weir , Truth Through Proof: A Formalist Foundation for Mathematics . Reviewed by.Julian C. Cole - 2012 - Philosophy in Review 32 (6):529-532.
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    Book Review: Jody Azzouni. Deflating Existential Consequence: A Case for Nominalism. [REVIEW]Julian C. Cole - 2005 - Notre Dame Journal of Formal Logic 46 (2):235-247.