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  1. Mathematical platonism and the causal relevance of abstracta.Barbara Gail Montero - 2022 - Synthese 200 (6):1-18.
    Many mathematicians are platonists: they believe that the axioms of mathematics are true because they express the structure of a nonspatiotemporal, mind independent, realm. But platonism is plagued by a philosophical worry: it is unclear how we could have knowledge of an abstract, realm, unclear how nonspatiotemporal objects could causally affect our spatiotemporal cognitive faculties. Here I aim to make room in our metaphysical picture of the world for the causal relevance of abstracta.
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  • The formal sciences discover the philosophers' stone.James Franklin - 1994 - Studies in History and Philosophy of Science Part A 25 (4):513-533.
    The formal sciences - mathematical as opposed to natural sciences, such as operations research, statistics, theoretical computer science, systems engineering - appear to have achieved mathematically provable knowledge directly about the real world. It is argued that this appearance is correct.
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  • Philosophy, mathematics and structure.James Franklin - 1995 - Philosopher: revue pour tous 1 (2):31-38.
    An early version of the work on mathematics as the science of structure that appeared later as An Aristotelian Realist Philosophy of Mathematics (2014).
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  • Normativity and Mathematics: A Wittgensteinian Approach to the Study of Number.J. Robert Loftis - 1999 - Dissertation, Northwestern University
    I argue for the Wittgensteinian thesis that mathematical statements are expressions of norms, rather than descriptions of the world. An expression of a norm is a statement like a promise or a New Year's resolution, which says that someone is committed or entitled to a certain line of action. A expression of a norm is not a mere description of a regularity of human behavior, nor is it merely a descriptive statement which happens to entail a norms. The view can (...)
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  • O matematyce i filozofii matematyki.Krzysztof Wójtowicz - 1998 - Zagadnienia Filozoficzne W Nauce 23.
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