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  1. An Aristotelian Realist Philosophy of Mathematics: Mathematics as the science of quantity and structure.James Franklin - 2014 - London and New York: Palgrave MacMillan.
    An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts of the physical world and (...)
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  • Ditching determination and dependence: or, how to wear the crazy trousersa.James Norton, Kristie Miller & Michael Duncan - 2018 - Synthese 198 (1):395-418.
    This paper defends Flatland—the view that there exist neither determination nor dependence relations, and that everything is therefore fundamental—from the objection from explanatory inefficacy. According to that objection, Flatland is unattractive because it is unable to explain either the appearance as of there being determination relations, or the appearance as of there being dependence relations. We show how the Flatlander can meet the first challenge by offering four strategies—reducing, eliminating, untangling and omnizing—which, jointly, explain the appearance as of determination relations (...)
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  • Ditching Dependence and Determination: Or, How to Wear the Crazy Trousers.Michael Duncan, Kristie Miller & James Norton - 2021 - Synthese 198 (1):395–418.
    This paper defends Flatland—the view that there exist neither determination nor dependence relations, and that everything is therefore fundamental—from the objection from explanatory inefficacy. According to that objection, Flatland is unattractive because it is unable to explain either the appearance as of there being determination relations, or the appearance as of there being dependence relations. We show how the Flatlander can meet the first challenge by offering four strategies—reducing, eliminating, untangling and omnizing—which, jointly, explain the appearance as of there being (...)
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