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  1. Between American History and History of Science.Nathan Reingold - 1996 - Studies in History and Philosophy of Science Part A 27 (1):115-129.
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  • An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Stucture.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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  • Corrupting the Youth: A History of Philosophy in Australia.James Franklin - 2003 - Sydney, Australia: Macleay Press.
    A polemical account of Australian philosophy up to 2003, emphasising its unique aspects (such as commitment to realism) and the connections between philosophers' views and their lives. Topics include early idealism, the dominance of John Anderson in Sydney, the Orr case, Catholic scholasticism, Melbourne Wittgensteinianism, philosophy of science, the Sydney disturbances of the 1970s, Francofeminism, environmental philosophy, the philosophy of law and Mabo, ethics and Peter Singer. Realist theories especially praised are David Armstrong's on universals, David Stove's on logical probability (...)
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  • Euler’s Königsberg: The Explanatory Power of Mathematics.Tim Räz - 2017 - European Journal for Philosophy of Science:1-16.
    The present paper provides an analysis of Euler’s solutions to the Königsberg bridges problem. Euler proposes three different solutions to the problem, addressing their strengths and weaknesses along the way. I put the analysis of Euler’s paper to work in the philosophical discussion on mathematical explanations. I propose that the key ingredient to a good explanation is the degree to which it provides relevant information. Providing relevant information is based on knowledge of the structure in question, graphs in the present (...)
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  • Two Caricatures, II: Leibniz's Best World.J. Franklin - 2002 - International Journal for Philosophy of Religion 52 (1):45-56.
    Leibniz's best-of-all-possible worlds solution to the problem of evil is defended. Enlightenment misrepresentations are removed. The apparent obviousness of the possibility of better worlds is undermined by the much better understanding achieved in modern mathematical sciences of how global structure constrains local possibilities. It is argued that alternative views, especially standard materialism, fail to make sense of the problem ofevil, by implying that evil does not matter, absolutely speaking. Finally, itis shown how ordinary religious thinking incorporates the essentials of Leibniz's (...)
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  • Euler’s Königsberg: The Explanatory Power of Mathematics.Tim Räz - 2018 - European Journal for Philosophy of Science 8 (3):331-346.
    The present paper provides an analysis of Euler’s solutions to the Königsberg bridges problem. Euler proposes three different solutions to the problem, addressing their strengths and weaknesses along the way. I put the analysis of Euler’s paper to work in the philosophical discussion on mathematical explanations. I propose that the key ingredient to a good explanation is the degree to which it provides relevant information. Providing relevant information is based on knowledge of the structure in question, graphs in the present (...)
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  • Non-Ontological Structuralism†.Michael Resnik - 2019 - Philosophia Mathematica 27 (3):303-315.
    ABSTRACT Historical structuralist views have been ontological. They either deny that there are any mathematical objects or they maintain that mathematical objects are structures or positions in them. Non-ontological structuralism offers no account of the nature of mathematical objects. My own structuralism has evolved from an early sui generis version to a non-ontological version that embraces Quine’s doctrine of ontological relativity. In this paper I further develop and explain this view.
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  • Certainty and Domain-Independence in the Sciences of Complexity: A Critique of James Franklin's Account of Formal Science.Kevin de Laplante - 1999 - Studies in History and Philosophy of Science Part A 30 (4):699-720.
    James Franklin has argued that the formal, mathematical sciences of complexity — network theory, information theory, game theory, control theory, etc. — have a methodology that is different from the methodology of the natural sciences, and which can result in a knowledge of physical systems that has the epistemic character of deductive mathematical knowledge. I evaluate Franklin’s arguments in light of realistic examples of mathematical modelling and conclude that, in general, the formal sciences are no more able to guarantee certainty (...)
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  • Response to Franklin's Comments on 'Certainty and Domain-Independence in the Sciences of Complexity'.Kevin de Laplante - 1999 - Studies in History and Philosophy of Science Part A 30 (4):725-728.
    Professor Franklin is correct to say that there are significant areas of agreement between his account of formal science (Franklin, 1994) and my critique of his account. We both agree that the domain-independence exhibited by the formal sciences is ontologically and epistemically interesting, and that the concept of ‘structure’ must be central in any analysis of domain-independence. We also agree that knowledge of the structural, relational properties of physical systems should count as empirical knowledge, and that it makes sense to (...)
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  • Structure and Domain-Independence in the Formal Sciences.James Franklin - 1999 - Studies in History and Philosophy of Science Part A 30:721-723.
    Replies to Kevin de Laplante’s ‘Certainty and Domain-Independence in the Sciences of Complexity’ (de Laplante, 1999), defending the thesis of J. Franklin, ‘The formal sciences discover the philosophers’ stone’, Studies in History and Philosophy of Science, 25 (1994), 513-33, that the sciences of complexity can combine certain knowledge with direct applicability to reality.
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