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  1. 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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  • Just What is Full-Blooded Platonism?Greg Restall - 2003 - Philosophia Mathematica 11 (1):82--91.
    Mark Balaguer's Platonism and Anti-Platonism in Mathematics presents an intriguing new brand of platonism, which he calls plenitudinous platonism, or more colourfully, full-blooded platonism. In this paper, I argue that Balaguer's attempts to characterise full-blooded platonism fail. They are either too strong, with untoward consequences we all reject, or too weak, not providing a distinctive brand of platonism strong enough to do the work Balaguer requires of it.
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  • The Metaphysics of Quantity.Brent Mundy - 1987 - Philosophical Studies 51 (1):29 - 54.
    A formal theory of quantity T Q is presented which is realist, Platonist, and syntactically second-order (while logically elementary), in contrast with the existing formal theories of quantity developed within the theory of measurement, which are empiricist, nominalist, and syntactically first-order (while logically non-elementary). T Q is shown to be formally and empirically adequate as a theory of quantity, and is argued to be scientifically superior to the existing first-order theories of quantity in that it does not depend upon empirically (...)
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  • Platonism in the Philosophy of Mathematics.Øystein Linnebo - 2009 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy.
    Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices. In this survey article, the view is clarified and distinguished from some related views, and arguments for and against the view are discussed.
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  • Determinates Vs. Determinables.David H. Sanford - 2008 - Stanford Encyclopedia of Philosophy.
    Everything red is colored, and all squares are polygons. A square is distinguished from other polygons by being four-sided, equilateral, and equiangular. What distinguishes red things from other colored things? This has been understood as a conceptual rather than scientific question. Theories of wavelengths and reflectance and sensory processing are not considered. Given just our ordinary understanding of color, it seems that what differentiates red from other colors is only redness itself. The Cambridge logician W. E. Johnson introduced the terms (...)
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  • Presentism and Properties.John Bigelow - 1996 - Philosophical Perspectives 10:35-52.
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  • Abstract Objects.Gideon Rosen - 2008 - Stanford Encyclopedia of Philosophy.
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  • Global and Local.James Franklin - 2014 - Mathematical Intelligencer 36 (4).
    The global/local contrast is ubiquitous in mathematics. This paper explains it with straightforward examples. It is possible to build a circular staircase that is rising at any point (locally) but impossible to build one that rises at all points and comes back to where it started (a global restriction). Differential equations describe the local structure of a process; their solution describes the global structure that results. The interplay between global and local structure is one of the great themes of mathematics, (...)
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  • Fictionalism in the Philosophy of Mathematics.Mark Balaguer - 2008 - Stanford Encyclopedia of Philosophy.
    Mathematical fictionalism (or as I'll call it, fictionalism) is best thought of as a reaction to mathematical platonism. Platonism is the view that (a) there exist abstract mathematical objects (i.e., nonspatiotemporal mathematical objects), and (b) our mathematical sentences and theories provide true descriptions of such objects. So, for instance, on the platonist view, the sentence ‘3 is prime’ provides a straightforward description of a certain object—namely, the number 3—in much the same way that the sentence ‘Mars is red’ provides a (...)
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  • Properties.Chris Swoyer - 2001 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (Spring 2001).
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  • Nominalism, Empiricism and Universals--I.Arthur Pap - 1959 - Philosophical Quarterly 9 (37):330-340.
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