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  1. Engineering the Philosophy of Science.Taft H. Broome - 1985 - Metaphilosophy 16 (1):47-56.
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  • The Nature of Number.Peter Forrest & D. M. Armstrong - 1987 - Philosophical Papers 16 (3):165-186.
    The article develops and extends the theory of Glenn Kessler (Frege, Mill and the foundations of arithmetic, Journal of Philosophy 77, 1980) that a (cardinal) number is a relation between a heap and a unit-making property that structures the heap. For example, the relation between some swan body mass and "being a swan on the lake" could be 4.
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  • Mathematical Necessity and Reality.James Franklin - 1989 - Australasian Journal of Philosophy 67 (3):286 – 294.
    Einstein, like most philosophers, thought that there cannot be mathematical truths which are both necessary and about reality. The article argues against this, starting with prima facie examples such as "It is impossible to tile my bathroom floor with regular pentagonal tiles." Replies are given to objections based on the supposedly purely logical or hypothetical nature of mathematics.
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  • Plenitude of Possible Structures.Phillip Bricker - 1991 - Journal of Philosophy 88 (11):607-619.
    Which mathematical structures are possible, that is, instantiated by the concrete inhabitants of some possible world? Are there worlds with four-dimensional space? With infinite-dimensional space? Whence comes our knowledge of the possibility of structures? In this paper, I develop and defend a principle of plenitude according to which any mathematically natural generalization of possible structure is itself possible. I motivate the principle pragmatically by way of the role that logical possibility plays in our inquiry into the world.
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  • The Application of Mathematics to Natural Science.Mark Steiner - 1989 - Journal of Philosophy 86 (9):449-480.
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  • The Application of Mathematics to Natural Science.Mark Steiner - 1989 - Journal of Philosophy 86 (9):449-480.
    The first part of the essay describes how mathematics, in particular mathematical concepts, are applicable to nature. mathematical constructs have turned out to correspond to physical reality. this correlation between the world and mathematical concepts, it is argued, is a true phenomenon. the second part of this essay argues that the applicability of mathematics to nature is mysterious, in that not only is there no known explanation for the correlation between mathematics and physical reality, but there is a good reason (...)
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  • Structure and Ontology.Stewart Shapiro - 1989 - Philosophical Topics 17 (2):145-171.
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  • Structure and Ontology.Stewart Shapiro - 1989 - Philosophical Topics 17 (2):145-171.
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  • Philosophy of Mathematics: Prospects for the 1990s.Penelope Maddy - 1991 - Synthese 88 (2):155 - 164.
    For some time now, academic philosophers of mathematics have concentrated on intramural debates, the most conspicuous of which has centered on Benacerraf's epistemological challenge. By the late 1980s, something of a consensus had developed on how best to respond to this challenge. But answering Benacerraf leaves untouched the more advanced epistemological question of how the axioms are justified, a question that bears on actual practice in the foundations of set theory. I suggest that the time is ripe for philosophers of (...)
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  • Non-Deductive Logic in Mathematics.James Franklin - 1987 - British Journal for the Philosophy of Science 38 (1):1-18.
    Mathematicians often speak of conjectures as being confirmed by evidence that falls short of proof. For their own conjectures, evidence justifies further work in looking for a proof. Those conjectures of mathematics that have long resisted proof, such as Fermat's Last Theorem and the Riemann Hypothesis, have had to be considered in terms of the evidence for and against them. It is argued here that it is not adequate to describe the relation of evidence to hypothesis as `subjective', `heuristic' or (...)
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  • Applying Idealized Scientific Theories to Engineering.Ronald Laymon - 1989 - Synthese 81 (3):353 - 371.
    The problem for the scientist created by using idealizations is to determine whether failures to achieve experimental fit are attributable to experimental error, falsity of theory, or of idealization. Even in the rare case when experimental fit within experimental error is achieved, the scientist must determine whether this is so because of a true theory and fortuitously canceling idealizations, or due to a fortuitous combination of false theory and false idealizations. For the engineer, the problem seems rather different. Experiment for (...)
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  • What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
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  • Classes Are States of Affairs.D. M. Armstrong - 1991 - Mind 100 (2):189-200.
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  • The Structuralist View of Mathematical Objects.Charles Parsons - 1990 - Synthese 84 (3):303 - 346.
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  • Mathematics, The Computer Revolution and the Real World.James Franklin - 1988 - Philosophica 42:79-92.
    The philosophy of mathematics has largely abandoned foundational studies, but is still fixated on theorem proving, logic and number theory, and on whether mathematical knowledge is certain. That is not what mathematics looks like to, say, a knot theorist or an industrial mathematical modeller. The "computer revolution" shows that mathematics is a much more direct study of the world, especially its structural aspects.
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  • Mathematics as a Science of Patterns: Ontology and Reference.Michael D. Resnik - 1981 - Noûs 15 (4):529-550.
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  • The `Encyclopedie' of Diderot and D'Alembert.J. H. Brumfitt & John Lough - 1956 - Philosophical Quarterly 6 (22):79.
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  • Mathematics and Reality.Stewart Shapiro - 1983 - Philosophy of Science 50 (4):523-548.
    The subject of this paper is the philosophical problem of accounting for the relationship between mathematics and non-mathematical reality. The first section, devoted to the importance of the problem, suggests that many of the reasons for engaging in philosophy at all make an account of the relationship between mathematics and reality a priority, not only in philosophy of mathematics and philosophy of science, but also in general epistemology/metaphysics. This is followed by a (rather brief) survey of the major, traditional philosophies (...)
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  • Program Verification: The Very Idea.James H. Fetzer - 1988 - Communications of the Acm 31 (9):1048--1063.
    The notion of program verification appears to trade upon an equivocation. Algorithms, as logical structures, are appropriate subjects for deductive verification. Programs, as causal models of those structures, are not. The success of program verification as a generally applicable and completely reliable method for guaranteeing program performance is not even a theoretical possibility.
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