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  1. Letter from the Editor.[author unknown] - forthcoming - Eleutheria.
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  • Mathematical activity.M. Giaquinto - 2005 - In Paolo Mancosu, Klaus Frovin Jørgensen & S. A. Pedersen (eds.), Visualization, Explanation and Reasoning Styles in Mathematics. Springer. pp. 75-87.
     
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  • Philosophy of Mathematics.Stewart Shapiro - 2003 - In Peter Clark & Katherine Hawley (eds.), Philosophy of Science Today. Oxford University Press UK.
    Moving beyond both realist and anti-realist accounts of mathematics, Shapiro articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.
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  • Two dogmas of empiricism.W. V. Quine - 2010 - In Darragh Byrne & Max Kölbel (eds.), Arguing about language. New York: Routledge.
  • Two Dogmas of Empiricism.W. Quine - 1951 - [Longmans, Green].
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  • The four-color problem and its philosophical significance.Thomas Tymoczko - 1979 - Journal of Philosophy 76 (2):57-83.
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  • Mathematical explanation.Mark Steiner - 1978 - Philosophical Studies 34 (2):135 - 151.
  • Thinking about mathematics: the philosophy of mathematics.Stewart Shapiro - 2000 - New York: Oxford University Press.
    This unique book by Stewart Shapiro looks at a range of philosophical issues and positions concerning mathematics in four comprehensive sections. Part I describes questions and issues about mathematics that have motivated philosophers since the beginning of intellectual history. Part II is an historical survey, discussing the role of mathematics in the thought of such philosophers as Plato, Aristotle, Kant, and Mill. Part III covers the three major positions held throughout the twentieth century: the idea that mathematics is logic (logicism), (...)
  • Mathematical explanation and the theory of why-questions.David Sandborg - 1998 - British Journal for the Philosophy of Science 49 (4):603-624.
    Van Fraassen and others have urged that judgements of explanations are relative to why-questions; explanations should be considered good in so far as they effectively answer why-questions. In this paper, I evaluate van Fraassen's theory with respect to mathematical explanation. I show that his theory cannot recognize any proofs as explanatory. I also present an example that contradicts the main thesis of the why-question approach—an explanation that appears explanatory despite its inability to answer the why-question that motivated it. This example (...)
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  • The Phenomenology of Mathematical Proof.Gian_carlo Rota - 1997 - Synthese 111 (2):183-196.
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  • Explanation, independence and realism in mathematics.Michael D. Resnik & David Kushner - 1987 - British Journal for the Philosophy of Science 38 (2):141-158.
  • Two Dogmas of Empiricism.W. V. O. Quine - 1951 - In Robert B. Talisse & Scott F. Aikin (eds.), The Pragmatism Reader: From Peirce Through the Present. Princeton University Press. pp. 202-220.
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  • Two Dogmas of Empiricism.W. V. Quine - 1951 - Philosophical Review 60 (1):20-43.
  • Two Dogmas of Empiricism.Willard V. O. Quine - 1951 - Philosophical Review 60 (1):20–43.
    Modern empiricism has been conditioned in large part by two dogmas. One is a belief in some fundamental cleavage between truths which are analytic, or grounded in meanings independently of matters of fact, and truth which are synthetic, or grounded in fact. The other dogma is reductionism: the belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience. Both dogmas, I shall argue, are ill founded. One effect of abandoning them is, as (...)
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  • It ain’t necessarily so.Hilary Putnam - 1962 - Journal of Philosophy 59 (22):658-671.
  • Two dogmatists.Charles Pigden - 1987 - Inquiry: An Interdisciplinary Journal of Philosophy 30 (1 & 2):173 – 193.
    Grice and Strawson's 'In Defense of a Dogma is admired even by revisionist Quineans such as Putnam (1962) who should know better. The analytic/synthetic distinction they defend is distinct from that which Putnam successfully rehabilitates. Theirs is the post-positivist distinction bounding a grossly enlarged analytic. It is not, as they claim, the sanctified product of a long philosophic tradition, but the cast-off of a defunct philosophy - logical positivism. The fact that the distinction can be communally drawn does not show (...)
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  • The nature of mathematical knowledge.Philip Kitcher - 1983 - Oxford: Oxford University Press.
    This book argues against the view that mathematical knowledge is a priori,contending that mathematics is an empirical science and develops historically,just as ...
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  • The Philosophy of Mathematics Education.Paul Ernest - 1991 - Falmer Press.
    Although many agree that all teaching rests on a theory of knowledge, this is an in-depth exploration of the philosophy of mathematics for education, building on the work of Lakatos and Wittgenstein.
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  • Proof and Knowledge in Mathematics.Michael Detlefsen - 1992 - Revue Philosophique de la France Et de l'Etranger 185 (1):133-134.
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  • Proof and Knowledge in Mathematics.Michael Detlefsen (ed.) - 1992 - New York: Routledge.
    These questions arise from any attempt to discover an epistemology for mathematics. This collection of essays considers various questions concerning the nature of justification in mathematics and possible sources of that justification. Among these are the question of whether mathematical justification is _a priori_ or _a posteriori_ in character, whether logical and mathematical differ, and if formalization plays a significant role in mathematical justification.
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  • What is Mathematics, Really?Reuben Hersh - 1997 - New York: Oxford University Press.
    Platonism is the most pervasive philosophy of mathematics. Indeed, it can be argued that an inarticulate, half-conscious Platonism is nearly universal among mathematicians. The basic idea is that mathematical entities exist outside space and time, outside thought and matter, in an abstract realm. In the more eloquent words of Edward Everett, a distinguished nineteenth-century American scholar, "in pure mathematics we contemplate absolute truths which existed in the divine mind before the morning stars sang together, and which will continue to exist (...)
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  • Review of Joseph Y. Halpern (ed.), Theoretical Aspects of Reasoning About Knowledge: Proceedings of the 1986 Conference. [REVIEW]William J. Rapaport - 1988 - Journal of Symbolic Logic 53 (2):669-670.
  • 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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  • Thinking about Mathematics: The Philosophy of Mathematics.Stewart Shapiro - 2002 - Philosophical Quarterly 52 (207):272-274.
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  • On the roles of proof in mathematics.Joseph Auslander - 2008 - In Bonnie Gold & Roger Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematical Association of America. pp. 61--77.