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Philosophy of Mathematics: Theories and Defense

+ 2 such that p is prime.53. (2) There is a number p greater than 100 such that both p and p + 2 are prime.54. 46 Johann von Neumann “The Formalist Foundations of Mathematics,” 1931, in Paul Benacerraf and. Hilary Putnam (ed), Philosophy of Mathematics: Selected Readings, 2nd ed., Cambridge, Cambridge University.


Philosophy of Mathematics

Benacerraf and Putnam, Philosophy of Mathematics: Selected. Readings. For quick introductory sketches and suggestions for further reading, see: Shapiro, Thinking about Mathematics. For more sustained introductions, see: Shapiro, The Oxford Handbook of Philosophy of Mathematics and. Logic. George and Velleman ...

phil of math 06-074.pdf

Putnam on Foundations: Models, Modals, Muddles

philosophy of mathematics, one work holds special prominence. The classic anthology of .... genuinely Quine-like reading, given what he was already on record as saying in MWF. Failure to attend to MWF has ...... 1964, eds., Philosophy of Mathematics: Selected Readings, 1st ed., Englewood Cliffs: Prentice-Hall. 1983, eds.


FIL2405/FIL4405 – Philosophical logic and the philosophy of

main readings several times. I have listed a number of further optional readings, which are not part of the official curriculum. Students should obtain copies of the following two books: • Stewart Shapiro, Thinking about Mathematics (Oxford UP, 2000). • Paul Benacerraf and Hilary Putnam, Philosophy of Mathematics: Selected ...


Philosophy of Mathematics: Selected Writings

Philosophy of Mathematics. Selected Writings. Charles S. Peirce. Edited by. Matthew E. Moore. INDIANA UNIVERSITY PRESS. Bloomington and Indianapolis. Beings of ... The purpose of this book is to make Peirce's philosophy of mathematics ... an exceptionally allusive writer, whose reading was so wide that it is natural.


Phil. 138 b: Philosophy of Mathematics Prof. Yourgrau Fall, 2017

Foundations of Arithmetic, which will be the focus of this class. We will also study contemporary attempts to answer these questions by some of the leading contemporary philosophers of mathematics. Texts: 1) G. Frege, The Foundations of Arithmetic. Philosophy Mathematics: Selected Readings ...


Teaching and the Philosophy of Mathematics. Martin E Flashman

Philosophy of Mathematics: Selected Readings, (Cambridge: Cambridge. University Press, 2nd edition, 1983.) –. The “bible” for much of twentieth century philosophy of Math till about 1980. Reading this will give a firm grounding on most issues of that period. Contains an extensive bibliography. •. Philip J. Davis, Reuben ...


Fictionalism in the Philosophy of Mathematics

Fictionalism in the philosophy of mathematics is the view that mathematical statements, such as. '8+5=13' and ... contrasted with other nominalist philosophical accounts of mathematics that propose a reinterpretation ..... Mathematics: Selected Readings, 2nd edition, Cambridge: Cambridge University Press, pp. 403–. 420.


Philosophy Faculty Reading List and Course Outline 2017-2018

Logic, and the Foundations of Mathematics. 2nd ed. (London: Wadsworth, 2000). [You can skip the "optional" chapters]. For classic essays on some of the conceptual issues discussed in the course see: BENACERRAF, Paul, and Hilary PUTNAM, eds., Philosophy of Mathematics: Selected. Readings. 2nd ed. ( Cambridge: ...


Syllabus for 'Philosophy of Mathematics' Thomas Donaldson; Winter

This course is a general survey of the philosophy of mathematics; we'll focus on epistemological issues. We begin with a .... Brouwer, “The Intuitionist Foundations of Mathematics” and “Disputation,” in Benacerraf and. Putnam (eds.) The Philosophy of Mathematics: Selected Readings. Week six. Hilbert's Program. Reading:.


Philosophy Faculty Reading List and Course Outline 2017-2018

Preliminary Reading. HART, W.D., ed., Philosophy of Mathematics (Oxford: Oxford University Press, 1996). HOOKWAY, Christopher, Quine (Cambridge: Polity, ..... Reprinted in P. Benecerraf and H. Putnam, eds., Philosophy of Mathematics: Selected. Readings. 1st ed. only (Oxford: Blackwell, 1964). ARNOLD, Jack, and ...


Some Proposals for Reviving the Philosophy of Mathematics

IN MATHEMATICS. 31, 3 l-50 (1979). Some Proposals for Reviving the Philosophy of Mathematics. REUBEN HERSH. Department of Mathematics,. University ...... 16-19. 11. K. GODEL, What is Cantor's continuum problem ? in “ Philosophy of Mathematics,. Selected Readings”. (P, Benacerraf and H. Putnam, Eds.), pp.


Consciousness, Philosophy, and Mathematics

classical mathematics uses logic to generate theorems, believes in the existence of unknown truths, and in ... this confinement classical mathematics, to define real numbers, has only predeterminate convergent infinite ..... Philosophy of mathematics : selected readings / edited by Paul. Benacerraf,... Title: Philosophy of ...

Brouwer - Consciousness Philosophy Mathematics.pdf


Philosophy of Mathematics: Selected Readings. Edited with Paul Benacerraf. Englewood. Cliffs, NJ: Prentice Hall, 1964. Includes an “Introduction” with Paul Benacerraf, 1–27. The 2nd edition (Cambridge, UK: Cambridge University Press, 1983) adds two chapters by Putnam: “Mathematics without Foundations” (1967),  ...



Benacerraf & H. Putnam (Eds.), Philosophy of mathematics: selected readings ( pp. 258 – 71 ). Cambridge : Cambridge. University Press . Berry , J.W. ( 1998 ). A cross - cultural view of intelligence . In R.J.. Sternberg & D.K. Detterman (Eds.), What is intelligence? Contemporary viewpoints on its nature and definition (pp.


Milton's Pandæmonium and the Infinitesimal Calculus [with

by these men might seem more theological than mathematical, as they speak in terms of God and creation, paradise and expulsion, and mathe- maticians who have “fallen” into a state of contradiction not unlike the. 1. David Hilbert, “On the Infinite,” in Philosophy of Mathematics: Selected Readings, (Cambridge,. Eng., 1983) ...


Philosophy Library database edited

Jan 24, 2013 ... Philosophy of Mathematics, Selected Readings. Benacerraf, Putnam. Paul, Hilary . Socrates Second Sailing: On Plato's Republic. Benardete. Seth. Infinity, An Esay in Metaphysics. Benardete. Jose A. Metaphysics: The Logical Approach. Benardete. Jose A. Critigue of Judgment (Immanuel Kant). Bernard.


Mathematics: Truth and Fiction? Review of Mark Balaguer's

Mathematics. ∗. Mark Colyvan. School of Philosophy. University of Tasmania. † and. Edward N. Zalta. Center for the Study of Language and Information. Stanford University. ‡. Mark Balaguer's project in this book is extremely ambitious; he sets out to defend both platonism and fictionalism about mathematical enti- ties.


Aristotle's Philosophy of Mathematics

Mar 13, 2006 ... Second, Aristotle's philosophy of mathematics is often labeled. Lila'enti 73e—37c , Republic 507eF527d. cf, Paul Benacerraf, “Mathematical. Truth,“ journal of Philosophy, 70 (1973), Kurt Giidel, “What is Cantor's Con- tinuum Problem?" in Phiioseph): of Mathematics: Selected Readings, ed. Paul. Benacerraf ...

Jstor Lear, J - Aristotle's Philosophy Of Mathematics(1982).pdf

Philosophy of Mathematics and Ontological Commitment On Quine's

This paper concerns Quine's classification of philosophies of mathematics as sketched in. "On what there is" and ... ontological positions in philosophy of mathematics: Realism, Conceptualism, and. Nominalism. Roughly ..... 1964: Philosophy of Mathematics: Selected Readings, Englewood Cliffs, New Jersey: Prentice-Hall.