Mathematics (Bibliography)

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Bibliography in support of prospective articles on Mathematics and the full variety of mathematical subjects.
  • Boole, George (1854), An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, Macmillan, 1854. Reprinted with corrections, Dover Publications, New York, NY, 1958.
  • Leibniz, G.W. (1679–1686 ?), "Addenda to the Specimen of the Universal Calculus", pp. 40–46 in G.H.R. Parkinson (ed. and trans., 1966), Leibniz: Logical Papers, Oxford University Press, London, UK.
  • Peirce, C.S. (1981–), Writings of Charles S. Peirce: A Chronological Edition, Peirce Edition Project (eds.), Indiana University Press, Bloomington and Indianoplis, IN. Cited as CE volume, page.
  • Peirce, C.S. (1885), "On the Algebra of Logic: A Contribution to the Philosophy of Notation", American Journal of Mathematics 7 (1885), 180–202. Reprinted as CP 3.359–403 and CE 5, 162–190.
  • Peirce, C.S. (c. 1886), "Qualitative Logic", MS 736. Published as pp. 101–115 in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, Volume 4, Mathematical Philosophy, Mouton, The Hague.
  • Peirce, C.S. (1886 a), "Qualitative Logic", MS 582. Published as pp. 323–371 in Writings of Charles S. Peirce: A Chronological Edition, Volume 5, 1884–1886, Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1993.
  • Peirce, C.S. (1886 b), "The Logic of Relatives: Qualitative and Quantitative", MS 584. Published as pp. 372–378 in Writings of Charles S. Peirce: A Chronological Edition, Volume 5, 1884–1886, Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1993.
  • Beaney, Michael (ed., 1997), The Frege Reader, Blackwell Publishers, Oxford, UK.
  • Brown, Frank Markham (2003), Boolean Reasoning: The Logic of Boolean Equations, 1st edition, Kluwer Academic Publishers, Norwell, MA. 2nd edition, Dover Publications, Mineola, NY, 2003.
  • Bourbaki, N. (1994), Elements of the History of Mathematics, John Meldrum (trans.), Springer-Verlag, Berlin, Germany.
  • Church, Alonzo (1962a), "Name Relation, or Meaning Relation", p. 204 in Dagobert D. Runes (ed.), Dictionary of Philosophy, Littlefield, Adams, and Company, Totowa, NJ.
  • Church, Alonzo (1962b), "Truth, Semantical", p. 322 in Dagobert D. Runes (ed.), Dictionary of Philosophy, Littlefield, Adams, and Company, Totowa, NJ.
  • Dummett, Michael (1991 a), Frege, Philosophy of Mathematics, Harvard University Press, Cambridge, MA.
  • Dummett, Michael (1991 b), Frege and Other Philosophers, Oxford University Press, Oxford, UK.
  • Dummett, Michael (1993), Origins of Analytical Philosophy, Harvard University Press, Cambridge, MA.
  • Garfield, Jay L., and Kiteley, Murray (1991), Meaning and Truth: The Essential Readings in Modern Semantics, Paragon House, New York, NY.
  • Halmos, P.R., Naive Set Theory, D. Van Nostrand Company, Princeton, NJ, 1960.
  • Hardy, G.H. (1940), A Mathematician's Apology, 1st published, 1940. Reprinted, C.P. Snow (foreword), 1967. Reprinted, Cambridge University Press, Cambridge, UK, 1992.
  • Huntley, H.E (1970), The Divine Proportion: A Study in Mathematical Beauty, Dover Publications, New York, NY.
  • Kelley, J.L. (1955), General Topology, Van Nostrand Reinhold, New York, NY.
  • Kleene, S.C. (1971), Introduction to Metamathematics, North–Holland Publishing Company, Amsterdam, Netherlands.
  • Kline, Morris (1959), Mathematics and the Physical World, Thomas Y. Crowell Company, New York, NY, 1959. Reprinted, Dover Publications, Mineola, NY, 1981.
  • Kline, Morris (1972), Mathematical Thought from Ancient to Modern Times, Oxford University Press, New York, NY.
  • Kneale, W., and Kneale, M. (1962), The Development of Logic, Oxford University Press, London, UK, 1962. Reprinted with corrections, 1975.
  • Kohavi, Zvi (1978), Switching and Finite Automata Theory, 1st edition, McGraw–Hill, 1970. 2nd edition, McGraw–Hill, 1978.
  • König, Julius (1905), "Über die Grundlagen der Mengenlehre und das Kontinuumproblem", Mathematische Annalen 61, 156–160. Reprinted, "On the Foundations of Set Theory and the Continuum Problem", Stefan Bauer-Mengelberg (trans.), pp. 145–149 in Jean van Heijenoort (ed., 1967).
  • Kripke, Saul A. (1980), Naming and Necessity, Harvard University Press, Cambridge, MA.
  • Lambek, J. and Scott, P.J. (1986), Introduction to Higher Order Categorical Logic, Cambridge University Press, Cambridge, UK.
  • Lawvere, F.W. (2000), and Schanuel, S.H., Conceptual Mathematics, A First Introduction to Categories, Cambridge University Press, Cambridge, UK, 1997. Reprinted with corrections, 2000.
  • Linsky, Leonard (ed., 1971), Reference and Modality, Oxford University Press, London, UK.
  • Mathematical Society of Japan (1993), Encyclopedic Dictionary of Mathematics, 2nd edition, 2 vols., Kiyosi Itô (ed.), MIT Press, Cambridge, MA. Cited as EDM.
  • Mili, A., Desharnais, J., Mili, F., with Frappier, M., Computer Program Construction, Oxford University Press, New York, NY, 1994. — Introduction to Tarskian relation theory and its applications within the relational programming paradigm.
  • Mitchell, J.C. (1996), Foundations for Programming Languages, MIT Press, Cambridge, MA.
  • Moody, Ernest A. (1953), Truth and Consequence in Mediaeval Logic, North-Holland, Amsterdam, Netherlands, 1953. Reprinted, Greenwood Press, Westport, CT, 1976.
  • Nestruev, J. (2003), Smooth Manifolds and Observables, Springer-Verlag, New York, NY.
  • Peirce, Benjamin (1870), "Linear Associative Algebra", § 1. See American Journal of Mathematics 4 (1881).
  • Peirce, C.S., Writings of Charles S. Peirce, A Chronological Edition, Peirce Edition Project (eds.), Indiana University Press, Bloomington and Indianoplis, IN, 1981–. Cited as CE (volume), (page).
  • Peirce, C.S. (1870), "Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole's Calculus of Logic", Memoirs of the American Academy of Arts and Sciences 9 (1870), 317–378. Reprinted (CP 3.45-149), (CE 2, 359-429).
  • Peirce, C.S. (1902), "The Simplest Mathematics", MS dated January–February 1902, intended as Chapter 3 of the "Minute Logic", CP 4.227–323 in Collected Papers.
  • Poizat, B. (2000), A Course in Model Theory: An Introduction to Contemporary Mathematical Logic, Moses Klein (trans.), Springer-Verlag, New York, NY.
  • Putnam, Hilary (1981), Reason, Truth, and History, Cambridge University Press, Cambridge, UK.
  • Quine, W.V. (1951), "Two Dogmas of Empiricism", Philosophical Review (January 1951). Reprinted, pp. 20–46 in W.V. Quine, From a Logical Point of View, 1980.
  • Quine, W.V. (1976), The Ways of Paradox, and Other Essays, 1st edition, 1966. Revised and enlarged edition, Harvard University Press, Cambridge, MA, 1976.
  • Quine, W.V. (1980), From a Logical Point of View, Logico-Philosophical Essays, 2nd edition, Harvard University Press, Cambridge, MA, 1980.
  • Quine, W.V. (1982), Methods of Logic, (1st ed. 1950), (2nd ed. 1959), (3rd ed. 1972), 4th edition, Harvard University Press, Cambridge, MA.
  • Quine, W.V. (1992), Pursuit of Truth, Harvard University Press, Cambridge, MA, 1990. Revised edition, Harvard University Press, Cambridge, MA, 1992.
  • Quine, W.V., and Ullian, J.S. (1978), The Web of Belief, 1st edition, 1970. 2nd edition, Random House, New York, NY, 1978.
  • Ramsey, F.P. (1927), "Facts and Propositions", Aristotelian Society Supplementary Volume 7, 153–170. Reprinted, pp. 34–51 in F.P. Ramsey, Philosophical Papers, David Hugh Mellor (ed.), Cambridge University Press, Cambridge, UK, 1990.
  • Ramsey, F.P. (1990), Philosophical Papers, David Hugh Mellor (ed.), Cambridge University Press, Cambridge, UK.
  • Rescher, Nicholas (1973), The Coherence Theory of Truth, Oxford University Press, Oxford, UK.
  • Robinson, Gilbert de B. (1959), The Foundations of Geometry, University of Toronto Press, Toronto, Canada, 1940, 1946, 1952, 4th edition 1959.
  • Royce, J., The Principles of Logic, Philosophical Library, New York, NY, 1961.
  • Russell, Bertrand (1912), The Problems of Philosophy, 1st published 1912. Reprinted, Galaxy Book, Oxford University Press, New York, NY, 1959. Reprinted, Prometheus Books, Buffalo, NY, 1988.
  • Russell, Bertrand (1913), Theory of Knowledge (The 1913 Manuscript), Elizabeth Ramsden Eames (ed.), Kenneth Blackwell (collab.), George Allen & Unwin, 1984. Reprinted, Routledge, London, UK, 1992.
  • Russell, Bertrand (1918), "The Philosophy of Logical Atomism", The Monist, 1918. Reprinted, pp. 177–281 in Logic and Knowledge: Essays 1901–1950, Robert Charles Marsh (ed.), Unwin Hyman, London, UK, 1956. Reprinted, pp. 35–155 in The Philosophy of Logical Atomism, David Pears (ed.), Open Court, La Salle, IL, 1985.
  • Russell, Bertrand (1940), An Inquiry into Meaning and Truth, 'The William James Lectures for 1940 Delivered at Harvard University', George Allen & Unwin, 1950. Reprinted, Thomas Baldwin (intro.), Routledge, London, UK, 1992.
  • Russell, Bertrand (1956), Logic and Knowledge: Essays 1901–1950, Robert Charles Marsh (ed.), Unwin Hyman, London, UK, 1956. Reprinted, Routledge, London, UK, 1992.
  • Russell, Bertrand (1985), The Philosophy of Logical Atomism, David Pears (ed.), Open Court, La Salle, IL.
  • Smullyan, Raymond M. (1993), Recursion Theory for Metamathematics, Oxford University Press, Oxford, UK.
  • Steiner, Mark (1998), The Applicability of Mathematics as a Philosophical Problem, Harvard University Press, Cambridge, MA.
  • Styazhkin, N.I. (1969), History of Mathematical Logic from Leibniz to Peano, MIT Press, Cambridge, MA.
  • Tait, W.W. (1986), "Truth and Proof: The Platonism of Mathematics", Synthese 69 (1986), 341–370. Reprinted, pp. 142–167 in W.D. Hart (ed., 1996).

Tarski, A. (1935), "Der Wahrheitsbegriff in den formalisierten Sprachen", Studia Philosophica 1, pp. 261–405. Translated as "The Concept of Truth in Formalized Languages", in Tarksi (1983), pp. 152–278.

  • Tarski, Alfred (1944), "The Semantic Conception of Truth and the Foundations of Semantics", Philosophy and Phenomenological Research 4 (3), 341–376.
  • Tarski, Alfred (1983), Logic, Semantics, Metamathematics: Papers from 1923 to 1938, J.H. Woodger (trans.), Oxford University Press, Oxford, UK, 1956. 2nd edition, John Corcoran (ed.), Hackett Publishing, Indianapolis, IN, 1983.
  • Ulam, S.M. (1990), Analogies Between Analogies: The Mathematical Reports of S.M. Ulam and His Los Alamos Collaborators, A.R. Bednarek and Françoise Ulam (eds.), University of California Press, Berkeley, CA.
  • Ulam, S.M. and Bednarek, A.R., "On the Theory of Relational Structures and Schemata for Parallel Computation", pp. 477-508 in A.R. Bednarek and Françoise Ulam (eds.), Analogies Between Analogies: The Mathematical Reports of S.M. Ulam and His Los Alamos Collaborators, University of California Press, Berkeley, CA, 1990.
  • van Heijenoort, Jean (ed. 1967), From Frege To Gödel: A Source Book in Mathematical Logic, 1879–1931, Harvard University Press, Cambridge, MA.
  • Venetus, P., Logica Parva, Translation of the 1472 Edition with Introduction and Notes, Alan R. Perreiah (trans.), Philosophia Verlag, Munich, Germany, 1984.
  • Wilder, Raymond L. (1952), Introduction to the Foundations of Mathematics, John Wiley and Sons, New York, NY.
  • Williams, Bernard (2002), Truth and Truthfulness: An Essay in Genealogy, Princeton University Press, Princeton, NJ.
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