How Peircean was the “‘Fregean’ Revolution” in Logic?
##plugins.themes.bootstrap3.article.sidebar##
Published:
03.05.2012
##plugins.themes.bootstrap3.article.main##
Abstract
The work in logic of Charles Peirce is surveyed in light of the characteristics enumerated by historian of logic J. van Heijenoort as defining the original innovations in logic of Frege and which together are said to be the basis of what has come to be called the “Fregean revolution” in logic and which are said to constitute the elements of Frege’s Begriffsschrift of 1879 as the “founding” document of modern logic.
##plugins.generic.usageStats.downloads##
##plugins.generic.usageStats.noStats##
##plugins.themes.bootstrap3.article.details##
How to Cite
Anellis I. How Peircean was the “‘Fregean’ Revolution” in Logic? // Logicheskie Issledovaniya / Logical Investigations. 2012. VOL. 18. C. 239-272.
Issue
Section
Papers
References
Anellis, I.H. Schroder material at the Russell archives, Modern Logic 1: 237-247, 1990/91.
Anellis, I.H. The Lowenheim-Skolem theorem, theories of quantification, and proof theory. In: T. Drucker, editor, Perspectives on the History of Mathematical Logic. Boston/Basel/Berlin: Birkhauser, 1991. Pp. 71-83.
Anellis, I.H. Peirce rustled, Russell pierced: How Charles Peirce and Bertrand Russell viewed each other’s work in logic, and an assessment of Russell’s accuracy and role in the historiography of logic, Modern Logic 5: 270-328, 1995; electronic version: http://www.cspeirce.com/menu/library/aboutcsp/anellis/cspbr.htm.
Anellis, I.H. Tarski’s development of Peirce’s logic of relations, in [Houser, Roberts, & Van Evra 1997], 271-303.
Anellis, I.H. The genesis of the truth-table device, Russell: the Journal of the Russell Archives (n.s.) 24: 55-70, 2004; on-line abstract available at: http://digitalcommons.mcmaster.ca/russelljournal/vol24/iss1/5/.
Anellis, I.H. Peirce’s truth-functional analysis and the origin of the truth table, History and Philosophy of Logic 33: 87-97, 2012; preprint available at: http://arxiv.org/abs/1108.2429.
Anellis, I.H. and Houser, N. The nineteenth century roots of universal algebra and algebraic logic: A critical-bibliographical guide for the contemporary logician. In: H. Andreka, J. D. Monk and I. Nemeti, editors, Colloquia Mathematica Societis Janos Bolyai 54. Algebraic Logic, Budapest (Hungary), 1988. Amsterdam/London/New York: Elsevier Science/North-Holland, 1991, pp. 1-36.
Badesa, C. El teorema de Lowenheim en el marco de la teoria de relativos. Ph.D. thesis, University of Barcelona; published: Barcelona: Publicacions, Universitat de Barcelona, 1991.
Badesa, C. (M. Maudsley, translator), The Birth of Model Theory: Lowenheim’s Theorem in the Frame of the Theory of Relatives. Princeton/Oxford: Princeton University Press, 2004.
Beatty, R. Peirce’s development of quantifiers and of predicate logic, Notre Dame Journal of Formal Logic 10: 64-76, 1969.
Berry, G.D.W. Peirce’s contributions to the logic of statements and quantifiers. In: P.P. Wiener and F.H. Young, editors, Studies in the Philosophy of Charles Sanders Peirce. Cambridge, MA: Harvard UniversityPress, 1952. Pp. 153-165.
Boole, G. An Investigation of the Laws of Thought, on which are founded the Mathematical Theories of Logic and Probabilities. London: Walton & Maberly, 1854.
Brady, G. From Peirce to Skolem: A Neglected Chapter in the History of Logic. Amsterdam/New York: North-Holland, 2000.
Bynum, T.W. On the life and work of Gottlob Frege. In: T.W. Bynum, editor and translator, Conceptual Notation and Related Articles. Oxford: Clarendon Press, 1972. Pp. 1-54.
Clark, W.G. New light on Peirce’s iconic notation for the sixteen binary connectives. In: [42], pp. 304-333.
Couturat, L. (Lydia Gillingham Robinson, translator), The Algebra of Logic. Chicago/London: The Open Court Publishing Company, 1914.
Crouch, J.B. Between Frege and Peirce: Josiah Royce’s structural logicism, Transactions of the Charles S. Peirce Society 46: 155-177, 2011.
Dauben, J. Peirce on continuity and his critique of Cantor and Dedekind, In: K.L. Ketner and J.N. Ransdell, editors, Proceedings of the Charles S. Peirce Bicentennial International Congress. Lubbock: Texas Tech University Press, 1981. Pp. 93-98.
Dedekind, R. Was sind und was sollen die Zahlen? Braunschweig: F. Vieweg, 1888.
De Waal, C. Why metaphysics needs logic and mathematics doesn’t: Mathematics, logic, and metaphysics in Peirce’s classification of the sciences, Transactions of the Charles S. Peirce Society 41: 283-297, 2005.
Dipert, R. Peirce’s propositional logic, Review of Metaphysics 34: 569-595, 1981.
Fisch, M.H. and Turquette, A.R. Peirce’s triadic logic, Transactions of the Charles S. Peirce Society 2: 71-85, 1966.
Frege, G. Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle: Verlagvon Louis Nebert, 1879.
Frege, G. Booles rechnende Logik und die Begriffsschrift (1880/81). In: [30], 9-52.
Frege, G. Booles logische Formelsprache und die Begriffsschrift (1882). In: [30], 53-59.
Frege, G. Uber den Zweck der Begriffsschrift, Jenaischer Zeitschrift fur Naturwissenschften 16(Suppl.-Heft II): 1-10, 1883.
Frege, G. Die Grundlagen der Arithmetik. Breslau: Verlag von Wilhelm Koebner, 1884.
Frege, G. Kritische Beleuchtung einiger Punkte in E. Schroders Vorlesungen uber die Algebra der Logik, Archiv fur systematische Philosophie 1: 433-456, 1895.
Frege, G. (H. Hermes, F. Kambartel, and F. Christian Simon Josef Kaulbach, editors, Nachgelassene Schriften. Hamburg: F. Meiner Verlag, 1969; 2nd enlarged ed., 1983.
Gana, F. Peirce e Dedekind: la definizione di insiemi finito, Historia Mathematica 12: 203-218, 1985.
Gillies, D.A. The Fregean revolution in logic // D.A. Gillies (ed.) Revolutions in Mathematics. Oxford: Clarendon Press, 1992; paperback edition, 1995.P. 265-305.
Grattan-Guinness, I. Wiener on the logics of Russell and Schroder: An account of his doctoral thesis, and of his discussion of it with Russell, Annals of Science 32: 103-132, 1975.
Griffin, N. (editor), The Selected Letters of Bertrand Russell, Vol. I: The Private Years, 1884-1914. Boston/New York/London, Houghton Mifflin, 1992.
Haack, S. Peirce and logicism: Notes towards an exposition, Transactions of the Charles S. Peirce Society 29: 33-56, 1993.
Haack, S. and Lane, R. (editors), Pragmatism, Old and New: Selected Writings. Amherst, NY: Prometheus, 2006.
Hawkins, B.S. Frege and Peirce on Properties of Sentences in Classical Deductive Systems. Ph.D. thesis, University of Miami, 1971.
Hawkins, B.S. Peirce’s and Frege’s systems of notation. In: K.L. Ketner, J.M. Ransdell, C. Eisele, M.H. Fisch, and C.S. Hardwick, editors, Proceedings of the C.S. Peirce Bicentennial International Congress, 1976. (Lubbock, Texas: Tech Press, 1991. P. 381-389.
Hawkins, B.S. Peirce and Russell: The history of a neglected ‘controversy’ // [42]. P. 111-146.
Herbrand, J. Recherches sur la theorie des demonstration. Ph.D. thesis, University of Paris, 1930; reprinted: Prace Towarzystwa Naukowego Warszawskiego, Wydzial III, no. 33, 1930.
Houser, N. On “Peirce and logicism": A response to Haack, Transactions of the Charles S. Peirce Society 29: 57-67, 1993.
Houser, N., Roberts, D., and Van Evra, J. (editors), Studies in the Logic of Charles Sanders Peirce. Indianapolis/Bloomington: Indiana University Press, 1997.
Husserl, E. Der Folgerungscalcul und die Inhaltslogik, Vierteljahrsschrift fur wissenschaftliche Philosophie 15: 168-189, 1891.
Jevons, W.S. The Principles of Science, a Treatise on Logic and Scientific Method. London: Macmillan & Co., 1874; 3rd ed., 1879.
Jourdain, P. E. B. Preface. In: [17], pp. i-v.
Ladd[-Franklin], C. On the algebra of logic. In: [67], 17-71, 1883.
Laita, L.M. A Study of the Genesis of Boolean Logic, Ph.D. thesis, University of Notre Dame, 1975.
Laita, L.M. The influence of Boole’s search for a universal method in analysis on the creation of his logic, Annals of Science 34:163-176, 1977.
Lane, R. Peirce’s triadic logic reconsidered, Transactions of the Charles S. Peirce Society 35: 284-311, 1999.
Langford, C.H. Some theorems on deducibility, Annals of Mathematics (2)28: 16-40, 1927.
Linke, P.(E. L. Schaub, translator), The present state of logic and epistemology in Germany, The Monist 36: 222-255, 1926. 76: 447-470, 1915.
Lowenheim, L. Uber Moglichkeiten im Relativkalkul, Mathematische Annalen
Lukasiewicz, J. O logice trojwartosciowej, Ruch filozorfczny 5: 169-171, 1920.
Martin, R.M. On individuality and quantification in Peirce’s published logic papers, 1867-1885, Transactions of the Charles S. Peirce Society 12: 231-245, 1976.
Mitchell, O.H. On a new algebra of logic. In: [67], 72-106.
Moore, G.H. Reflections on the interplay between mathematics and logic, Modern Logic 2: 281-311, 1992.
Moore, M.E. Peirce’s Cantor. In: M.E. Moore, editor, New Essays on Peirce’s Mathematical Philosophy. Chicago/La Salle: Open Court, 2010. Pp. 323-362.
Nubiola, J. C.S. Peirce: Pragmatism and logicism, Philosophia Scienti 1(2): 121-130, 1996.
Panteki, M. Relationships between Algebra, Differential Equations and Logic in England: 1800-1860; Ph.D. thesis, C.N.A.A., London. 1992.
Peano G. Arithmetices principia, nova methodo exposita. Torino: Bocca, 1889.
Peano, G. Notations de logique mathematique (Introduction au Formulaire de mathematiques). Torino: Tipografia Guadagnini, 1894.
Peckhaus, V. Ernst Schroder und die “pasigraphischen Systeme” von Peano und Peirce, Modern Logic 1: 174-205, 1990/91.
Peirce, C.S. On an improvement in Boole’s calculus of logic (Paper read on 12 March 1867), Proceedings of the American Academy of Arts and Sciences 7: 250-261, 1868.
Peirce, C.S. 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 9: 317-378, 1870.
Peirce, C.S. On the algebra of logic, American Journal of Mathematics 3: 15-57, 1880.
Peirce, C.S. On the logic of number, American Journal of Mathematics 4: 85-95, 1881.
Peirce, C.S. editor, Studies in Logic by Members of the Johns Hopkins University. Boston: Little, Brown & Co., 1883.
Peirce, C.S. The logic of relatives. In: [67], 187-203.
Peirce, C.S. On the algebra of logic: a contribution to the philosophy of notation, American Journal of Mathematics 7: 180-202, 1885.
Peirce, C.S. The regenerated logic, The Monist 7: 19-40, 1896.
Peirce, C.S. (C. Hartshorne and P. Weiss, editors), Collected Papers of Charles Sanders Peirce, Vol. IV: The Simplest Mathematics. Cambridge, Mass., Harvard University Press, 1933; 2nd ed., 1961.
Peirce, C.S. (C. Hartshorne and P. Weiss, editors), Collected Papers of Charles Sanders Peirce, vol. V: Pragmatism and Pragmaticism. Cambridge, Mass.: Harvard University Press, 1934.
Peirce, C.S. (C.J.W. Kloesel, editor), Writings of Charles S. Peirce: A Chronological Edition, vol. 4: 1879-1884. Bloomington/Indianapolis: Indiana University Press, 1989.
Peirce, C.S. (C.J.W. Kloesel, editor), Writings of Charles S. Peirce: A Chronological Edition, vol. 5: 1884-1886. Bloomington/Indianapolis: Indiana University Press, 1993.
Peirce, C.S. (M.E. Moore, editor), Philosophy of Mathematics: Selected Writings. Bloomington/Indianapolis: Indiana University Press, 2010.
Post, E.L. Introduction to a General Theory of Elementary Propositions, Ph.D. thesis, Columbia University. Abstract presented in Bulletin of the American Mathematical Society 26: 437; abstract of a paper presented at the 24 April meeting of the American Mathematical Society, 1920.
Post, E.L. Introduction to a general theory of elementary propositions, American Journal of Mathematics 43: 169-173, 1921.
Putnam, H. Peirce the logician, Historia Mathematica 9: 290-301, 1982.
Pycior, H.M. George Peacock and the British origins of symbolical algebra, Historia Mathematica 8: 23-45, 1981.
Pycior, H.M. Augustus De Morgan’s algebraic work: The three stages, Isis 74: 211-226, 1983.
Quine, W. Methods of Logic. London: Routledge & Kegan Paul, 2nd ed., 1962.
Quine, W. In the logical vestibule, Times Literary Supplement, July 12, 1985, p. 767; reprinted as MacHale on Boole. In: W. Quine, Selected Logic Papers. Cambridge, MA: Harvard University Press, enlarged edition, 1995. Pp. 251-257.
Quine, W. Peirce’s logic. In: K.L. Ketner, editor, Peirce and Contemporary Thought: Philosophical Inquiries. New York: Fordham University Press, 1995. Pp. 23-3.(An abbreviated version appears in the enlarged edition of his Selected Logic Papers, pp. 258-265.
Rosser, J.B. Boole and the concept of a function, Celebration of the Centenary of “The Laws of Thought" by George Boole, Proceedings of the Royal Irish Academy 57, sect. A, no. 6, 117-120, 1955.
Russell, B. Principles of Mathematics. Cambridge: Cambridge University Press, 1903.
Russell, B. Mathematical logic as based on the theory of types, American Journal of Mathematics 30: 222-262, 1908.
Russell, B. (G.H. Moore, editor), Towards the “Principles of Mathematics 1900-02, vol. 3 of The Collected Papers of Bertrand Russell. London/New York: Routledge, 1993.
Ryle, G. Introduction. In: A.J. Ayer, et. al., The Revolution in Philosophy. London: Macmillan & Co.; New York: St. Martin’s Press, 1957. Pp. 1-12.
Schroder, E. Rezension von G. Freges Begriffsschrift, Zeitschrift fur Mathematik und Physik, Historisch-literaturische Abteilung 25: 81-93, 1880.
Schroder, E. Vorlesungen uber die Algebra der Logik (exacte Logik), 3 vols. Leipzig: B. G. Teubner, 1890-1905.
Schroder, E. Uber Pasigraphie, ihren gegenwartigen Stand und die pasigraphische Bewegung in Italien. In F. Rudio, Hsg., Verhandlungen des Ersten Internazionalen Mathematiker-Kongressses in Zurich von 9. bis 11. August 1897. Leipzig: B. G. Teubner, 1898. Pp. 147-162.
Schroder, E. On pasigraphy: Its present state and the pasigraphic movement in Italy, The Monist 9: 44-62, 320, 1898.
Shields, P. Charles S. Peirce on the Logic of Number. Ph.D. thesis, Fordham University, 1981.
Shields, P. Peirce’s axiomatization of arithmetic. In: [42], pp. 43-52.
Shosky, J. Russell’s use of truth tables, Russell: the Journal of the Russell Archives (n.s.) 17: 11-26, 1997.
Skolem, T. Logisch-kombinatorische Untersuchungen uber die Erfullbarkeit oder Beweisbarkeit mathematischer Satze nebst einem Theoreme uber dichte Mengen, Videnkapsselskapels Skrifter (Mathematisk-naturvidenskabelig klasse), 1(4):1-36, 1920.
Sluga, H. Gottlob Frege. London: Routledge & Kegan Paul, 1980.
Sluga, H. Frege against the Booleans, Notre Dame Journal of Formal Logic 28: 80-98, 1987.
Stroll, A. On the first flowering of Frege’s reputation, Journal of the History of Philosophy 4: 72-81, 1966.
Tarski, A. 0 wyrszie peirwotnym logistyki, Prezglad Filozoficzny 2: 68-89, 1923.
Tarski, A. On the calculus of relations, Journal of Symbolic Logic 6: 73-89, 1941.
Tarski, A. and Givant, S. A Formalization of Set Theory without Variables. Providence: American Mathematical Society, 1987.
Turquette, Atwell R. Peirce’s icons for deductive logic. In: E.C. Moore & R.S. Robins (eds.), a Studies in the Philosophy of Charles Sanders Peirce(2nd Series). Amherst: University of Massachusetts Press, pp. 95-108, 1964.
Van Heijenoort, J. (editor), From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931. Cambridge, MA: Harvard University Press, 1967.
Van Heijenoort, J. Logic as calculus and logic as language, Synthese 17, 324-330, 1967.
Van Heijenoort, J. Historical development of modern logic, Modern Logic 2: 242-255, 1992.
Venn, J. Review of G. Frege, Begriffsschrift, Mind (o.s.) 5: 297, 1880.
Vilkko, R. The reception of Frege’s Begriffsschrift, Historia Mathematica 25: 412-422, 1998.
Voigt, A. Was ist Logik?, Vierteljahrsschrift fur wissenschaftliche Philosophie 16: 289-332, 1892.
Whitehead, A.N.W. A Treatise of Universal Algebra. Cambridge: Cambridge University Press, 1898.
Whitehead, A.N. and Russell, B. Principia Mathematica, 3 vols. Cambridge: Cambridge University Press, 1910-13.
Whitehead, A.N. and Russell, B. Principia Mathematica, vol. I. Cambridge: Cambridge University Press, 2nd ed., 1925.
Wiener, N. A Comparison between the Treatment of the Algebra of Relatives by Schroeder and that by Whitehead and Russell. Ph.D. thesis, Harvard University (Harvard transcript and MIT transcript), 1913.
Wittgenstein, L. (C.K. Ogden, translator, with an introduction by B. Russell), Tractatus logico-philosophicus/Logisch-philosophische Abhandlung. London: Routledge & KeganPaul, 1922.
Zellweger, S. Untapped potential in Peirce’s iconic notation for the sixteen binary connectives. In: [42], pp. 334-386.
Zeman, J. The birth of mathematical logic, Transactions of the Charles S. Peirce Society 22: 1-22, 1986.
Жегалкин, И. И. О технике вычислений предложений в символической логике, Математический сборник (1) 34:9-28, 1927.
Жегалкин, И. И. Арифметизация символической логики, Математический сборник (1) 35: 11-77, 1928; 36: 205-338, 1929.
Anellis, I.H. The Lowenheim-Skolem theorem, theories of quantification, and proof theory. In: T. Drucker, editor, Perspectives on the History of Mathematical Logic. Boston/Basel/Berlin: Birkhauser, 1991. Pp. 71-83.
Anellis, I.H. Peirce rustled, Russell pierced: How Charles Peirce and Bertrand Russell viewed each other’s work in logic, and an assessment of Russell’s accuracy and role in the historiography of logic, Modern Logic 5: 270-328, 1995; electronic version: http://www.cspeirce.com/menu/library/aboutcsp/anellis/cspbr.htm.
Anellis, I.H. Tarski’s development of Peirce’s logic of relations, in [Houser, Roberts, & Van Evra 1997], 271-303.
Anellis, I.H. The genesis of the truth-table device, Russell: the Journal of the Russell Archives (n.s.) 24: 55-70, 2004; on-line abstract available at: http://digitalcommons.mcmaster.ca/russelljournal/vol24/iss1/5/.
Anellis, I.H. Peirce’s truth-functional analysis and the origin of the truth table, History and Philosophy of Logic 33: 87-97, 2012; preprint available at: http://arxiv.org/abs/1108.2429.
Anellis, I.H. and Houser, N. The nineteenth century roots of universal algebra and algebraic logic: A critical-bibliographical guide for the contemporary logician. In: H. Andreka, J. D. Monk and I. Nemeti, editors, Colloquia Mathematica Societis Janos Bolyai 54. Algebraic Logic, Budapest (Hungary), 1988. Amsterdam/London/New York: Elsevier Science/North-Holland, 1991, pp. 1-36.
Badesa, C. El teorema de Lowenheim en el marco de la teoria de relativos. Ph.D. thesis, University of Barcelona; published: Barcelona: Publicacions, Universitat de Barcelona, 1991.
Badesa, C. (M. Maudsley, translator), The Birth of Model Theory: Lowenheim’s Theorem in the Frame of the Theory of Relatives. Princeton/Oxford: Princeton University Press, 2004.
Beatty, R. Peirce’s development of quantifiers and of predicate logic, Notre Dame Journal of Formal Logic 10: 64-76, 1969.
Berry, G.D.W. Peirce’s contributions to the logic of statements and quantifiers. In: P.P. Wiener and F.H. Young, editors, Studies in the Philosophy of Charles Sanders Peirce. Cambridge, MA: Harvard UniversityPress, 1952. Pp. 153-165.
Boole, G. An Investigation of the Laws of Thought, on which are founded the Mathematical Theories of Logic and Probabilities. London: Walton & Maberly, 1854.
Brady, G. From Peirce to Skolem: A Neglected Chapter in the History of Logic. Amsterdam/New York: North-Holland, 2000.
Bynum, T.W. On the life and work of Gottlob Frege. In: T.W. Bynum, editor and translator, Conceptual Notation and Related Articles. Oxford: Clarendon Press, 1972. Pp. 1-54.
Clark, W.G. New light on Peirce’s iconic notation for the sixteen binary connectives. In: [42], pp. 304-333.
Couturat, L. (Lydia Gillingham Robinson, translator), The Algebra of Logic. Chicago/London: The Open Court Publishing Company, 1914.
Crouch, J.B. Between Frege and Peirce: Josiah Royce’s structural logicism, Transactions of the Charles S. Peirce Society 46: 155-177, 2011.
Dauben, J. Peirce on continuity and his critique of Cantor and Dedekind, In: K.L. Ketner and J.N. Ransdell, editors, Proceedings of the Charles S. Peirce Bicentennial International Congress. Lubbock: Texas Tech University Press, 1981. Pp. 93-98.
Dedekind, R. Was sind und was sollen die Zahlen? Braunschweig: F. Vieweg, 1888.
De Waal, C. Why metaphysics needs logic and mathematics doesn’t: Mathematics, logic, and metaphysics in Peirce’s classification of the sciences, Transactions of the Charles S. Peirce Society 41: 283-297, 2005.
Dipert, R. Peirce’s propositional logic, Review of Metaphysics 34: 569-595, 1981.
Fisch, M.H. and Turquette, A.R. Peirce’s triadic logic, Transactions of the Charles S. Peirce Society 2: 71-85, 1966.
Frege, G. Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle: Verlagvon Louis Nebert, 1879.
Frege, G. Booles rechnende Logik und die Begriffsschrift (1880/81). In: [30], 9-52.
Frege, G. Booles logische Formelsprache und die Begriffsschrift (1882). In: [30], 53-59.
Frege, G. Uber den Zweck der Begriffsschrift, Jenaischer Zeitschrift fur Naturwissenschften 16(Suppl.-Heft II): 1-10, 1883.
Frege, G. Die Grundlagen der Arithmetik. Breslau: Verlag von Wilhelm Koebner, 1884.
Frege, G. Kritische Beleuchtung einiger Punkte in E. Schroders Vorlesungen uber die Algebra der Logik, Archiv fur systematische Philosophie 1: 433-456, 1895.
Frege, G. (H. Hermes, F. Kambartel, and F. Christian Simon Josef Kaulbach, editors, Nachgelassene Schriften. Hamburg: F. Meiner Verlag, 1969; 2nd enlarged ed., 1983.
Gana, F. Peirce e Dedekind: la definizione di insiemi finito, Historia Mathematica 12: 203-218, 1985.
Gillies, D.A. The Fregean revolution in logic // D.A. Gillies (ed.) Revolutions in Mathematics. Oxford: Clarendon Press, 1992; paperback edition, 1995.P. 265-305.
Grattan-Guinness, I. Wiener on the logics of Russell and Schroder: An account of his doctoral thesis, and of his discussion of it with Russell, Annals of Science 32: 103-132, 1975.
Griffin, N. (editor), The Selected Letters of Bertrand Russell, Vol. I: The Private Years, 1884-1914. Boston/New York/London, Houghton Mifflin, 1992.
Haack, S. Peirce and logicism: Notes towards an exposition, Transactions of the Charles S. Peirce Society 29: 33-56, 1993.
Haack, S. and Lane, R. (editors), Pragmatism, Old and New: Selected Writings. Amherst, NY: Prometheus, 2006.
Hawkins, B.S. Frege and Peirce on Properties of Sentences in Classical Deductive Systems. Ph.D. thesis, University of Miami, 1971.
Hawkins, B.S. Peirce’s and Frege’s systems of notation. In: K.L. Ketner, J.M. Ransdell, C. Eisele, M.H. Fisch, and C.S. Hardwick, editors, Proceedings of the C.S. Peirce Bicentennial International Congress, 1976. (Lubbock, Texas: Tech Press, 1991. P. 381-389.
Hawkins, B.S. Peirce and Russell: The history of a neglected ‘controversy’ // [42]. P. 111-146.
Herbrand, J. Recherches sur la theorie des demonstration. Ph.D. thesis, University of Paris, 1930; reprinted: Prace Towarzystwa Naukowego Warszawskiego, Wydzial III, no. 33, 1930.
Houser, N. On “Peirce and logicism": A response to Haack, Transactions of the Charles S. Peirce Society 29: 57-67, 1993.
Houser, N., Roberts, D., and Van Evra, J. (editors), Studies in the Logic of Charles Sanders Peirce. Indianapolis/Bloomington: Indiana University Press, 1997.
Husserl, E. Der Folgerungscalcul und die Inhaltslogik, Vierteljahrsschrift fur wissenschaftliche Philosophie 15: 168-189, 1891.
Jevons, W.S. The Principles of Science, a Treatise on Logic and Scientific Method. London: Macmillan & Co., 1874; 3rd ed., 1879.
Jourdain, P. E. B. Preface. In: [17], pp. i-v.
Ladd[-Franklin], C. On the algebra of logic. In: [67], 17-71, 1883.
Laita, L.M. A Study of the Genesis of Boolean Logic, Ph.D. thesis, University of Notre Dame, 1975.
Laita, L.M. The influence of Boole’s search for a universal method in analysis on the creation of his logic, Annals of Science 34:163-176, 1977.
Lane, R. Peirce’s triadic logic reconsidered, Transactions of the Charles S. Peirce Society 35: 284-311, 1999.
Langford, C.H. Some theorems on deducibility, Annals of Mathematics (2)28: 16-40, 1927.
Linke, P.(E. L. Schaub, translator), The present state of logic and epistemology in Germany, The Monist 36: 222-255, 1926. 76: 447-470, 1915.
Lowenheim, L. Uber Moglichkeiten im Relativkalkul, Mathematische Annalen
Lukasiewicz, J. O logice trojwartosciowej, Ruch filozorfczny 5: 169-171, 1920.
Martin, R.M. On individuality and quantification in Peirce’s published logic papers, 1867-1885, Transactions of the Charles S. Peirce Society 12: 231-245, 1976.
Mitchell, O.H. On a new algebra of logic. In: [67], 72-106.
Moore, G.H. Reflections on the interplay between mathematics and logic, Modern Logic 2: 281-311, 1992.
Moore, M.E. Peirce’s Cantor. In: M.E. Moore, editor, New Essays on Peirce’s Mathematical Philosophy. Chicago/La Salle: Open Court, 2010. Pp. 323-362.
Nubiola, J. C.S. Peirce: Pragmatism and logicism, Philosophia Scienti 1(2): 121-130, 1996.
Panteki, M. Relationships between Algebra, Differential Equations and Logic in England: 1800-1860; Ph.D. thesis, C.N.A.A., London. 1992.
Peano G. Arithmetices principia, nova methodo exposita. Torino: Bocca, 1889.
Peano, G. Notations de logique mathematique (Introduction au Formulaire de mathematiques). Torino: Tipografia Guadagnini, 1894.
Peckhaus, V. Ernst Schroder und die “pasigraphischen Systeme” von Peano und Peirce, Modern Logic 1: 174-205, 1990/91.
Peirce, C.S. On an improvement in Boole’s calculus of logic (Paper read on 12 March 1867), Proceedings of the American Academy of Arts and Sciences 7: 250-261, 1868.
Peirce, C.S. 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 9: 317-378, 1870.
Peirce, C.S. On the algebra of logic, American Journal of Mathematics 3: 15-57, 1880.
Peirce, C.S. On the logic of number, American Journal of Mathematics 4: 85-95, 1881.
Peirce, C.S. editor, Studies in Logic by Members of the Johns Hopkins University. Boston: Little, Brown & Co., 1883.
Peirce, C.S. The logic of relatives. In: [67], 187-203.
Peirce, C.S. On the algebra of logic: a contribution to the philosophy of notation, American Journal of Mathematics 7: 180-202, 1885.
Peirce, C.S. The regenerated logic, The Monist 7: 19-40, 1896.
Peirce, C.S. (C. Hartshorne and P. Weiss, editors), Collected Papers of Charles Sanders Peirce, Vol. IV: The Simplest Mathematics. Cambridge, Mass., Harvard University Press, 1933; 2nd ed., 1961.
Peirce, C.S. (C. Hartshorne and P. Weiss, editors), Collected Papers of Charles Sanders Peirce, vol. V: Pragmatism and Pragmaticism. Cambridge, Mass.: Harvard University Press, 1934.
Peirce, C.S. (C.J.W. Kloesel, editor), Writings of Charles S. Peirce: A Chronological Edition, vol. 4: 1879-1884. Bloomington/Indianapolis: Indiana University Press, 1989.
Peirce, C.S. (C.J.W. Kloesel, editor), Writings of Charles S. Peirce: A Chronological Edition, vol. 5: 1884-1886. Bloomington/Indianapolis: Indiana University Press, 1993.
Peirce, C.S. (M.E. Moore, editor), Philosophy of Mathematics: Selected Writings. Bloomington/Indianapolis: Indiana University Press, 2010.
Post, E.L. Introduction to a General Theory of Elementary Propositions, Ph.D. thesis, Columbia University. Abstract presented in Bulletin of the American Mathematical Society 26: 437; abstract of a paper presented at the 24 April meeting of the American Mathematical Society, 1920.
Post, E.L. Introduction to a general theory of elementary propositions, American Journal of Mathematics 43: 169-173, 1921.
Putnam, H. Peirce the logician, Historia Mathematica 9: 290-301, 1982.
Pycior, H.M. George Peacock and the British origins of symbolical algebra, Historia Mathematica 8: 23-45, 1981.
Pycior, H.M. Augustus De Morgan’s algebraic work: The three stages, Isis 74: 211-226, 1983.
Quine, W. Methods of Logic. London: Routledge & Kegan Paul, 2nd ed., 1962.
Quine, W. In the logical vestibule, Times Literary Supplement, July 12, 1985, p. 767; reprinted as MacHale on Boole. In: W. Quine, Selected Logic Papers. Cambridge, MA: Harvard University Press, enlarged edition, 1995. Pp. 251-257.
Quine, W. Peirce’s logic. In: K.L. Ketner, editor, Peirce and Contemporary Thought: Philosophical Inquiries. New York: Fordham University Press, 1995. Pp. 23-3.(An abbreviated version appears in the enlarged edition of his Selected Logic Papers, pp. 258-265.
Rosser, J.B. Boole and the concept of a function, Celebration of the Centenary of “The Laws of Thought" by George Boole, Proceedings of the Royal Irish Academy 57, sect. A, no. 6, 117-120, 1955.
Russell, B. Principles of Mathematics. Cambridge: Cambridge University Press, 1903.
Russell, B. Mathematical logic as based on the theory of types, American Journal of Mathematics 30: 222-262, 1908.
Russell, B. (G.H. Moore, editor), Towards the “Principles of Mathematics 1900-02, vol. 3 of The Collected Papers of Bertrand Russell. London/New York: Routledge, 1993.
Ryle, G. Introduction. In: A.J. Ayer, et. al., The Revolution in Philosophy. London: Macmillan & Co.; New York: St. Martin’s Press, 1957. Pp. 1-12.
Schroder, E. Rezension von G. Freges Begriffsschrift, Zeitschrift fur Mathematik und Physik, Historisch-literaturische Abteilung 25: 81-93, 1880.
Schroder, E. Vorlesungen uber die Algebra der Logik (exacte Logik), 3 vols. Leipzig: B. G. Teubner, 1890-1905.
Schroder, E. Uber Pasigraphie, ihren gegenwartigen Stand und die pasigraphische Bewegung in Italien. In F. Rudio, Hsg., Verhandlungen des Ersten Internazionalen Mathematiker-Kongressses in Zurich von 9. bis 11. August 1897. Leipzig: B. G. Teubner, 1898. Pp. 147-162.
Schroder, E. On pasigraphy: Its present state and the pasigraphic movement in Italy, The Monist 9: 44-62, 320, 1898.
Shields, P. Charles S. Peirce on the Logic of Number. Ph.D. thesis, Fordham University, 1981.
Shields, P. Peirce’s axiomatization of arithmetic. In: [42], pp. 43-52.
Shosky, J. Russell’s use of truth tables, Russell: the Journal of the Russell Archives (n.s.) 17: 11-26, 1997.
Skolem, T. Logisch-kombinatorische Untersuchungen uber die Erfullbarkeit oder Beweisbarkeit mathematischer Satze nebst einem Theoreme uber dichte Mengen, Videnkapsselskapels Skrifter (Mathematisk-naturvidenskabelig klasse), 1(4):1-36, 1920.
Sluga, H. Gottlob Frege. London: Routledge & Kegan Paul, 1980.
Sluga, H. Frege against the Booleans, Notre Dame Journal of Formal Logic 28: 80-98, 1987.
Stroll, A. On the first flowering of Frege’s reputation, Journal of the History of Philosophy 4: 72-81, 1966.
Tarski, A. 0 wyrszie peirwotnym logistyki, Prezglad Filozoficzny 2: 68-89, 1923.
Tarski, A. On the calculus of relations, Journal of Symbolic Logic 6: 73-89, 1941.
Tarski, A. and Givant, S. A Formalization of Set Theory without Variables. Providence: American Mathematical Society, 1987.
Turquette, Atwell R. Peirce’s icons for deductive logic. In: E.C. Moore & R.S. Robins (eds.), a Studies in the Philosophy of Charles Sanders Peirce(2nd Series). Amherst: University of Massachusetts Press, pp. 95-108, 1964.
Van Heijenoort, J. (editor), From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931. Cambridge, MA: Harvard University Press, 1967.
Van Heijenoort, J. Logic as calculus and logic as language, Synthese 17, 324-330, 1967.
Van Heijenoort, J. Historical development of modern logic, Modern Logic 2: 242-255, 1992.
Venn, J. Review of G. Frege, Begriffsschrift, Mind (o.s.) 5: 297, 1880.
Vilkko, R. The reception of Frege’s Begriffsschrift, Historia Mathematica 25: 412-422, 1998.
Voigt, A. Was ist Logik?, Vierteljahrsschrift fur wissenschaftliche Philosophie 16: 289-332, 1892.
Whitehead, A.N.W. A Treatise of Universal Algebra. Cambridge: Cambridge University Press, 1898.
Whitehead, A.N. and Russell, B. Principia Mathematica, 3 vols. Cambridge: Cambridge University Press, 1910-13.
Whitehead, A.N. and Russell, B. Principia Mathematica, vol. I. Cambridge: Cambridge University Press, 2nd ed., 1925.
Wiener, N. A Comparison between the Treatment of the Algebra of Relatives by Schroeder and that by Whitehead and Russell. Ph.D. thesis, Harvard University (Harvard transcript and MIT transcript), 1913.
Wittgenstein, L. (C.K. Ogden, translator, with an introduction by B. Russell), Tractatus logico-philosophicus/Logisch-philosophische Abhandlung. London: Routledge & KeganPaul, 1922.
Zellweger, S. Untapped potential in Peirce’s iconic notation for the sixteen binary connectives. In: [42], pp. 334-386.
Zeman, J. The birth of mathematical logic, Transactions of the Charles S. Peirce Society 22: 1-22, 1986.
Жегалкин, И. И. О технике вычислений предложений в символической логике, Математический сборник (1) 34:9-28, 1927.
Жегалкин, И. И. Арифметизация символической логики, Математический сборник (1) 35: 11-77, 1928; 36: 205-338, 1929.