How Peircean was the “‘Fregean’ Revolution” in Logic?
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03.05.2012
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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.
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Анеллис И. How Peircean was the “‘Fregean’ Revolution” in Logic? // Логические исследования / Logical Investigations. 2012. Т. 18. C. 239-272.
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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.
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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.
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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.
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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.
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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.
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