no. 2
Rhematische Graphen : Über Peirce' Theorien der diagrammatischen Nachbildung von Propositionen
Philosophia Scientiae, Tome 4 (2000) no. 2, pp. 67-131.

Depuis que les recherches sur l'AI ses concentrent sur les qualités formelles des structures conceptuelles, la théorie de Charles Peirce qui voudrait developper la logique de la future avec ses Graphs Existenciels (EG) semble finalement justifié. Ce qui suit présente avec les “Graphs Rhématiques” (RG) le fondement catégorique des EG et range les RG au cadre d'une sémiotique fondée sur une logique relationelle. Les RG figurent des prédicats indécomposables et leurs connections par lignes d'identité. Ce qui concerne la connectivité, on peut distinguer des modes extensifs, réflexifs, recursifs et diminuitifs. La reconstruction de deux exemples, à partir desquels Peirce établit sa thèse de l'élémentarité des relations triadiques, va permettre également de juger le potential et les limites des RG.

Now that research of AI has begun to concentrate itself on the formal qualities of conceptual structures, Charles Peirce's confidence of having designed the logic of the future with his theory of Existential Graphs (EG) seems to be finally justified. The following presents the “Rhematical Graphs” (RG) as the categorical foundation of EG and puts them in line with semiotics resting on the logic of relations. RG depict indecomposable predicates and their connections by lines of identity. Among the latter, one can distinguish between extensive, reflective, recursive and diminuitive modes. By means of reconstructing two examples Peirce discussed to establish his thesis of the elementarity of triadic relations the potential and limitations of RG will be judged.

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von Pückler, Constantin. Rhematische Graphen : Über Peirce' Theorien der diagrammatischen Nachbildung von Propositionen. Philosophia Scientiae, Tome 4 (2000) no. 2, pp. 67-131. http://archive.numdam.org/item/PHSC_2000__4_2_67_0/

[1] Allwein, G./Barwise, J. (Eds.) 1996.- Logical Reasoning with Diagrams. New York. | MR

[2] Arnauld, Antoine 1662.- Die Logik oder die Kunst des Denkens. Darmstadt.

[3] Barwise, Jon/Etchemedy, John 1991.- Visual Information and Valid Reasoning. In : Allwein, G./Barwise, J. (Eds.) 1996, 49-78. | MR

[4] Benedict, George A. 1985.- What are Representamens ? Transactions of the Charles Sanders Peirce Society 21, 243-270.

[5] Biggs, Norman L./Lloyd, E. Keith/Wilson, Robin J. (Eds.) 1976.- Graph Theory 1736 - 1936. Oxford. | MR

[6] Burch, Robert W. 1991a.- A Peircean Reduction Thesis. The Foundations of Topological Logic. Lubbock. | MR

[7] Burch, Robert W. 1991b.- Valency, Adicity, and Adity in Peirce's MS 482. Transactions of the Charles Sanders Peirce Society 27, 237-244.

[8] Burch, Robert W. 1994.- Die logischen Operationen in Peirce' „Beschreibung einer Notation für die Logik der Relative“. In : Pape, H. (Hg.), Kreativität und Logik. Charles S. Peirce und das philosophische Problem des Neuen. Frankfurt/M., 77-113.

[9] Chandrasekaran, B./Glasgow, J./Hari Narayanan, N. (Eds.) 1995.- Diagrammatic Reasoning. Cognitive and Computational Perspectives. Menlo Park.

[10] Christopherson, Rosemarie/Johnstone, Jr., Henry W. 1981.- Triadicity and Thirdness. Transactions of the Charles Sanders Peirce Society 17, 241-246.

[11] Dougherty, William P. 1993.- The Play of Interpretants : A Peircean Approach to Beethoven's Lieder. In : Shapiro, M. (Ed.), The Peirce Seminar Papers. An Annual of Semiotic Analysis, Vol. 1. Providence, 67-95.

[12] Esposito, Joseph L. 1980.- Evolutionary Metaphysics : The Development of Peirce's Theory of Categories. Athens.

[13] Euler, Leonhard 1761.- Briefe an eine deutsche Prinzessin über verschiedene Gegenstände aus der Physik und Philosophie. Braunschweig.

[14] Faris, J.A. 1981.- C.S. Peirce's Existential Graphs. Bulletin of the Institute of Mathematics and its Applications 17, 226-233. | MR | Zbl

[15] Feibleman, James K. 1946.- An Introduction to Peirce's Philosophy, Interpreted as a System. London. | MR

[16] Ferrater Mora, José 1955.- Peirce's Conception of Architectonic and Related Views. Philosophy and Phenomenological Research 15, 351-359.

[17] Fisch, Max/Turquette, Atwell 1966.- Peirce's Triadic Logic. Transactions of the Charles Sanders Peirce Society 2, 71-85. | MR

[18] Frege, Gottlob 1879.- Begriffsschrift. Eine der arithmetischen nachgebildete Formelsprache des Denkens. 2. Auflage, hg. v. Ignacio Angelelli. Hildesheim 1964.

[19] Frege, Gottlob 1892.- Über Begriff und Gegenstand. In : Frege : Funktion, Begriff, Bedeutung. Fünf logische Studien, hg. v. G. Patzig. Göttingen 1962, 66-80.

[20] Ganter, Bernhard/Wille, Rudolf 1996.- Formale Begriffsanalyse. Berlin. | MR

[21] Gardner, Martin 1958.- Logic Machines and Diagrams. New York. | Zbl

[22] Greenlee, Douglas 1968.- Peirce's Hypostatic and Factorial Categories. Transactions of the Charles Sanders Peirce Society 4, 49-58.

[23] Hawkins, Benjamin S. 1981.- Peirce's and Frege's Systems of Notation. In : Ketner, K.L./Ransdell, J.M./Eisele, C./Fisch, M.H./Hardwick, C.S. (Eds.) : Proceedings of the C.S. Peirce Bicentennial International Congress. Lubbock, 381-390.

[24] Herzberger, Hans 1981.- Peirce's Remarkable Theorem. In : Slater, J./Wilson, T./Sumner, T. (Eds.) : Pragmatism and Purpose : Essays Presented to Thomas A. Goudge. Toronto, 41-58.

[25] Hookway, Christopher 1985.- Peirce. London. (Eds.)

[26] Houser, N./Roberts, D.D./Van Evra, J. 1997.- Studies in the Logic of Charles Sanders Peirce. Bloomington.

[27] Kant, Immanuel 1781.- Kritik der reinen Vernunft. Werke in 12 Bänden, hg. v. Wilhelm Weischedel, Bd. III und IV. Frankfurt/M. 1974.

[28] Kempe, Arthur 1886.- Memoir on the Theory of Mathematical Form. Philosophical Transactions of the Royal Society of London, 1-70.

[29] Kent, Beverly 1987.- C.S. Peirce - Logic and the Classification of the Sciences. Kingston.

[30] Ketner, Kenneth Laine 1981.- The Best Example of Semiosis and Its Use in Teaching Semiotics. American Journal of Semiotics 1, 47-83.

[31] Ketner, Kenneth Laine 1986a.- Peirce's „Most Lucid and Interesting Paper“ : An Intoduction to Cenopythagoreanism. International Philosophical Quarterly 26, 375-392.

[32] Ketner, Kenneth Laine 1986b.- Semiotic is an Observational Science75-94.

[33] Leibniz, Gottfried Wilhelm 1687.- Brief an Antoine Arnauld, September 1687. In : Hauptschriften zur Grundlegung der Philosophie, hg. v. E. Cassirer. 2 Bde., Hamburg 1966, Bd. 2, 232ff.

[34] Lieb, Irvin C. 1953.- On Peirce's Classifications of Signs. In : S&S 160-166.

[35] Locke, John 1690.- Versuch über den menschlichen Verstand. 2 Bde., Hamburg 1981.

[36] Mccarthy, Jeremiah E. 1984.- Semiotic Idealism. Transactions of the Charles Sanders Peirce Society 20, 394-433.

[37] Mertz, Donald W. 1979.- Peirce : Logic, Categories, and Triads. Transactions of the Charles Sanders Peirce Society 15, 158-175.

[38] Müller, Ralf 1999.- Die dynamische Logik des Erkennens von Charles S. Peirce. Würzburg. | Zbl

[39] Murphey, Murray G. 1961.- The Development of Peirce's Thought. Cambridge/Mass..

[40] Nagl, Ludwig 1992.- Charles Sanders Peirce. Frankfurt/M.. (Eds.)

[41] Nagle, T.E./Nagle, J.A./Gerholz, L.L./Eklund, P.W. 1992.- Conceptual Structures. Current research and Practice. New York.

[42] Ogden, Charles Kay/Richards, Ivor Armstrong 1923.- Die Bedeutung von Bedeutung. Eine Untersuchung über den Einfluß der Sprache auf das Denken und über die Wissenschaft des Symbolismus. Frankfurt/M. 1974.

[43] Peano, Guiseppe 1891.- The Principles of Mathematical Logic. In : Peano : Selected Writings, ed. by H.C. Kennedy. Toronto 1973, 153-161.

[44] Peirce, Charles Sanders CP.- Collected Papers, Vol. I-VI, ed. by Charles Hartshorne and Paul Weiss (Cambridge/Mass. 1931ff) ; Vol. VII-VIII, ed. by Arthur W. Burks (Cambridge/Mass. 1958). | MR

[45] Peirce, Charles Sanders FÜ.- Die Festigung der Überzeugung und andere Schriften, hg. v. Elisabeth Walther. Baden-Baden o.J.

[46] Peirce, Charles Sanders SLM.- Zur semiotischen Grundlegung von Logik und Mathematik. Unpublizierte Manuskripte, hg. v. Max Bense und Elisabeth Walther. Stuttgart 1976.

[47] Peirce, Charles Sanders SPP.- Schriften zum Pragmatismus und Pragmatizismus, hg. v. Karl-Otto Apel. Frankfurt/M. 1976.

[48] Peirce, Charles Sanders NEM.- The New Elements of Mathematics, ed. by Carolyn Eisele. 4 Vols., The Hague 1976

[49] Peirce, Charles Sanders S&S.- Semiotic and Significs. The Correspondence between Charles S. Peirce and Victoria Lady Welby, ed. by Charles S. Hardwick. Bloomington 1977.

[50] Peirce, Charles Sanders CE.- Writings of Charles S. Peirce. A Chronological Edition, ed. by the Peirce Edition Project. 5 Vols., Bloomington 1982ff.

[51] Peirce, Charles Sanders PLZ.- Phänomen und Logik der Zeichen, hg. v. Helmut Pape. Frankfurt/M. 1983

[52] Peirce, Charles Sanders SS.- Semiotische Schriften, hg. v. Christian W. Kloesel und Helmut Pape. 3 Bde., Frankfurt/M. 1986ff.

[53] Peirce, Charles Sanders VP.- Vorlesungen über Pragmatismus, hg. v. Elisabeth Walther. Hamburg 1991

[54] Peirce, Charles Sanders NZ.- Naturordnung und Zeichenprozeß. Schriften über Semiotik und Naturphilosophie, hg. v. Helmut Pape. Frankfurt/M. 1991.

[55] Pfeiffer, H.D./Nagle, T.E. (Eds.) 1993.- Conceptual Structures : Theory and Implementation. Annual Workshop, Las Cruces, NM, USA, July 8-10, 1992. Berlin. | Zbl

[56] Potter, Vincent G./Shields, Paul B. 1977.- Peirce's Definitions of Continuities. Transactions of the Charles Sanders Peirce Society 13, 3-22.

[57] Putnam, Hilary 1982.- Peirce the Logician. Historia Mathematica 9, 290-301. | MR | Zbl

[58] Quine, Willard Van Orman 1954.- Reduction to a Dyadic Predicate. In : Selected Logical Papers. New York 1966, 224ff.

[59] Roberts, Don D. 1973.- The Existential Graphs of Charles S. Peirce. The Hague. | MR

[60] Roberts, Don D. 1997.- A Decision Method for Existential Graphs. In : Houser et. al (Eds.), 387-401. | MR

[61] Robin, Richard S. 1967.- Annotated Catalogue of the Papers of Charles S. Peirce. Cambridge/ Mass. (= MS). | MR

[62] Sanders, Gary 1970.- Peirce's Sixty-Six Signs ? Transactions of the Charles Sanders Peirce Society 6, 3-16.

[63] Schönrich, Gerhard 1999.- Semiotik zur Einführung. Hamburg.

[64] Sheriff, John K. 1994.- Charles Peirce's Guess at the Riddle : Grounds for Human Significance. Bloomington.

[65] Shin, Sun-Joo 1994.- The Logical Status of Diagrams. Cambridge/Mass. | MR | Zbl

[66] Sowa, John F. 1984.- Conceptual Structures. Information Processing in Mind and Machine. Reading. | MR | Zbl

[67] Sowa, John F. 1997.- Matching Logical Structure to Linguistic Structure. In : Houser et al. (Eds.), 418-444. | MR

[68] Spinks, Carl W. 1991.- Peirce and Triadomania. A Walk in the Semiotic Wilderness. Berlin.

[69] Tepfenhart, W. M./Dick, J. P./Sowa, J. F. (Eds.) 1994.- Conceptual Structures : Current Practices. Second International Conference on Conceptual Structures, ICCS '94. College Park, Maryland, USA, August 1994. Berlin.

[70] Thibaud, Pierre 1975.- La Logique de Charles Sanders Peirce. De l'Algèbre aux Graphes. Aix-en-Provence.

[71] Tienne, André De 1992.- Peirce's Semiotic Monism. In : Balat, M./Deledalle-Rhodes, J. (Eds.) : Signs of Humanity. L'homme et ses signes. Proceedings of the IVth International Association of Semiotic Studies, Barcelona/Perpignan, March 30-April 6, 1989. Berlin, Vol. 3, 1291-1298.

[72] Tienne, André De 1993.- Peirce's Definitions of the Phaneron. In : Moore, E.C. (Ed.) : Charles S. Peirce and the Philosophy of Science. Papers from the Harvard Sesquicentennial Congress. Tuscaloosa, 279-288.

[73] Walther, Elisabeth 1974.- Allgemeine Zeichenlehre. Einführung in die Grundlagen der Semiotik. Stuttgart.

[74] Walther, Elisabeth 1989.- Charles Sanders Peirce : Leben und Werk. Baden-Baden.

[75] Zeman, J.Jay 1964.- Existential Graphs and Natural Deduction. In : Moore, E.C./Robin, R.S. (Eds.) : The Philosophy of Charles Sanders Peirce, Second Series. Amherst 1964, 109-121.

[76] Zeman, J.Jay 1967.- A System of Implicit Quantification. Journal of Symbolic Logic 32, 484-509. | MR | Zbl

[77] Zeman, J.Jay 1968.- Peirce's Graphs : The Continuity Interpretation. Transactions of the Charles Sanders Peirce Society 4, 144-154.