Peirce’s Dragon-Head Logic (R 501, 1901)

Aristotle. 1831. Aristoteles Graece. Two volumes, ed. Theodor Waitz. Leipzig: Georg Reimer. (Peirce’s Library, the item currently at Johns Hopkins University, JHU) [Peirce mentions Aristotle’s Posterior Analytics. Peirce also listed as his volume “Aristotelis opera, with the commentaries of Averroes, usually referred to in the middle ages as the Commentator, simply. Venice, 1489. Gothic character. 2 vols folio”.] Aristotle. 1844–1846. Aristotelis Organon graece, ed. Theodor Waitz. Lipsiae: Sumtibus Hahnil. (Peirce’s Library, JHU) [A later edition that Peirce also owned.] Batens, D. 2004. Extending the realm of logic. The adaptive-logic programme. In Alternative logics. Do sciences need them?, ed. P. Weingartner, 149–164. Berlin: Springer. Bellucci, F. 2017. Peirce’s speculative grammar: Logic as semiotics. New York: Routledge. Bellucci, F., and A.-V. Pietarinen. 2016. Existential graphs as an instrument for logical analysis. Part 1: Alpha. The Review of Symbolic Logic 9 (2): 209–237. https://doi.org/10.1017/S1755020315000362. Bellucci, F., and A.-V. Pietarinen. 2017. From Mitchell to Carus: 14 years of logical graphs in the making. Transactions of the Charles S. Peirce Society 52 (4): 539–575. https://doi.org/10.2979/trancharpeirsoc.52.4.02. Bellucci, F., and A.-V. Pietarinen. 2020. Notational differences. Acta Analytica 35: 289–314. https://doi.org/10.1007/s12136-020-00425-1. Bellucci, F., X. Liu, and A.-V. Pietarinen. 2020. On linear existential graphs. Logique et Analyse 251: 261–296. https://doi.org/10.2143/LEA.251.0.3288641. Bellucci, F., A.-V. Pietarinen, and F. Stjernfelt, eds. 2014. Peirce: 5 questions. Copenhagen: VIP/Automatic Press. Bobrova, A., and A.-V. Pietarinen. 2019. Thoughts, things and logical guidance. In Peirce and Husserl: Mutual insights on logic, mathematics and cognition. Logic, epistemology, and the unity of science, vol. 46, ed. M. Shafiei and A.-V. Pietarinen. Cham: Springer. https://doi.org/10.1007/978-3-030-25800-9_3. Clark, G. 1997. New light on Peirce’s iconic notation for the sixteen binary connectives. In Studies in the logic of Charles S. Peirce, ed. N. Houser, D. Roberts, and J. Van Evra, 304–333. Indianapolis, IN: Indiana University Press. Dekker, P. 2001. Dynamics and pragmatics of ‘Peirce’s Puzzle’. Journal of Semantics 18: 211–241. Dipert, R. 1995. Peirce’s underestimated place in the history of logic: A response to Quine. In Peirce and contemporary thought, ed. K.L. Ketner, 32–58. New York: Fordham University Press. Dipert, R. 2004. Peirce’s deductive logic: Its development, influence, and philosophical significance. In The Cambridge companion to Peirce, ed. C. Misak, 257–286. Cambridge, MA: Cambridge University Press. Euclid. 1883–1916. Euclidis Opera Omnia, ed. J. L. Heiberg and H. Menge, 8 volumes. Lipsiae: B. G. Teubneri. (Peirce’s Library.) Fisch, M.H. 1982. Peirce’s place in American life. Historica Mathematica 9: 265–287. Fisch, M.H. 1986. Peirce, semeiotic, and pragmatism: Essays by Max H. Fisch, ed. K.L. Ketner and C.J.W. Kloesel. Bloomington and Indianapolis, IN: Indiana University Press. Gentzen, G.K.E. 1934. Untersuchungen über das logische Schließen. I. Mathematische Zeitschrift 39 (2): 76–210. Hamblin, C.L. 1967. One-valued logic. Philosophical Quarterly 17: 38–45. Hilpinen, R. 1982. On C. S. Peirce’s theory of the proposition: Peirce as a precursor of game-theoretical semantics. The Monist 65 (2): 182–188. Hilpinen, R. 2004. Peirce’s logic. In Handbook of the history of logic. Vol. 3: The rise of modern logic from Leibniz to Frege, ed. Dov M. Gabbay and John Woods, 611–658. Amsterdam: Elsevier. Hilpinen, R. 2009. Conditionals and possible worlds: On C. S. Peirce’s conceptions of conditionals and modalities. In The Development of Modern Logic, ed. L. Haaparanta, 551–561. Oxford: Oxford University Press. Hintikka, J. 1996. The place of C. S. Peirce in the history of logical theory. In The rule of reason: The philosophy of Charles Sanders Peirce, ed. J. Brunning and P. Forster, 13–33. Toronto: University of Toronto Press. Houser, N., D. Roberts, and J. Van Evra, eds. 1997. Studies in the logic of Charles S. Peirce. Bloomington: Indiana University Press. Kent, B. 1987. Charles S. Peirce: Logic and the classification of the sciences. Kingston: McGill-Queen’s University Press. Lewis, C.I. 1918. A survey of symbolic logic. Berkeley: University of California Press. Lewis, D. 1973. Counterfactuals. Oxford: Blackwell Publishing. Ma, M. 2018. Peirce’s logical graphs for Boolean algebras and distributive lattices. Transactions of the Charles S. Peirce Society 54 (3): 320–340. Ma, M., and A.-V. Pietarinen. 2017a. Proof analysis of Peirce’s alpha system of graphs. Studia Logica 105 (3): 625–647. Ma, M., and A.-V. Pietarinen. 2017b. Graphical sequent calculi for modal logics. Electronic Proceedings in Theoretical Computer Science 243: 91–103. https://doi.org/10.4204/EPTCS.243.7. Ma, M., and A.-V. Pietarinen. 2017c. Gamma graph calculi for modal logics. Synthese 195: 3621. https://doi.org/10.1007/s11229-017-1390-3. Ma, M., and A.-V. Pietarinen. 2018a. Peirce’s calculi for classical propositional logic. Review of Symbolic Logic 13 (3): 509–540. Ma, M., and A.-V. Pietarinen. 2018b. A graphical deep inference system for intuitionistic logic. Logique et Analyse 245: 73–114. Ma, M., and A.-V. Pietarinen. 2018c. A weakening of alpha graphs: Quasi-Boolean algebras. In Diagrammatic representation and inference. Diagrams 2018. Lecture Notes in Computer Science, vol. 10871, ed. P. Chapman, G. Stapleton, A. Moktefi, S. Perez-Kriz, and F. Bellucci, 549–564. Cham: Springer. Majer, O., A.-V. Pietarinen, and T. Tulenheimo. 2009. Introduction to logic and games. In Games: Unifying logic, language, and philosophy, ed. O. Majer, A.-V. Pietarinen, and T. Tulenheimo, ix–xxiii. Dordrecht: Springer. Mitchell, O..H. 1883. On a new algebra of logic. In Studies in logic, by members of Johns Hopkins University, ed. C.S. Peirce, 72–106. Boston: Little, Brown & Company. Mill, John Stuart. 1846. A System of Logic, Ratiocinative and Inductive. New York. (Peirce’s Library) [Peirce mentions “the first edition of his System of Logic, Ratiocinative and Inductive, published in March, 1843” (LoF 3), and that “Mill’s went through 9 editions (though with the advantage of containing no special novelty)” (LoF 3). Peirce’s copy at Houghton is the heavily annotated edition A System of Logic, Ratiocinative and Inductive: being a connected view of the principles of evidence and the methods of scientific investigation. Longmans, Green, and co., 1886 (London), knows as “People’s edition”.] Moore, M., ed. 2010. New essays on Peirce’s mathematical philosophy. Chicago: Open Court. Peirce, C.S. 1880. On the algebra of logic. American Journal of Mathematics 3 (1): 15–57. (Reprinted in: C.J.W. Kloesel (ed.), Writings of C.S. Peirce: A Chronological Edition, Vol. 4, Bloomington, IN: Indiana University Press, 1989, pp. 163–209.) Peirce, C.S., ed. 1883. Studies in logic by members of the Johns Hopkins University. Boston: Little, Brown, and Co. Peirce, C.S. 1885. On the algebra of logic: A contribution to the philosophy of notation. American Journal of Mathematics 7 (2): 180–196. Peirce, C.S. 1891a. Algebra of the copula [Version 1]. In Writings of Charles S. Peirce. Vol. 8 (1890–1892), pp. 210–211. Indiana University Press, 2010. Peirce, C.S. 1891b. Algebra of the copula [Version 2]. In Writings of Charles S. Peirce. Vol. 8 (1890–1892), pp. 212–216. Indiana University Press, 2010. Peirce, C.S. 1893a. Grand logic. Division I. Stecheology. Part I. Non relative. Chapter VIII. The algebra of the copula (R 411). Peirce, C.S. 1893b. Grand logic. Chapter XI. The Boolean calculus (R 417). Peirce, C.S. 1893c. Grand logic. Book II. Division I. Part 2. Logic of relatives. Chapter XII. The algebra of relatives (R 418). Peirce, C.S. 1894. Letter to Francis C. Russell. (R L 387). Peirce, C.S. 1896. The regenerated logic. The Monist 7 (1): 19–40. Peirce, C.S. 1896-7. On logical graphs. (R 482). In LoF 1, 211–261. Peirce, C.S. 1897b. The logic of relatives. The Monist 7(2)(January): 161–217. (Reprinted in CP 3.456–552). Peirce, C.S. 1898. On existential graphs, F4 (R 484). In LoF 1. Peirce, C.S. 1900. Letter to Christine Ladd-Franklin, November 9, 1900 (R L 237). In LoF 3/2. Peirce, C.S. 1901. New elements (Kaina stoicheia) (R 517). Houghton Library. (Reprinted in NEM IV, pp. 235–263; EP 2, pp. 300–324). Peirce, C.S. c.1901a. A proposed logical notation (R 530). In LoF 1. Peirce, C.S. c.1901b. On the first principles of logical algebra (R 515). In LoF 1. Peirce, C.S. c.1901c. On the basic rules of logical transformation (R 516). In LoF 1. Peirce, C.S. 1902. Minute logic. Chapter III. The simplest mathematics (Logic III) (R 430). In LoF 1. Peirce, C.S., and C. Ladd-Franklin. 1902. Symbolic logic, or algebra of logic. In Dictionary of philosophy and psychology, vol. 2, ed. James Mark Baldwin, 640–651. London: Macmillan and Co., Ltd. In LoF 3/2. Peirce, C.S. 1903a. Logical tracts. No. 1. On existential graphs (R 491). In LoF 2/1. Peirce, C.S. 1903b. Logical tracts. No. 2. On existential graphs, Euler’s diagrams, and logical algebra (R 492). In LoF 2/1. Peirce, C.S. 1903c. Some topics of logic bearing on questions now vexed (The Lowell Lectures of 1903). Lecture II(b) (R 455-456, R S-29, R S-33). In LoF 2/2. Peirce, C.S. 1903d. Some topics of logic bearing on questions now vexed (The Lowell Lectures of 1903). Lecture III(c) (R 464). In LoF 2/2. Peirce, C.S. 1903e. Syllabus of some topics of logic bearing on questions now vexed (The Lowell Lectures of 1903) (R 478). In LoF 2/2. Peirce, C.S. 1905a. What pragmatism is. The Monist 15 (2)(April): 161–181. (Reprinted in CP 5.411–437). Peirce, C.S. 1905b. A logical analysis of some demonstrations in high arithmetic (D) (R 253). In LoF 1. Peirce, C.S. 1905c. Issues of pragmaticism. The Monist 15 (4)(October): 481–499. (Reprinted CP 5.438–463). Peirce, C.S. 1906. Prolegomena to an apology for pragmaticism. The Monist 16(4) (October): 492–546. Errata: The Monist 17(1) (January), 1907, p. 160. (Reprinted in CP 4.530–572). Peirce, C.S. 1908a. One, two, three (R 905). In LoF 3/1. Peirce, C.S. 1908b. A neglected argument for the reality of God. Hibbert Journal 7: 90–112. (Reprinted in CP 6.452–485; EP 2, pp. 434–450). Peirce, C.S. 1908c. Some Amazing Mazes. The Monist 28(2), pp. 227–241. (Reprinted in CP 4.585–593). Peirce, C.S. 1908d. Some amazing mazes (Conclusion). Explanation of curiosity the first. The Monist 28 (3): 416–464. (Reprinted in CP 4.594–642). Peirce, C.S. 1909a. Some amazing mazes, a second curiosity. The Monist 29 (1): 36–45. (Reprinted CP 4.643–646). Peirce, C.S. 1931–1966. The collected papers of Charles S. Peirce, 8 vols., ed. by C. Hartshorne, P. Weiss and A.W. Burks, Cambridge: Harvard University Press. Cited as CP followed by volume and paragraph number. Peirce, C.S. 1967. Manuscripts in the Houghton Library of Harvard University. Identified by Richard Robin, Annotated Catalogue of the Papers of Charles S. Peirce, Amherst: University of Massachusetts Press, 1967, and The Peirce Papers: A supplementary catalogue. Transactions of the C. S. Peirce Society 7 (1971), pp. 37–57. Cited as R followed by manuscript number. Peirce, C.S. 1976. The new elements of mathematics by Charles S. Peirce, 4 vols., ed. by C. Eisele, The Hague: Mouton. Cited as NEM followed by volume and page number. Peirce, C.S. 1982-. Writings of Charles S. Peirce: A chronological edition. 7 vols., ed. E.C. Moore, C.J.W. Kloesel et al. Bloomington: Indiana University Press. Cited as W followed by volume and page number. Peirce, C.S. 1998. The essential Peirce. Volume II, ed. by Peirce Edition Project. Bloomington: Indiana University Press. Cited as EP 2 followed by page number. Peirce, C.S. 2010. Philosophy of mathematics: Selected writings, ed. M. Moore. Bloomington: Indiana University Press. Cited as PoM. Peirce, C.S. 2020. Charles S. Peirce. Semiotic writings, ed. F. Bellucci, Berlin & Boston: De Gruyter. Cited as SW followed by page number. Peirce, C.S. 2019–2021. Logic of the future: Writings on existential graphs, A.-V. Pietarinen, Vol.1: History and Applications, 2019; Vol. 2/1: The Logical Tracts; 2/2: The 1903 Lowell Lectures; Vol.3/1: Pragmaticism; Vol.3/2: Correspondence. De Gruyter (2019–2021). Cited as LoF followed by volume and page number. Pietarinen, A.-V. 2001. Most even budged yet: Some cases for game-theoretic semantics in natural language. Theoretical Linguistics 27 (1): 20–54. Pietarinen, A.-V. 2003. Peirce’s game-theoretic ideas in logic. Semiotica 144 (14): 33–47. Pietarinen, A.-V. 2006a. Signs of logic: Peircean themes on the philosophy of language, games, and communication. Dordrecht: Springer. Pietarinen, A.-V. 2006b. Interdisciplinarity and Peirce’s classification of the sciences: A centennial reassessment. Perspectives on Science 14 (2): 127–152. Pietarinen, A.-V. 2007. Game theory and linguistic meaning. (Current Research in the Semantics/Pragmatics Interface 18). Oxford: Elsevier Science. Pietarinen, A.-V. 2010. Peirce’s pragmatic theory of proper names. Transactions of the Charles S. Peirce Society 46 (3): 341–363. Pietarinen, A.-V. 2012. Why is the normativity of logic based on rules? In The normative thought of Charles S. Peirce, ed. Cornelis De Waal and Kristof P. Skowronski, 172–184. Fordham: Fordham University Press. Pietarinen, A.-V. 2013. Logical and linguistic games from Peirce to Grice to Hintikka. Teorema 33 (2): 121–136. Pietarinen, A.-V. 2015a. Two papers on existential graphs by Peirce. Synthese 192: 881–922. Pietarinen, A.-V. 2015b. Signs systematically studied: Invitation to Peirce’s theory. Sign Systems Studies 43 (4): 372–398. Recent Studies on Signs: Commentary and Perspectives, pp. 616–650; [Division of Signs, by Charles Peirce], pp. 651–662. Pietarinen, A.-V. 2019. Semeiotic completeness in the theory of signs. Semiotica: Journal of the International Association for Semiotic Studies/Revue de l’Association Internationale de Sémiotique 228: 237–257. Pietarinen, A.-V., F. Bellucci, A. Bobrova, N. Haydon, and M. Shafiei. 2020. The blot. Lecture Notes in Artificial Intelligence, vol. 12169, 225–238. Cham: Springer. Pietarinen, A.-V., and F. Stjernfelt. 2021. Semiotics of mathematics and logic. In Bloomsbury companion of semiotics, ed. J. Pelkey. London: Bloomsbury Publishing. Pratt, V. 1992. Origins of the calculus of binary relations. In Proceedings of seventh annual IEEE symposium on logic in computer science, Vol. 1, 248–254. Putnam, H. 1982. Peirce the logician. Historia Mathematica 9: 290–301. Roberts, D.D. 1973. The existential graphs of Charles S. Peirce. The Hague: Mouton. Riemann, Bernhard. 1854/1867. “Über die Hypotheses, welche der Geometrie zu Grunde liegen”. Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen 13, 132–152. [Riemann’s inaugural lecture read in 1854 and published in 1867.] Sanford, D.H. 1989. If P then Q: Conditionals and the foundations of reasoning. London: Routledge. Shin, S.-J. 2002. The iconic logic of Peirce’s graphs. Cambridge, MA: MIT Press. Short, T. 2007. Peirce’s theory of signs. Cambridge, MA: Cambridge University Press. Stalnaker, R.C. 1968. A theory of conditionals. In Studies in logical theory, ed. N. Rescher, 98–112. Oxford: Blackwell. Stjernfelt, F. 2007. Diagrammatology. Dordrecht: Springer. Sowa, J. 2006. Peirce’s contributions to the 21st century. In Proceedings of the 14th international conference on conceptual structures. Lecture Notes in Computer Science, vol. 4068, 54–69. Wadding, Luke (ed.). 1639. Scotus, Duns. Ioannis Duns Scoti Opera Omnia. Twelve Volumes. London: Laurent Durand. (Peirce’s Library, JHU) [Peirce owned Volumes 1–4 of Duns Scotus’s Opera Omnia, together with at least thirteen other 15th, 16th and early 17th century works by Scotus (JHU). Thomas of Erfurt’s Tractatus de modis significandi sive Grammatica Speculativa is included in Volume 1 of the Wadding edition.] Wolff, Christian. 1713. Vernünfftige Gedancken Von den Kräfften des menschlichen Verstandes Und ihrem Richtigen Gebrauche In Erkäntnißder Wahrheit. Halle im Magdeburgischen Renger Halle, Saale Halle. [Peirce’s citation was to “Vernünftige Gedanken von den Kräften des menschlichen Verstanden, 1710” (LoF 1). Peirce owned at least thirteen volumes of Wolff’s works, current provenance at JHU.] Zalamea, F. 2012. Peirce’s logic of continuity: A mathematical and conceptual approach. New York: Docent Press. Zellweger, S. 1997. Untapped potential in Peirce’s iconic notation for the sixteen binary connectives. In Studies in the logic of Charles S. Peirce, ed. N. Houser, et al., 334–386. Indianapolis, IN: Indiana University Press. Zeman, J. 1964. The graphical logic of Charles S. Peirce, Ph.D. thesis, University of Chicago.