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HOW PEIRCEAN WAS THE “‘FREGEAN’ REVOLUTION” IN LOGIC? 42 34 Sluga [1987, 95] disagrees with van Heijenoort only in arguing the relevance of the question of the claimed universality for the logic of the Begriffsschrift; in Frege, Sluga argues, concepts result from analyzing judgments, whereas in Boole, judgments results from analyzing concepts. [Korte 2010, 285] holds, contrary to all other suggestions on the question of why the Begriffsschrift properly is a language, that it is so because of Frege’s logicism, and nothing else. In attempting to understand Peirce’s position with regard to whether his logic of relatives is a language or a calculus, we are therefore returned to the debate regarding the question of whether, and if so, how and to what extent, Peirce was a logicist in the sense of Frege and Peano; see supra, n. 18. 35 Peirce tended to conflate Russell and Whitehead even with respect to Russell’s Principles of Mathematics, even prior to the appearance of the co-authored Principia Mathematica [Whitehead and Russell 1910-13], presumably because of their earlier joint work “On Cardinal Numbers” [Whitehead 1902] in the American Journal of Mathematics, to which Russell contributed the section on, a work with which Peirce was already familiar. 36 I owe this historical point to Nathan Houser. 37 [Zerman 1977, 30] refers, imprecisely, to the English translation at [van Heijenoort 1967a, 13] of [Frege 1879], but not to Frege’s original, and does not explain the nature of Frege’s failure to distinguish logic as proof-theoretic from semantic. The reference is to the discussion in [Frege 1879, §4]. 38 [Zeman 1977, 30] has in mind [Gödel 1930; 1931]. 39 The problem of the existential import thus became a major issue of contention between traditional logicians and mathematical or symbolic logicians; [Wu 1962] is a brief history of the question of existential import from Boole through Strawson. 40 I would suggest that it is in measure precisely against this backdrop that Russell became so exercised over Meinongian propositions referring to a non-existent present bald king of France as to not only work out his theory of definite descriptions in “On Denoting” [Russell 1905], but to treat the problem in The Principles of Mathematics [Russell 1903] and in Principia Mathematica [Whitehead & Russell 1910], as a legitimate problem for logic as well as for philosophy of language and for metaphysics. 41 See, e.g. [Michael 1976a] on Peirce’s study of the medieval scholastic logicians. [Martin 1979] and [Michael 1979b] treat individuals in Peirce’s logic, and in particular in Peirce’s quantification theory. [Dipert 1981, 574] mentions singular propositions in passing in the discussion of Peirce’s propositional logic. 42 In a letter to Jourdain of March 15 1906, Russell wrote (as quoted in [Russell 1994, xxxiii]: “In April 1904 I began working at the Contradiction again, and continued at it, with few intermissions, till January 1905. I was throughout much occupied by the question of Denoting, which I thought was probably relevant, as it proved to be. ...The first thing I discovered in 1904 was that the variable denoting function is to be deduced from the variable propositional function, and is not to be taken as an indefinable. I tried to do without i as an indefinable, but failed; my success later, in the article “On Denoting”, was the source of all my subsequent progress.” 43 We cannot entirely discount the relevance of Peirce’s isolation from his academic colleagues following his involuntary resignation from his position at Johns Hopkins University in 1884 (see, e.g. [Houser 1990/1991, 207]). This may perhaps underline the significance of Schröder’s seeking, in his letter to Peirce of March 2, 1897 (see [Houser 1990/1991, 223], to “to draw your attention to the pasigraphic movement in Italy. Have you ever noticed the 5 vols. of Peano’s Rivista di Matematica together with his “Formulario” and so many papers of Burali-Forti, Peano, Pieri, de Amicis, Vivanti, Vailati, etc. therein, as well as in the reports of the Academia di Torino and in other Italian periodicals (also in the German Mathematische Annalen).” 44 Reviews of the Begriffsschrift have been collected and published in English in [Frege 1972]; the introductory essay [Bynum 1972] presents the familiar standard interpretation that Frege’s work was largely ignored until interest in it was created by Bertrand Russell; more recent treatments, e.g. [Vilkko 1998], argue that Frege’s work was not consigned to total oblivion during Frege’s lifetime. 45 [Gray 2008, 209] would appear to suggest a strong influence “of the algebraic logic of Boole, Jevons, and others” on Frege, who thought that “a deep immersion [in their work] might drive logicians to new and valuable questions about logic.” There is no virtually evidence for accepting this supposition, however. 46 See [Wehmeier & Schmidt am Busch 2000] on the fate of Frege’s Nachlaβ. 47 [Macbeth 2005] is clearly unaware of [Russell ca. 1900-1901], Russell’s notes on [Peirce 1880] and [Peirce 1885]. 48 See [Russell 1983] for Russell’s log “What Shall I Read?” covering the years 1891–1902. References ANELLIS, Irving H. 1990/1991. “Schröder Material at the Russell Archives”, Modern Logic 1, 237–247. _______. 1991. “The Löwenheim-Skolem Theorem, Theories of Quantification, and Proof Theory”, in Thomas Drucker (ed.), Perspectives on the History of Mathematical Logic (Boston/Basel/Berlin: Birkhäuser), 71–83.
HOW PEIRCEAN WAS THE “‘FREGEAN’ REVOLUTION” IN LOGIC? 43 _______. 1992. “Review of The Peirce Edition Project, Writings of Charles S. Peirce: A Chronological Edition, volumes I–IV”, Modern Logic 3, 77–92. _______. 1994. Van Heijenoort: Logic and Its History in the Work and Writings of Jean van Heijenoort. Ames, IA: Modern Logic Publishing. _______. 1995. “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; electronic version: http://www.cspeirce.com/menu/library/aboutcsp/anellis/csp& br.htm. _______. 1997. “Tarski’s Development of Peirce’s Logic of Relations”, in [Houser, Roberts, & Van Evra 1997], 271–303. _______. 2004a. “The Genesis of the Truth-table Device”, Russell: the Journal of the Russell Archives (n.s.) 24 (Summer), 55–70; on-line abstract: http://digitalcommons.mcmaster.ca/russelljournal/vol24/iss1/5/. _______. 2004b. Review of [Brady 2000], Transactions of the Charles S. Peirce Society 40, 349–359. _______. 2004-2005. “Some Views of Russell and Russell’s Logic by His Contemporaries”, Review of Modern Logic 10:1/2, 67– 97; electronic version: “Some Views of Russell and Russell’s Logic by His Contemporaries, with Particular Reference to Peirce”, http://www.cspeirce.com/menu/library/aboutcsp/anellis/views.pdf. _______. 2011. “Did the Principia Mathematica Precipitate a “Fregean Revolution”?”; http://pm100.mcmaster.ca/, special issue of Russell: the Journal of Bertrand Russell Studies 31, 131–150; simultaneous published: Nicholas Griffin, Bernard Linsky, & Kenneth Blackwell, (eds.), Principia Mathematica at 100 (Hamilton, ONT: The Bertrand Russell Research Centre, McMaster University, 2011), 131–150. _______. 2012. “Peirce’s Truth-functional Analysis and the Origin of the Truth Table”, History and Philosophy of Logic 33, 87–97; preprint: http://arxiv.org/abs/1108.2429 (cite as arXiv:1108.2429v1 [math.HO]); _______. forthcoming. “Logique et la théorie de la notation (sémiotiques) de Peirce”, in Jean-Yves Béziau (ed.), La Pensée symbolique (Paris: Editions Petra). ANELLIS, Irving H., & Nathan HOUSER. 1991. “The Nineteenth Century Roots of Universal Algebra and Algebraic Logic: A Critical-bibliographical Guide for the Contemporary Logician”, in Hajnal Andréka, James Donald Monk, & István Németi (eds.), Colloquia Mathematica Societis Janos Bolyai 54. Algebraic Logic, Budapest (Hungary), 1988 (Amsterdam/London/New York: Elsevier Science/North-Holland, 1991), 1–36. BADESA [CORTÉZ], Calixto. 1991. El teorema de Löwenheim en el marco de la teoría de relativos; Ph.D. thesis, University of Barcelona; published: Barcelona: Publicacións, Universitat de Barcelona. _______. 2004. (Michael Maudsley, trans.), The Birth of Model Theory: Löwenheim’s Theorem in the Frame of the Theory of Relatives. Princeton/Oxford: Princeton University Press. BEATTY, Richard. 1969. “Peirce’s Development of Quantifiers and of Predicate Logic”, Notre Dame Journal of Formal Logic 10, 64–76. BERGMAN, Mats, & Sami PAAVOLA. 2003-. (eds.), The Commens Dictionary of Peirce’s Terms, http://www.helsinki. fi/science/ commens/dictionary.html. BERNATSKII, Georgii Genrikhovich. 1986. “Ch. S. Pirs i sillogistika Aristotelya”, Filosofskie problemy istorii logiki i metodologii nauki (Moscow: Institute of Philosophy, Academy of Sciences of the USSR), ch. 2, 12–14. _______. 1990. “Ch. S. Pirs i sillogistika Aristotelya”, in Ya. A. Slinin, Iosif Nusimovich Brodskii, Oleg Fedorovich Serebyannikov, Eduard Fedorovich Karavæv, & V. I. Kobzar’ (eds.), Nauchnaya konferentsiya “Sovremennaya logika: Problemy teorii, istorii i primeneniya v nauke”, 24–25 Maya 1990 g. Tezisy dokladov, Chast’ I (Leningrad: Leningradskii Universitet), 12–14. BERNAYS, Paul. 1950. “Mathematische Existenz und Widerspruchsfreiheit”, in Études de philosophie des sciences, en hommage à F. Gonseth à l’occasion de son soixantième anniversaire (Neuchâtel: Éditions du Griffon), 11–25. BERRY, George D.W. 1952. “Peirce’s Contributions to the Logic of Statements and Quantifiers”, in Philip P. Wiener & Francis H. Young (eds.), Studies in the Philosophy of Charles Sanders Peirce (Cambridge, MA: Harvard U. Press), 153–165. BÍARD, Joël. 1989. “Les sophismes du savoir: Albert de Saxe entre Jean Buridan et Guillaume Heytesbury”, Vivarium XXVII, 36– 50. _______. 1991. “Sémiologie et théorie des catégories chez Albert de Saxe”, in J. Bíard (éd.), Itinéraires d’Albert de Saxe, Paris- Vienne au XIV e siècle (Paris: Librairie Philosophique J. Vrin), 87–100. BOOLE, George. 1847. The Mathematical Analysis of Logic. Cambridge: Macmillan; London, George Bell; reprinted: Oxford: Basil Blackwell, 1965. _______. 1854. An Investigation of the Laws of Thought, on which are founded the Mathematical Theories of Logic and Probabilities. London: Walton & Maberly; reprinted: New York: Dover Publishing Co., 1951. BOZZO, Alexander Paul. 2010-11. “Functions or Propositional Functions” [review of Michael Potter and Tom Rickets (eds.). The Cambridge Companion to Frege], Russell: the Journal of Bertrand Russell Studies (n.s.) 30, 161–168. BRADY, Geraldine. 2000. From Peirce to Skolem: A Neglected Chapter in the History of Logic. Amsterdam/New York: North- Holland/Elsevier Science. BURCH, Robert W. 2011. “Royce, Boolean Rings, and the T-Relation”, Transactions of the Charles S. Peirce Society 46, 221–241. BYNUM, Terrell Ward. 1972. “On the Life and Work of Gottlob Frege”, in [Frege 1972], 1–54.
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