P HILOSOPHIA S CIENTIÆ JAIME N UBIOLA C.S. Peirce: pragmatism and logicism Philosophia Scientiæ, tome 1, no 2 (1996), p. 109-119 <http://www.numdam.org/item?id=PHSC_1996__1_2_109_0> © Éditions Kimé, 1996, tous droits réservés. L’accès aux archives de la revue « Philosophia Scientiæ » (http://poincare.univ-nancy2.fr/PhilosophiaScientiae/) implique l’accord avec les conditions générales d’utilisation (http://www. numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ C.S. Peirce: Pragmatism and Logicism Jaime Nubiola University ofNavarra - Spain Philosophia Scientiœ, 1 (2), 1996, 109-119. 3aime Nubiola Abstract.- This paper has two separate aims, with obvious links between them. First, to présent Charles S. Peirce and the pragmatist movement in a historical framework which stresses the close connections of pragmatism with the mainstream of philosophy; second, to deal with a particular controversial issue, that of the supposed logicistic orientation of Peirce's work. 1. Pragmatism, Analytic Philosophy and Peirce American pragmatism has commonly been seen as something parochial and outside the mainstream of philosophy. Among European philosophers pragmatism is often understood as an 'American way' of dealing with knowledge and truth, but as something alien to the gênerai discussion. As Rorty noted, although philosophers in Europe study Quine and Davidson, "they tend to shrug offthe suggestion that thèse contemporary philosophers share their basic outlook with American philosophers who wrote prior to the so-called linguistic turn" [Rorty 1990, 1] It was not so in the first décade of our century. In the World Congress of Philosophy at Heidelberg on 1908 the pragmatist movement held a central position in the debates [Elsenhans 1909]. With the ascent of logical empiricism in the 1920s pragmatism began to fade from the philosophical scène, as if pragmatism had exhausted its créative potential [Bernstein 1992, 815]. The dispersion of the Vienna Circle and the Second World War moved the center of philosophical discussion from Europe to the United States. In my view, that transplantation of the Vienna Circle was successful owing to the common ground established by the gênerai pragmatist orientation of American académie philosophy in the previous décades. Analytic philosophy in the hands of European émigrés took over the departments of philosophy in the American universities of the fifties. With few exceptions [Nagel 1956, xii; Murphy 1991], a deep affinity between analytical philosophy and the pragmatist tradition has been commonly overlooked. Not only were many of the issues and basic ideas common, but both movements — in a broadbrush philosophical approach — shared similar goals, similar views about the relation between philosophy and science and about how philosophical work had to be conducted. In récent years there has been an increasing amount of scholarship trying to understand both pragmatism and analytic philosophy as différent aspects of one broad philosophical attitude. In my view, a key source for developing an integrated study of both currents is to be found in Charles S. Peirce (1839-1914), the founder of pragmatism, who was interpreted by Karl-Otto Apel as the 110 C.S. Peirce: Pragmatism and Logicism milestone in the semiotic transformation of transcendental philosophy into analytic philosophy [Apel 1972, 1981, 1993]. Very recently, von Wright said along thèse lines that Peirce "may infact be counted anotherfounding father of analytic philosophy —alongside Russell andMoore and the figure in their background, Frege" [von Wright 1993,41] In this 'flashback' process, it is even possible to discover a continuous tradition within American thought, which has its beginnings in the work of Peirce, James and Dewey, and flourishes in Quine, Putnam and Rorty [Putnam 1990, 267]. Instead of viewing the analytic movement as representing a sharp rupture with pragmatism, the most récent résurgence of pragmatism suggests that there has been on the contrary a continuity between both movements [Bernstein 1992, 823]: the later one can be understood as a refinement, as a genuine development of the earlier movement. The figure of Charles S. Peirce has an ever increasing relevance in very différent areas of knowledge [Fisch, 1980], and his influence is still growing [von Wright 1993, 41]: in astronomy, metrology, geodesy, mathematics, logic, philosophy, theory and history of science, semiotics, linguistics, econometrics, and psychôlogy. In ail thèse fields Peirce has been considered a pioneer, a forerunner or even a 'father' or 'founder' (of semiotics, of pragmatism). It is very common to find gênerai évaluations like Russell's: beyond doubt /.../ he was one ofthe most original minds of the later nineteenth century, and certainly the greatest American thinker ever" [Russell 1959, 276], or Umberto Eco's: "Peirce was [„.] the greatest American philosopher ofthe turn ofthe century and beyond doubt one the greatest thinkers ofhis time" [Eco 1989, x-xi]. Popper described Peirce as "one of the greatest philosophers of ail times" [Popper 1972, 212] and Putnam called him "a towering giant among American philosophers" [Putnam 1990, 252]. Factors which hâve increased the growing interest in Peirce's thought are his personal participation in the scientific community of his time, his valuable contribution to the logic of relatives, and his sound knowledge of the philosophy of Kant as well as of the Scholastic tradition, in particular Duns Scotus. It should be noted that the interprétation of Peirce's thought and its évolution from his early writings in 1865 until his death for many years provoked wide disagreement amongst Peirce scholars. In part this was caused by the fragmentary présentation ofhis work in Peirce's Collée ted Pape rs. In more récent years a deeper understanding of the architectural nature of his thought and of his whole évolution has been gaining gênerai agreement [Hausman 1993, xiv-xv; Houser 1992, xxix]. In the last décade the basic cohérence and undeniable systematization of 111 3aime Nubiola Peirce's thought has been widely recognized by the Peircean scholarship [Santaella 1993, 401]. Christopher Hookway has characterized Peirce as a traditional and systematic philosopher, but one dealing with the modem problems of science, truth and knowledge from a very valuable Personal expérience as a logician and an expérimental researcher in the bosom of an international community of scientists and thinkers [Hookway 1985, 1-3]. Moreover, it has been held that the best approach for understanding Peirce is to see him as an analytic philosopher avant la lettre, anticipating the intersubjective 'linguistic turn' in philosophy with his gênerai theory of signs [Hookway 1985, 141; Bernstein 1992, 814]. Although Richard Rorty detected the similarities between Wittgenstein's Philosophical Investigations (1953) and the philosophical framework of Peirce thirty years ago [Rorty 1961], académie philosophy in the English speaking world has virtually neglected the study of Peirce and pragmatism. It may be even said that Peirce's thought has been rediscovered by Continental philosophers (such as Popper, Habermas, and Eco) and reintroduced by them into the world of philosophical reflection. In Peirce's work there is not only a parallel development of thèmes found in the work of Frege, Russell or Wittgenstein, but also the framework for an integraied theory of culture [Hookway 1985,120]. Peirce saw the pursuit of truth as a corporate task rather than an individual search for foundations. This framework "not only challenges the characteristic Cartesian appeal to foundations, but adumbrates an alternative understanding of scientific knowledge without such foundations" [Bernstein 1983,71-72] In this sensé — as Debrock highlighted — Peirce's thought offers suggestions for tackling some of the most stubborn problems in contemporary philosophy, but in particular he may help us to résume a philosophical responsibility which has been largely abdicated by much of 20th century philosophy [Debrock 1992, 1]. 2. Peirce and Logicism: Logic, Mathematics, and Continuity In this framework, the second goal of my paper is to explore tentatively the issue of how the relation between Peirce and logicism has been understood, as a way of throwing some light on the essential harmony of Peirce's thought. I will summarize the récent debate between Susan Haack and Nathan Houser about that issue, but trying to présent a more historical perspective, Peirce's work has sometimes been understood as a forerunner in some substantial areas of Whitehead and Russell's Principia Mathematica [Collected Papers 3.43-4n.; Weiss 1934, 400; Nagel 1939, xvii; Eisele 1979, 12; 112 C.S. Peirce: Pragmatism and Logicism Haack 1993,34-5], but scholars who seek to classify Peirce under the label of logicism find it extremely difficult to accommodate his exact words. Justus Buchler, in his séminal work on Peirce, noticed some — at least apparent — contradiction between Peirce's words about the relation between mathematics and logic and what Buchler called "Peirce's attempts to dérive arithmetic from logic" [Buchler 1939a, 224]. Richard Dedekind, "one of the principal logico-mathematicians of Peirce's dayy\ regarded mathematics as a branch of logic. Peirce opposed that claim arguing that both disciplines hâve widely divergent aims. Peirce provided in défense of his position the distinction — which he says was intended by his father Benjamin, a well known Harvard mathematician — between mathematics as the science that draws necessary conclusions and logic as the science of drawing necessary conclusions [Collected Papers 4.239, 1902][Kent 1987,72][Murphey 1961,229]. The mathematician draws conséquences, the logician studies and classifies the conditions under which thèse conséquences are drawn. Far from mathematics being a branch of logic, it is almost [...] the only science which stands in need of no aid from a science of logic [Collected Papers 2.81; c. 1902][Buchler 1939a, 221]. Mathematics — Peirce wrote in the same year 1902 — has no neèd of any appeal to logic. [...] Just as it is not necessary, in order to talk, to understand the theory of the formation of vowel sounds, it is not necessary, in order to reason, to be in possession of the theory of reasoning [Collected Papers 4.242 c. 1902]. The aims of both sciences are very différent: while the function of logic is the 'analysis and theory of reasoning', the function of mathematics is 'the practice of it* [Collected Papers 4.134]. Buchler concluded that Peirce's studies toward defining traditional mathematical relations in terms of 'logical', and deriving mathematical propositions from a small set of analytic propositions, were an important contribution, "foreshadowing modem logistic and culminating in the work ofthe Whitehead-Russell Principia Mathematica". In support of that claim Buchler mentioned Lewis's account of Peirce's work along thèse Unes in A Survey of Symbolic Logic [1918]. Buchler eschewed the apparent inconsistency by explaining that "although mathematical propositions may be derivedfrom logical propositions, the process of dérivation is on this view itself a 'mathematical process, with a mathematical criterion of validity independent of logical analysis" [Buchler 1939a, 224], but at last he had to assert that Peirce's thought "on the foundations of mathematics and logic does not form a systematic body of opinion" [Buchler 1939a, 227 and 1939b, 215]. Peirce's approach to this relation between philosophy, 113 3aime Nubiola mathematics and logic may be better understood recalling his own words in the Cambridge Lectures (1898): metaphysics must draw its principles from logic, and that logic must draw its principles [...] from mathematics. [Peirce 1992, 123] According to Peirce, mathematics is an observational science, and mathematical knowledge dépends on expérience,1 on the construction, manipulation and observation of diagrams, created by the human mind [Goudge 1950, 56; Haack 1995]. As Hilary Putnam suggested, it is fascinating that Peirce and Frege, the two inventors of predicate calculus disagreed on sp fundamental a rnetaphysical issue, Frege seeing logic as totally nonempirical and Peirce seeing logic itself as involving something like mental expérimentation with diagrams. [Peirce 1992, 72] It is possible to achieve greater clarity on this question through the récent debate between Susan Haack and Nathan Houser on Peirce's disputed commitment to logicism. After providing an impressive set of texts from Peirce, Haack concludes that Peirce was and was not a logicist, because logicism is a two-fold doctrine: Logicism is a formai thesis (Mathematics, at least arithmetics, is reducible to logic) and an epistemological thesis (Logic is more basic, and epistemically foundational for mathematics). Haack claims that Peirce resolutely rejected that epistemological logicism, but sympathized with the formai thesis, with the reducibility of at least arithmetic to logic. Houser, on the contrary, doubts that Peirce was a formai logicist and holds that if the reducibility of a part of mathematics to logic is accepted that logic would be epistemically prior to mathematics, or which would be the same, that it is not possible to disentangle both faces of logicism [Houser 1993; Haack 1993]. According to Haack, the explanation for Peirce's apparent sympathy with the formai thesis and his clear répudiation of the epistemological thesis "lies, at least in part, in an ambiguity on Peirce's use of the tenu 'logic'" between 'logic' meaning "mathematical formalization of necessary reasoning" and 'logic' meaning "theory of reasoning" [Haack 1993, 45]. But, in my view, the key to understanding Peirce's position should be traced back, first, as Haack and Houser realized, to Peirce's classification of the sciences [Collected Papers 4.134, 1895], and second, to the acknowledgement of two différent mathematical traditions. During his life, Peirce made many attempts to work out a gênerai classification of the sciences, understood as an epistemic ladder ofthe sciences [Collected Papers 1.180ff ; Kent 1987, 71-72], as the différent "branches ofendeavor to ascertain truth" [Peirce L75]. 114 C.S. Peirce: Pragmatism and Logicism The mature Peirce established a clear-cut distinction between formai logic as a mathematical branch of the science of discovery and pure theoretical mathematics as the most abstract of ail sciences [Collected Papers 4.244, 4.263, c.1902; 1.180, 1903; 1.52, c. 1896]. According to Peirce's classification of the sciences, there is a hierarchy in human knowledge: mathematics is at the head and logic occupies a subordinate position [Haack 1993, 48]. Reasonings of pure mathematics are perfectly évident and hâve no need of any separate theory of logic to reinforce them. Mathematics is its own logic. [Peirce L75, draft A, 29-33] Logic is not a foundational science, but a normative one. Human reasoning is not a Cartesian search for foundations, but a coopérative and fallible activity of inquiry, which has no need of any such foundations [Bernstein 1992, 814]. In particular mathematics, the highest type of human reasoning, requires no foundation; as Goudge wrote, the only thing from which mathematics can be 'derived' is our native capacity for thinking rigorously, "our natural power of reason" [Collected Papers 4.242] or "a natural instinct for right reasoning" [Collected Papers 2.3] [Goudge 1950, 58]. Peirce did not seek to reduce mathematics to logic. Reductionism was not an aim of Peirce's conception of scientific inquiry, nor did he think that mathematics need appeaï to logic to ascertain the validity of its reasoning, "for nothing can be more évident thon its own unaided reasonings" [Collected Papers 7.524, n.d.; Kent 1987, 72]. This leads us to the second reason that may enable us to understand better Peirce's position in a historical framework. As Grattan-Guinness has highlighted, Peirce belongs to a mathematical tradition ("algebraic logic, rooted in French revolutionary 'Logique' and algebras and culminating, via Boole and De Morgan, in the Systems of Peirce and Schroeder") really différent from 'mathematical logic' of Frege, Whitehead and Russell where the logicist project was pursued [Grattan-Guinness 1988]. The contrast is striking: the algebraic logicians, following Boole, applied mathematics to logic and drew upon algebras for their mathematical background whereas logicism entailed the application of logic to mathematics and took its main Unes out of mathematical analysis. [GrattanGuinness 1990, 297] Putnam has noted that the standard historiography of modem logic tends to stress the importance of Frege, dismissing "the entire Boolean school — of which Peirce was, in a sensé, the last and greatest figure." [Putnam 1990, 252-260] 115 3aime Nubiola This biased account blurs the différences between both traditions, making then really difficult to grasp the contrast between them. Instead of looking for a réduction of mathematics to logic Peirce, especially in his later period, realized that the idea of continuity was "the keystone of the arch" of ail his thought, as he wrote to William James on 25 November 1902 [Collected Papers 8.257]. "Of ail conceptions continuity is byfar the most difficult for philosophy to handle", Peirce said in the opening words of his eighth Cambridge Lecture entitlecl The l&gic of Continuity [Peirce 1992, 242]. His reflections on continuity stem from mathematics and geometry, but he extended the principle of continuity to the human mind and the universe, as a reply to the inadequacy of mechanicist scientific explanations: the universe is not a mère mechanical resuit ofthe opération of blind law. The most obvious of ail its characters cannot be so explained. It is ihe multitudinous facts of ail expérience that show us this; but that which has opened our eyes to thèse facts is the principle of fallibilism. [Collected Papers 1.162] The idea of continuity, which is the "leading idea" of differential calculus and of ail the useful branches of mathematics, and which has a décisive rôle in scientific thought, is the master key which unlocks the arcana of philosophy [Collected Papers 1.163]. As Hausman has stressed, in Peirce's thought the idea of spontaneity and radical creativity is interwoven with his view on continuity: Both continuity and spontaneity are constitutive of the universe through the function of infinitesimals [Hausman 1993, 190]. In that gênerai framework of an evolutionary realism the search for a logicist foundation for mathematics would appear as totally doomed to failure. Références Apel, K.O. 116 1972 Transformation der Philosophie, Frankfurt : Suhrkamp. 1981 Charles S. Peirce. From Pragmatism to Pragmaticism, Amherst, MA : University of Massachusetts Press. 1993 Transcendentat Semiotics and Truth: The Relevance of a Peircean Consensus-Theory of Truth in the Présent Debate About Truth-theories, in : M. A. Bonfantini and A. Martone (Eds.)» Peirce in ïtalia, Naples : Liguori, 191-208. C.S. Peirce: Pragmatism and Logicism Bernstein, RJ. 1981 Introduction, in [Apel 1981] 1983 Beyond Objectivism and Relativism: Science, Hermeneutics, and Praxis, Oxford : Blackwell. 1992 The Résurgence of Pragmatism, Social Research 59, 813-840. Buchler, J. 1939a Charles Peirce's Empiricism, New York : Harcourt. 1939b Peirce's Theory of Logic, Journal of Philosophy 36, 197-215. Debrock, G. 1992 Peirce, a Philosopher for the 2lst Century. Introduction, Transactions ofthe Ch. S. Peirce Society 28, 1-18. Eco, U. 1989 Introduction, in : C. K. Ogden and I. A. Richards, The Meaning of Meaning, 4th éd., San Diego, CA : Harcourt. Elsenhans, T. (Ed.) 1909 Fisch, M. 1980 Bericht iiber den III. Internationalen Kongress fur Philosophie zu Heidelberg L bis 5. September 1908, reprint 1974, Nendeln, Liechtenstein : Kraus. The Range of Peirce's Relevance, The Monist 63,269-276; 64,123-141. Grattan-Guinness, I. 1988 Living Together and Living Apart: On the Interactions between Mathematics and Logics from the French Révolution to the First World War, South African Journal of Philosophy 7, 73-82. 1990 Bertrand Russell (1872-1970). After Twenty Years, Notes and Records ofthe Royal Society ofLondon 44, 2180-2306. Haack, S. 1993 Peirce and Logicism: Notes Towards an Exposition, Transactions ofthe Ch. S. Peirce Society 39, 33-56. 1996 Pragmatism, in : N. Bunnin and P. Tsui-James (Eds.), The Blackwell Companion to Philosophy, Oxford : Blackwell. Hausman, C.R. 1993 Charles S. Peirce*s Evolutionary Philosophy, New York : Cambridge University Press. Hookway, C. 1985 Peirce, London : Routledge & Kegan Paul. 117 Jaime Nubiola Houser, N. and Kloesel, C. (Eds.) 1992 The Essential Peirce. Selected Philosophical Bîoomington : Indiana University Press. Writings, Houser, N. 1993 On "Peirce and Logicism". A Response to Haack, Transactions ofthe Ch. S. Peirce Society 39, 57-67. Kent, B. 1987 Charles S. Peirce: Logic and the Classification ofthe Sciences, Kingston and Montréal : McGill-Queen's University Press. Murphey, M.G. 1961 The Development of Peirce's Philosophy, Cambridge, MA : Harvard University Press. Murphy, J.P. 1990 Pragmatism from Peirce to Davidson, Boulder, CO : Westview. Nagel, E. 1939 Foreword, in : J. Buchler, Charles Peirce's Empiricism, New York : Harcourt, xiii-xvii . 1956 Peirce, C.S. 1936-58 1992 Logic Without Metaphysics, Glencoe, IL : Free Press. Collected Papers of Charles Sanders Peirce, edited by C. Hartshorne, P. Weiss, and A. Burks, Cambridge, MA : Harvard University Press. Reasoning and the Logic ofThings. The Cambridge Conférences Lectures of 1898, edited by K. L. Ketner, Cambridge, MA : Harvard University Press. Popper, K. 1972 Objective Knowledge: An Evolutionary Approach, Oxford : Clarendon Press. Putnam, H. 1990 Realism with a Human Face, Cambridge, MA : Harvard University Press. Rorty, R. 1961 Pragmatism, Catégories, and Language, Philosophical Review 70, 197-223. 1990 Pragmatism as Anti-Representationalism, in [Murphy 1990]. Russell, B. 1959 118 Wisdom ofthe West, Garden City, New York : Doubleday. CS. Peirce : Pragmatism and Logicism Santaella Braga, L. 1993 Difficultés and Stratégies in Applying Peirce's Semiotics, Semiotica 97, 401-410. Weiss, P. 1934 Charles Sanders Peirce, in : D. Malone (Ed.), Dictionary of American Biography, Vol. 14, New York : Scribner, 398-403. Wright, G,H. von 1993 The Tree of Knowledge and OtherEssays, Leiden : Brill. 119