***************************************************************** * * Titel: Wittgenstein Versus Russell On Logical Realism Autor: Emamuele Riverso, Salerno - Italien Dateiname: 17-2-95.TXT Dateilänge: 21 KB Erschienen in: Wittgenstein Studies 2/95, Datei: 17-2-95.TXT; hrsg. von K.-O. Apel, N. Garver, B. McGuinness, P. Hacker, R. Haller, W. Lütterfelds, G. Meggle, C. Nyíri, K. Puhl, T. Rentsch, J.G.F. Rothhaupt, J. Schulte, U. Steinvorth, P. Stekeler-Weithofer, W. 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Those articles and excerpts from * * articles which the subscriber wishes to use for his own * * private academic purposes are excluded from this * * restrictions. * * * ***************************************************************** Summary. 1. In l9l3 Bertrand Russell was credited as the supporter of a sort of Platonism in which a world of relations served as the framework for all existing and possible knowledges. 2.In his works on mathematics and logic he employed logistics to build up all branches of mathematics using only logical relations. 3.Instead Wittgenstein had no inclination to conceive of logic as a description of a particular sort of objects.He wanted to find in logic the means of discovering the structure of facts and its projection in the language. 4. Russell was prompted by Wittgenstein to abandon his Platonism. 5. He tried to salvage his logistic achievements by separating them from Platonism of relations. 6. He adopted the principle of extensionality and declared logic as purely linguistic but could not satisfy Wittgenstein's requirements. 7.He could not make logic self-sufficient as Wittgenstein required. 8 .The view of Wittgenstein remained very different because what he cared for was only clarification of thought and of facts as we conceive them. 1.1. George Santayana, a professor at Harvard University and a renowed philosopher of the last and present centuries in a book of l913 described the philosophy of Bertrand Russell as a sort of mathematical Platonism in which "the most trivial truths of logic are as necessary and eternal as the most important" *1*. Santayana gave much credit for the knowledge of Russell's thought to THE PROBLEMS OF PHILOSOPHY that Russell had published in 1912 *2*. 1.2. In this little book Russell had pictured a world of Universals with a declared analogy to Plato's world of ideas, and had expressed the belief that there must be such entities as Universals and that their being cannot be merely mental *3*. The most important among Universals are relations; moreover, though this is not said in THE PROBLEMS, Russell thought that all Universals are in fact relations, therefore the world of Universals is a world of relations and relations SUBSIST while physical objects exist *4*. We are acquainted with such beings just as we are acquainted with sense-data. There is a sort of acquaintance that underlies our knowledge of logic, that is the acquaintance with logical objects or relations. 2.1. As the notes of the world of Universals (unchangeable, rigid, exact, delightful to mathematicians, to logicians, to builders of metaphysical systems and to all who love perfection more than life) *5* in THE PROBLEMS of l912 are the same ones of the world of mathematics ( truth, supreme beauty, a beauty cold and austere, sublimely pure, rigidly logical, independent of us and our thoughts) described in THE STUDY OF MATHEMATICS of 1902 *6*, we can draw the conclusion that during the years from l902 to 1912 Russell lived and worked with a strong feeling that his logical inquiries into the fundaments of mathematics were leading him towards real objects of a particular sort whose best graphic representation was attainable by the notations of logistics he had invented . 2.2. There is no doubt that such a feeling assisted and supported him emotionally throughout the years he worked with A.N.Whitehead in the painstaking production of PRINCIPIA MATHEMATICA. 2.3.In this huge work and in the logical papers he wrote during the same years he aimed to arrive at the deepest possible analysis of the ideas occurring in mathematical propositions to attain the primitive and undefinable elements of such ideas and to represent the steps in the trains of reasoning which lead from these elements to the most complex achievements in mathematics. 2.4. He was convinced that the exact representation of such elements and of their compositions, both belonging to the world of relations, are not attainable by means of ordinary language because the grammatical structure of this language "is adapted to a wide variety of usages. Thus it possesses no unique simplicity in representing the few simple, though highly abstract, processes and ideas arising in the deductive trains of reasoning .... Its grammatical structure does not represent uniquely the relations between the ideas involved" *7* ; the notation he used was thought by him as representative of logical realities and was particularly useful to provide a detailed presentation of the logical structure of some misleading sentences of ordinary language as the ones containing descriptions *8*. 3.1. It is beyond question that Russell was led to believe in a rational world of logical elements represented by logistic notation because he had had a scholarly education in which Plato's dialog ues had been prominent; of course his psychological attitude of those years was also strongly influential on his philosophical views of logic. 3.2. Both education and psychological attitude induced him to believe that notations like logical constants are representative (or denotative) of objective relations and these are independent of our thought and of all representations, both in the case that these are correct as logistic notation and if they are less correct as words and sentences of ordinary language. 3.3. But Ludwig Wittgenstein, with whom Russell had been in contact since October l911, had had a different scholarly education (technic and engineering) and was the bearer of a different psychological attitude, as we know from his biography. When he met Russell and benefited from his teaching, he arrived at the view that logic is concerned with possibilities of states of affairs of the world and their representation in logical space *9* by means of signs and their syntactical employment *10* ; both states of affairs and their representations existing in the same and only world. As in Wittgenstein's view, the structure of a state of affairs is shown and not represented, his fundamental idea was that the logical constants are not representatives and there can be no representative of the logic of facts *11*. 3.4. Consequently the whole of the Platonic world of relations or logical entities cherished by Russell was disposed of altogether by him. Later Russell confessed that "the eternal Platonic world " had given him something non-human to admire and he had suffered when Wittgenstein had discouraged him from identifying mathematics with the study of that world by inducing him to regard it as nothing but tautologies *12*. In fact the suggestion that mathematics is tautologies is connected with the view that logical constants are not representative. 4.1. In my opinion the challenge posed by the young Wittgenstein against the world of autonomous logical forms prompted Russell to give this world up also because of a deep psychological crisis he underwent during the years from l910 to 1914 *13*. He aknowledged that Wittgenstein was right and thought it necessary to conceive of logic ( and mathematics ) not as an inquiry about a particular sort of objects but as an inquiry about language that could be expressed in a language of a level higher than the one described . He expressed this view in the INTRODUCTION to the English edition of the TRACTATUS *14*, where he is much more concerned with language than in the years he had been a Platonist, when he had considered it almost irrelevant for logic *15*. 4.2. This was not in agreement with Wittgenstein's opinion that logical structures of facts show themselves in the language but cannot be represented. But as he had given up the world of logical objects, Russell was pledged to find a new STATUS for logic that could salvage the results of the enormous amount of work he had spent in the elaboration of PRINCIPIA MATHEMATICA. Perhaps he thought, and many students agreed, that the logistic apparatus enclosed in the three volumes of this work was independent of the metaphysical belief he had endorsed during their preparation, to the point that another metaphysical belief could be substituted without serious problems. 5.1. Actually he did not hesitate to bring about various devices to transform his logistic apparatus from a representation of the world of logical objects into a syntax fit for a language that could describe perfectly empirical facts. He took some cues from Wittgenstein as he had understood him. 5.2. In a manuscript book (never published before the COLLECTED PAPERS) composed in May-June 1913 *16* he endeavored to give a comprehensive arrangement and an assessment of his views on knowledge that he had only sketched in previous writings . So he had to resume the item of acquaintance of logical data *17* and affirmed that " there certainly is such a thing as 'logical experience' ... which seems fitly described as 'acquaintance with logical objects' " *18* . He touched on the question of logical constants, when he affirmed that " 'logical constants', which might seem to be entities occurring in logical propositions, are really concerned with pure FORM, and are not actually constituents of the propositions in the verbal expression of which their names occur " *19*. Here the verbal expression is still kept separate from logical form though logical form "is not a ' thing', not another constituent along with objects that were previously related in that form" *20*, but it is what remains of a complex when all its constituents have been enumerated, and can be described as the way in which the constituents are combined in the complex. 5.3. To represent or symbolyze this way of combination it is convenient to replace in a phrase the words denoting the entities of the complex by letters having no meaning. Such a procedure had been used by Russell in his logical works. It required two languages, a language descriptive of facts and things and a language representative of the logical forms of facts. 5.4. Russell gave an elaborated presentation of this view in his lectures and papers on logical atomism *21* and thought he had satisfied Wittgenstein's criticism of his logical realism. The logistic apparatus he had built up to make a representation of the Platonic world of subsistent relations had demolished almost all entities of traditional metaphysics by the theory of descriptions and had wholly dispensed with classes as objects, nevertheless it was not an apparatus that could easily be transported on pure facts as he hoped and some adjustement was necessary, for which he made provision in the second edition of PRINCIPIA through the addition of a new introduction and some appendices *22*. 6.1.The most important adjustments were obtained through the adoption of the principle of extensionality that can be regarded as fundamental in the TRACTATUS and is suggested by the logic of PRINCIPIA. Much has been said about this principle by Russell, Ramsey, Carnap, Weinberg, Favrholdt, etc. As understood by Russell it was intended as a device to adapt his logistic to a strictly empirical view of knowledge and reality, and during the heyday of Logical Empiricism the logic of the second edition of PRINCIPIA that made use of that principle was strictly associated with TRACTATUS and employed as the best tool to build up science without metaphysics. 6.2. Perhaps philosophers like Alfred Jules Ayer that became acquainted with Russell and his work in those years, barely suspected that his most relevant achievements in logic had been accomplished with the assistance of a Platonic metaphysics *23* . Russell himself, in the new context of the success that Logical Empiricism had obtained for the logic of PRINCIPIA second ed. and in the light of the increasing interest philosophers were paying to semiotics and problems of language, did not hesitate to affirm that logical constants, "if we are to be able to say ANYTHING definite about them, must be treated as part of the language, not as part of what the language speaks about. In this way, logic become much more linguistic than I believed it to be at the time I wrote the 'Principles' " *24* . 7.1.It is interesting to see how Russell struggled with the problems arising from the view that the nature of logic is purely linguistic both in the Introduction to the second ed. of PRINCIPLES (l937) and in AN INQUIRY INTO MEANING AND TRUTH *25* Nevertheless he did not find a way to make logic self-sufficient and was increasingly obliged to enlarge the field from which logic could obtain a meaning and a justification despite the fact that Wittgenstein had proclaimed that " die Logik muss für sich selber sorgen" *26*. He felt obliged to build up the metaphysics of neutral monism, a new theory of knowledge and a new concept of the physical world. He strongly opposed the formalist interpretation of mathematics, particularly that of David Hilbert, but did not succeed in offering a satisfactory assessment of the logical import of the language of logistics without being involved in practical applications and semantic problems. In fact the logical system of PRINCIPIA, after the separation from its original Platonic background, ultimately proved unable to suppy a really useful framework for the empirical reconstruction of scientific theories . 7.2.It revealed new problems on the way of reaching full coherence and completness in its internal organization and became of a reduced philosophical interest and of a strictly formal account; consequently it was superseded by the more operationally effective systems of formalists, that were able to face the new and more severe demands for formalization suggested by the works of Hilbert and Gödel. 8.l. Wittgenstein had a very different view since his earliest acquaintance with logic as he never sought an ontology that would build up a world of surer and eternal entities that could be superimposed onto the world of sensible things to organise and warrant them by a solid metempirical structure . He needed only an ontology of real and possible facts representable in the language as in a mirror . So the only objects he could conceive of were things occurring in states of affairs and bearing in themselves the possibility of facts *27*. 8.2. He did not look for what is fundamental, basic and beyond doubts as a ground on which to build the structure of sciences through a deductive procedure . He adopted the symbols of Russell's formalism and Sheffer's functor only as a way to obtain a neat picture of states of affairs in their linguistic mirroring, not to operate a deduction of complex from simple. "In philosophy there are no deductions; it is purely descriptive", he wrote in NOTES ON LOGIC *28* and in TRACTATUS *29* he added: " Der Zweck der Philosophie ist die logische Klärung der Gedanken / Die Philosophie ist keine Lehre, sondern eine Tätigkeit ", and what philosophy aims at clarifying is not logical objects added to states of affairs or discovered in them but the very structure of states of affairs through the clarification of propositions that mirror such states and bring about the understanding of their constituents and forms. 8.3.Nevertheless this role of mirroring the structure of real and possible facts that Wittgenstein entrusted to logic entailed the commitment to a sort of ontology of the world of experience and science that kept him away from formalist's view thoug h his treatement of logistics approached sometimes their technics. NOTES *1* G.Santayana, Winds of Doctrine. Studies in Contemporary Opinion, London, Dent and Sons, New York, Scribner's l940 p. 122, the text is the same of the ed. of 1913. *2* Home University Library l912 first ed. *3* The Problems of Philosophy, London, Oxford University Press l970 p.55. *4* Ibid. p.57. *5* Ibid. *6* The paper was written in London in Oct. 1902, The Collected Papers of B.R. vol.12 London, Allen and Unwin l985 pp. 83-93. *7* Introduction to the first ed.(l9l0) of A.N.Whitehead and B.Russell, Principia mathematica, Cambridge, Cambridge University Press l950 vol. I p. 2. *8* Ibid. vol.I pp. 66-70, l73-l86. *9* Tractatus logico-philosophicus, London, Routledge and Kegan Paul l963, 2.202. *10* Ibid.3.327. *11* Ibid.4.0312. *12* B.Russell, My Mental Development, in P.A.Schilpp, The Philosophy of B. Russell, New York, Tudor l951, 3. ed. p.19. In the Introduction to the second ed. of Principles ( London, Allen and Unwin l937 p.l0 ) Russell remembered: " I shared with Frege a belief in the Platonic reality of numbers, which, in my imagination, peopled the timeless realm of Being.It was a comforting faith, which I later abandoned with regret". *13* E.Riverso, Il pensiero di Bertrand Russell, Napoli Libreria Scientifica Editrice III ed. pp. 33-35 and Id. Ayer's Treatment of Russell, in L.E.Hahn ed. The Philosophy of A.J.Ayer, La Salle, Open Court l992 pp.519-523; see also I.K.Blackwell, Our Knowledge of OUR KNOWLEDGE, in RUSSELL l973, XII pp. 11-13. *14* In the cited ed. of Tractatus pp.XII, XX-XXII; cfr. also B.Russell, My Phylosophical Development, London, Allen and Unwin l959 pp.113-114. *15* It is interesting to remark that the index of Principles (1903) has no entry for language and the entry for sign concerns only relations. *16* Theory of Knowledge, publ. the first time in Coll.Papers, vol.7, London, Allen and Unwin; the existence of the manuscript has been unknown till the papers of Russell's Archives were catalogued in 1967 to be sold to McMaster University. From this B.Russell took suggestions and pages for separate papers and books. *17* Ibid. pp.97-1o1. *18* Ibid.p.97. *19* Ibid.p.98. *20* Ibid. *21* B. Russell's writings on logical atomism in Coll.Papers vol.8, London, Allen and Unwin 1986. *22* E. Riverso, Il pensiero di Bertrand Russell, Napoli l958, I ed.Napoli, Istituto Ed.del Mezzogiorno pp.215-223. *23* A.J. Ayer in L.E.Hahn ed.The Philosophy of A.J.Ayer, pp. 542-543. *24* B. Russell, Introduction to the second ed. of The Principles of Mathematics, London, Allen and Unwin l937 p.XI. *25* London, Allen and Unwin 1940. *26* Tractatus, 5.473 a. *27* Ibid. 2.0121. *28* Wittgenstein, Notebooks 1914-1916, Oxford, B. Blackwell 1961, App.I p.93. *29* Tractatus 4.112.