Sybille Kramer Sybille Kdimer is professor for phi­ Freie Universitat Berlin, FE Philosophic losophy (epistemology, themy of mind) at the Institute for Philoso­ phy, Free University of Berlin. Her publications arc on rationalism, his­ Mind, Symbolism, Formalism: tory of formalization, philosophical aspects of Artificial Intelligence, Is Leibniz a Precursor of consciousness, metaphors, theory of melancholy, computer as a medium Artificial Intelligence? and media-theory.

Kramer, S.: Mind, symbolism, formalism: Is Leibniz a computer is transferable to the human mind. What hap­ precursor of Artificial Intelligence'! pens within our mind is the unconscious working of a Knowl.Org. 23(1 996)No.2, p.84-87, 31 refs. computer-like mechanism. Thus the computer is an ex­ The assumption that Gottfried Wilhelm Lcibniz is a precursor planative model ofthe human mind: the mind is a kind of of the idea of Artificial Intelligence is misleading. The argu­ computer. ment is to distinguish between epistcmc and mind, recognition and cognition. Leibniz interpreted fo rma! symbolic operations But the idea of a fu nctional analogy between the as a mere epistemological instrument, but not as a description machine and the human mind, is not a rationalistic one. of what actually happens within the mind: Leibniz denied that More over: This assumption is inconsistent with the a machine can be used as an explanative model of cognition. rationalistic concept of the mind: Leibniz (II) - as before (Author) him Descartes (12) - explicitly excluded that a machine is ofuse as a model ofthe mind. If the association ofLeibniz with Artificial Intelligence is based on the assumption 1. The Relation between Artificial Intelligence and that a machine gives us an explanative model of the Leibniz: a Common Misunderstanding human mind, then this assumption is wrong. There is a broadly shared opinion within contemporary But we have a more modest version of what Artificial theories of mind: Rationalism in 17th century and espe­ Intelligence is about: Artificial Intelligence creates real cially Gottiiied Wilhelm Leibniz' version, is a precursor machines which are capable ofexecuting virtual symbolic of the fundamental ideas of Artificial Intelligence and machines. Computational Thcory of Mind (1,2, 3). Rene Descartes' The history of the human mind comprises the evolu­ "mathesis universalis" interpreted as the project of a tion of the exterior instruments of human reasoning, universal artificial language for producing and represent­ particularly artificiallycreated symbolic systems. If such ing quantifiable knowledge (4); Gottfried Wilhelm a symbolic system is organized in form of an interpreted Leibniz' "characteristica universalis" interpreted as an calculus, it can be characterized as a "symbolic machine" instrument to derive and to demonstrate all true sentences (13). Symbolic machines are culturally created epistemie automatically (5): Are these ideas not the early versions technologies. They rationalize the process of problem­ of a research program which the pioneers of Artificial solving by means of external algorithmic processes of Intelligence, Allen Newell and Herbert Simon claimed symbol manipUlation. Interpreted in the context of this with their dictum (6): That a mechanized physical symbol non-connectionistic symbolic technologies, Artificial system is the necessary and sufficientcondition for intel­ Intelligence creates automatized symbolic machines. ligent behavior? And which the Computational Theory of Leibniz was an upholder ofthe epistemological useful­ Mind (7, 8) condensed to the thesis that cognition is ness of symbolic machines. He developed the idea of a nothing but the computational manipUlation of mental formal system as a general instrument of knowledge representations (9, p.I I)? procedures and he discovered the possibility oftransform­ Butto claim ArtificialIntelligence as a successor ofthe ing a virtual formal system into a real machine. Thus rationalistic philosophy in the 17th century is much to there is a relationship between the Leibnitian theory of sweeping a statement (10). It is - in a certain _sense - knowledge and the Artificial Intelligence program exte­ misleading and wrong. riorizing and mechanizing human intellectual activity. To get this sense, wc have to introduce a distinction. But to interprete Leibniz as the pioneer of Artificial­ What Artificial Intelligence isabout can be interpreted in Intelligence-as-a-model-of-the-mind constmcts a conti­ a double way: we can sketch a quite excessive or a more nuity where we actually finda significantgap. It is the gap prosaic picture. between a certain external epistemical technique and its Here is the excessive version: Artificial Intelligence is internalization into internal mental processes (14). In this a kind of operative research on the human mind. Insofar view, mechanized symbolic operations function for Leibniz as human cognition can be described as an algorithmic as a methodological prescription and not as an explana­ formal operation, and insofar the computer is a machine tive model: A fo rmal system establishes a norm how we to execute fo rmal procedures, the functioning of the should think if we want to get hue knowledge, but it is by

Knowl. Org. 23(l996)No.2 83 Sybille Kramer: Mind, Symbolism, Formalism

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2.1 From "Ontological" to "Operative Symbolism" supported, that to operate with intellectual symbols pre­ supposes a permanent awareness of the symbolized ob­ "Ontological symbolism" means that a symbol refers to jects (4). But Leibniz discharged this awareness with the an object which exists independent of its symbolic repre­ fo llowing arguments: sentation. If our intellect operates symbolically, it really operates with the "things" the symbols stand fo r. Under (a) All our reasoning is based on sign processes: this condition the idea of rules to manipulate symbolic "ratiocinatio omnis in usu characterum constitit" (16). The reason for the indispensible semiotic nature of the expressions which arc independent of its interpretation cannot arise. Within ontological symbolism formalism is human intellect is, that the finite human mind is insuffi­ excluded. cient fo r grasping the infinitely many attributes which things possess. Thus instead of having an unmediated This changes, however, with "operative symbolism". experience with the objects of knowledge, we build sym­ Here the interpretation of symbolic systems is detached bolic stmctures to represent these objects (17). But this from its construction; the rules of fo rming and transform­ can be done in multiple ways. ing the symbols are not depending on their meaning any longer. Within operative symbolism the process of sym­ (b) Our natural language is the most influential repre­ bolic activity gets a certain self-sufficiency. The charac­ sentational medium. With its vagueness, its metaphoricity teristic feature ofthe operative symbolism is the calculus, and its grammatical variability, every day language serves a fo rmal system which can be interpreted in different very well for our communicative behavior, Qut it is ways. inadequate fo r our cognitive activities (16). Thus we have to look for a language which can be used as a technique. Although "ontological" and "operative" symbolism Such a symbolic instrument for reasoning cannot be are idealized categories, we may recognize that during found, it must be produced - mtificially. Greek antiquity - the era of the formation of classical tragedy, science and philosophy - "ontological symbol­ In contrast to the fleeting natureof human speech, such ism" was the dominant model - even in mathematics. But a "language" should be a system with an ongoing fixed in the premodern era of the 15th, 16th and 17th century materiality, which speaks not to the ears but to the eyes. the idea of operative symbolism got more and more Leibniz called such graphical signs which m'e independant influential. of speech, "charaeteres". Characters are of permanent material stability, with the consequence that they can be The basic idea of operative symbolism is that we have manipulated. Within mathematics, systems of characters not to take care of the meaning of the symbols when we have already been established which successfully func­ manipulate symbols corresponding to pregiven rules. tion as cognitive instruments (17). These are the socalled This independence ofthe signs from the signified objects, calculi.

84 Know!. Org. 23(1996)No.2 Sybille Kramer: Mind, Symbolism, Formalism https://doi.org/10.5771/0943-7444-1996-2-83 Generiert durch IP '170.106.202.58', am 28.09.2021, 13:03:43. Das Erstellen und Weitergeben von Kopien dieses PDFs ist nicht zulässig. (c) The prominent example for the operative use of a toire of characters and rules to form and transform strings calculus is the decimal numeral system. Like evelY calcu­ of characters. (b) An interpretation for the calculus must lus it has a double fu nction: It is al1lediu1J1for representing be discovered, which stated a connection between the infinitely many numbers with a finite alphabet ofnumer­ objects and the calculus in such a way, that the legal als and at the same time it is an instrument to operate with formulae of the calculus correspond to true sentences numbers by the manipulation of the numerals according about the objects represented. Insofar as (a) and (b) is to algorithmic rules. With the decimal numeral system, fulfilled, problems of the domain in question can be written reckoning becomes a cultural technique. For solved by the aid of mechanized symbolic operations. A Leibniz a reckoning-rule has the status of a rule to complex and complicated intellectual action can be re­ transform signs (18): The concept of the algorithm is duced to the rule governed manipulation of signs. The born. calculus serves as a ,jililimAriadne" which directs recog­ With the dissemination of the decimal system the use nition under the condition, that we have no immediate of a formal language became a model even for higher access to the world. Leibniz calls this kind of calculized, mathematics. The invention ofLetter Algebra by Francois non-intuitive recognition "blind or symbolic reasoning" Vietc, Analytical GeametJ}' by Rene Descartes, and - last (25). not least - infinitesimal Calculus created by Leibniz (f) Leibniz tries to generalize the operative fu nction of himself: these mathematical achievements were all based formalizing. He had the vision of a "sci entia generalis" on the construction of calculi. organised as an "ars characteristica" (16). Within this (el)The dodge of a calculus is, that the rules offorming "calculus ratiocinator" all true sentences would be me­ and transforming the characters do not refer to the chanically derived and refering to each sentence it would meaning but only to the syntactical features of the char­ be decidable, ifit is well formed or not, that means, if the acters. The construction and the interpretation of calculi sentence is true or wrong. With such a "calclilus diverged. Leibniz was aware of this detachment: ratiocinator" all knowledge acquisition and all knowl­ edge proving would be an effective procedure. Errors of He characterizes the profits of his infinitesimal calcu­ reasoning would be pure mistakes of calculization. lus as the possibility that the mathematical operation with the differentials becomes independent of beliefs concern­ The research of Godel, Church and Kleene in the 20th ing the "ontological nature" of infinite mathematical century has demonstrated, that such a universal calculus obj ects (19). Unlike the proponents and the opponents of is logically impossible. But what is not impossible, is the his calculus, who both interpret his calculus in a invention of "local" calculi; that are formal systems denotational manner, Leibniz emphasized that the inner which represent a limited region of objects (26). coherence of his calculus does not depend on the meta­ physical dispute how to interpret the differential symbol­ 2.3 Followers of the Leibnizian Program ism (20). To calculate correctly does not presuppose an Concenling the connection between Leibniz and Arti­ answer to the question, if an infinitesimal magnitude ficial Intelligence, it is of importance only, that the exists as an actual or as a potential infinity (21). Leibnizian program of calculized reasoning as a "scien­ Even concerning his logical calculi Leibniz stressed tific practice" and as a "prophetic concern" has estab­ the autarky of his systems in relation to special interpre­ lished a certain tradition. The precursor of this tradition tationo: His logical calculi developed about 1686 can be is the Katalanian philosopher and theologicianRaimundus interpreted in a multiple perspective, as extensional, Lullus (1235-1315), its followers are George Boole (1815- intensional or modal systems (22, 23). As Detlef Thiels 1 864), Gottlob Frege (1848-1925), the young Wittgenstein argued: They do not only allow different interpretations, and Rudolf Carnap. This tradition is marked by four but seem to be constructed for different interpretations assumptions: (24). (a) Rational thinking can be made explicit by algorith­ When Leibniz sketched his aI's combinataria, the mic procedures within a formal symbolic system. variations, permutations and combinations of the strings (b) These formal procedures can be interpreted 111 a of signs do not refer to a special referent: A diversity of numerical and in a logical perspective. referential domains is possible. Leibniz stresses: If we (c) The semantics of the formal e'xpressions is a interpret the signs as multitudes, we get Algebra; if we compositional semantics, that is: semantical differ­ interpret them as spatial points, we get Geometry, and if ences are definable as syntactical differences. we interpret them as terms, logic is the result (17, p.531). (d) All knowledge is propositional or can in principle be (e) ButLeibniz was not only a practicianofcaiculization, transformed into a propositional fOlmat. he also got the concept of a calculus and of ealculizing But what is missing is the idea, that calculi zed opera­ reasoning. A concept which is ex�mplary realized in, but tions on symbolic .representations is something which not limited to Mathematics and Logie (16). happens inside the human mind. Neither for Leibniz nor To use a calculus as an intellectual instrument, two for Boole, Frege, Wittgenstein, or for Carnap formal conditions have to be taken into account: (a) There must procedures are explanations of mental processes which be given a symbolic system consisting of a finite reper- actually take place, if we are thinking. Mechanized

Know!. Org. 23(1996)No.2 85 Sybille Kra.mer: Mind, Symbolism, Formalism

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3.1 Consciousness Cannot be Explained in Mecha­ mistake: Abstract essence would be confused with con­ nized Terms crete existence. But the machine did not serve as a model for the human Because mechanized recognition is an epistemological mind. Lcibniz - as Descartes - refused the idea of an ideal, the inference from epistemic procedures to the analogy between the machine and the mind. The most fu nctioning of the human mind is inadmissible. Thus famous reference is his thought-experiment in the Leibniz excluded that the machine can serve as an ex­ "Monadologie" (30). Leibniz argued: Imagine that we planative model of the human mind. could design a machine capable of perception, thinking, c and consciousness. Imagine further that we ould enlarge 3.3 The Compnter not a Tool, but a Medium of the the machine to the dimensions of a mill so that we could Human Mind enter it. What we will find inside is the mechanical It is not by chance that the Leibnitian program of movement ofthe parts ofthe machine, but we look in vain calculized reasoning is located within the area ofEnlight­ for something which can explain consciousness. Thus enment. Striving to enlighten the people, was based on the consciousness or perception "is inexplicable by means of assumption that the natural light of human reason was mechanical reasons, that is by means of shape and move­ distributed to everybody and it was ofrelevance only to get ment" (30, § 17). people to use their mind in a correct way. Calculized We seem to be confronted with a paradoxical configu­ thinking was the project of transforming truth into cor­ ration. With regard to calculi zed reasoning, thinking can rectness, an epistemological knowledge-technique, nec­ be externalized as a formal operation, that is: it can in essary just because the normal activity of our mind is not principle be mechanized. But concerningmental activity, wworking in this way. that means: the concrete working of the human mind, If we interpret symbol-oriented ArtificialIntelligence thinking cannot be explained in technical terms. The split in the horizon of the long lasting history of calculizing off between mind and consciousness is possible for the and nowadays even automatizing the exterior symbolic epistemic operations, but impossible for our cognitive operations, this perspective gives us a fruitful explana­ behaviour. The question is: why? tion of what is happening within AI. But to pretend that

86 Know!. Grg. 23(J996)No.2 Sybille Kramer: Mind, Symbolism, Formalism

https://doi.org/10.5771/0943-7444-1996-2-83 Generiert durch IP '170.106.202.58', am 28.09.2021, 13:03:43. Das Erstellen und Weitergeben von Kopien dieses PDFs ist nicht zulässig. the formal procedures ofthe computers are an example for (12) Descartes, R. : Von dcr Methode des riehtigcn the inner functioning of the mind, transforms a culturally Vernunftgebrauchesund derwisscnschafUichen Forsehung. Ham­ created medium into the natural equipment of the mind. burg: Felix Meiner 1960. (13) Kramer, S.· Symbolisehe Maschincll. Die Idee der For Leibniz the situation is the other way round: The Formalisierung in gesehiehtlichem AbriJ3, Darmstadt: impossibility to explain the phenomenon of conscious­ WisscnsehafU. Buchgcsellscha1l 1988. ness in technical terms, is a hint that our mind in its ([4) Kramer, S.: Denken aIs Reehenprozedur: Zur Genese eines mental life docs not v/Ork like a mechanism, because it kognitiolls\vissenschaftlichenParadigmas,Kognitionswissenschaft realizes an indispensible subjective point of vie'w. But (1991)2, p.I-1O intersubjectivity as an epistemological ascription cannot (15) Kramer, S.: Bercchenbare Vernunft. Kalklil und Rational ismus substitute subjectivity as a cognitive description. im 17. lahrhundcrt. Berlin, New York: de Gruytcr 1991. (16) Leibniz, G.W.: Die philosophischen Sehriftcn. Gerhnrdt, c.I. \Vhatclo \ve learn from this story? Whatever a machine (Ed.) Hildesheim: Olms 1965. Vol. VII, 1'.205, 31, 191 is doing, should not be expressed in terms of substihlting (17) Lcibniz, G.W.: Opuseulcs et fragments inedits de Lcibniz. human beings. Incredible overestimation and groundless COllturat, L. (Ed.). Hildesheim: Olms 1966. p.43 1, 513, 155 fear, both are founded on such an anthropomorphic ([ 8) Scholz, H.: Leibniz und die matbematische conception of technical artefacts. Symbolic Artificial Grllncllageniorschung. ln: Scholz, E.: Mathesis UniversaIis. Basel Intelligence physically realizes symbolic machines. It 1961. p.128-51 creates a kind ofentities the use ofwhich is notto do better (19) Leibniz, G.W.: Mathematische Schriftcll. Gcrhardt, Cl. (Ed.). what humans already do quite well, but to facilitate I-lildesheim: Olms 1965. Vol. IV, p. 92 ' experiences, we do not have without thc computational (20) Kr�imer, S.: Zur Begriinclung des InfinilesimalkalkiHs. Philosophia Natural is 28(1991), p. 117-146 apparatus. The computer should be interpreted not as a (21) Lcibniz, G.W.: f-listoria et Origino calculi differentialis a tool - or a model - of the human mind, but as a medium G.G. Leibnitio conseripta. Gerhardt, c.l. (Ed.). Hannoyer 1846. of human knmv ledge. 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Yon: Leibniz als Ahnherr del Kybernetik - ein dations ofCognitiYe Science, Cambridge, MA: MIT Press [981. ' bisher unbekanntcr Leibniz'sehcr Vorsehlag einer "Machina (8) Pylyshyn, Z. W.: Computation and Cognition. Toward a aritilmetieadyadicac". Stud.Leibnit. SupplXII I. Wiesbaden: Steincr foundation for Cognitive Science. Cambridge MA: MIT Press 1972. p. 255-268 1986. (30) Leibniz, G.W.: Monadologie. In: Philosophische Schriftell. (9) Huth, M.: Symbolic and Sub-symbolic Knowledge Organiza­ Gerhardt, c.I. (Ed.). Vol. VI. Hildesheim: Olms 1965. '.607-23 tion. Know!. Org. 22(1995)No. l, p. 10-16 1 (3 1)Jalabert, J.: La notion d'essence ct d'existenee dans la (J 0) Kramer, S.: Rationalismlls und Kiinstliche Intelligenz: Zur philosophic de Leibniz. Stud. Leibnitiana, Suppl. Wicsbaden: Korrektur cines MiBverstiindnisses. Kiil1stLInteiligenz (1993)No. 1. Steiner [968. p.13-21 I, p.31-35 (I I) Leibniz, G.W.: Monado[ogie. In: Hauptschrirten zur Grllnd[egullg del' Philosophic, Bd.II. Hamburg: Felix Meiner Prof Dr. Sybille Kramer, FU Berlin, FB Philosophic (WE 1), 1966. I' 435-457 Habelschwerdter Allee 30, D-14195 Berlin

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