On The Logical Status of Dialectic (*) -Historical Development of the Argument in Japan- Shigeo Nagai Naoki Takato 1 The term "logic" seems to be used in two different ways. One is in its narrow sense; the other is in its broad sense. In the narrow sense, logic would be the aggregation of analytic knowledge. All logically valid statements, whether they are those which are based on object-theory consisting of object-language or are those which are based on meta-theory consisting of meta-language, must be analytic. Logically valid inferences, whether deductive or inductive, are also formed by only analytic statements within the framework of meta-theory, so logic in the narrow sense should be analytic-theory. Logic in the narrow sense would be divided into two levels, logic as philosophy and logic as individual science. As logic as philosophy develops in a particular field, it comes to be an individual science. On the other hand, logic in the broad sense is much wider. It includes methodology, which consists of epistemology and methodology of inquiry. The classification of logic we have in mind is figured as follows: Logic (in the broad sense) logic (in the narrow sense) methodology logic as philosophy logic as individual science epistemology methodology of inquiry The purpose of this paper is to analyze and explicate the nature of Dialectic according to the classification of logic mentioned above, paying special attention to the contributions on the subject by the Japanese philosophers of science. The point we are going to make here is that Dialectic is, in our opinion, tightly connected with all the branches of logic in the broad sense. In order to make this point clear, we shall describe and make some comments on T. Sugihara's "logic of motion", H. Kurosaki's "natural dialectics" and N. Nakano's arguments on Hegel's dialectic. Finally we should like to introduce "the logic of philosophical reflection", which we suppose is suggested in Carnap's idea "explication", and to explicate an important aspect of Dialectic. 2 The investigation into dialectic in Japan has been conducted independently of western tradition. Main concern has focused on the Sugihara, who has made great achievements in modal and many-valued logics, suggested in his early papers that it would be possible to establish "logic of motion" based on "logic of time" to which he had devoted himself for years(1). Formal logic (including symbolic logic), as V. I. Lenin claimed, had not been thought able to deal 1
with the law of motion and development. All logic could do is to formalize so-called logical relationships between two propositions, in which temporal and motional relations are ignored. Lenin asserted, on the other hand, that dialectical logic could comprise the elements of time and motion. Lenin's criticism, however, does not seem justified. Dialectical logic had not and has not succeeded in formalizing itself nor given any evidence that formal logic could not intrinsically be logic of motion at all. On the contrary Professor Sugihara's study on the logic of time seems to show that formal logic could prepare the way for establishing the logic of motion in the future. Briefly described, his argument is based on his uniquely introduced standard of classifying logic. On the basis of his standard he distinguished ancient logic from modern logic. He mentioned Euclid's The Thirteen Books as a typical work written within the framework of ancient logic, and Newton's Mathematical Principles of Natural Philosophy as that of the other kind of logic. Ancient logic developed through the systematization by Aristotle to contemporary symbolic logic, in which non-temporal and non-motional relations are exclusively concerned. Modern logic, which has not satisfactorily systematized itself yet, has been taking a different way. It has been developing in the field of physics. Physics, of course, deals with temporal and motional logical relations, so the logic on which physics depends naturally must be able to deal with these elements. We think his suggestion that the logic of motion based on the logic of time will be established in the near future is quite acceptable, if we remember the process of establishing inductive logic, which started as a branch of the theory of classic probability and finally gained a position in its own right. It seems to me that the same thing could be said about the logic of motion. If the logic of motion is formalized as formal logic, we have to admit that it should belong to logic in the narrow sense, that is, to an individual science, which would be called dialectical logic. 3 Hiroshi Kurosaki, who has come to philosophy of science through physics, published a paper titled 'The Nature of Dialectical Materialism' in the sixties (2). In those days he was devoted to the study of the epistemology of natural science under the influence of R. Carnap and G. Hempel. He grasped a core idea of "natural dialectics" advocated by F. Engels as "the law of transformation of quantity into quality" and tried to analyze and explicate the law. He began by contrasting the law of nature (in a broad sense) with the law of natural dialectics. He described these laws, (W) as an instance of the law of nature and (E1) as an instance of the law of natural dialectics. They are as follows: (W) There is a relationship between water and temperature, that is to say, water changes into solid at 0 and gas at 100 as its temperature is continuously raised or lowered under the standard barometric pressure and while such changes are happening, the temperature remains the same. (E1) Qualitative changes in the natural world take place in a definite way rigidly fixed on each occasion, only when the quantitative changes (increasing or decreasing) of materials or motion (namely, energy) occur. He pointed out that there was an undeniable difference between these two laws. From (W), we can logically deduce factual propositions and verify or falsify them, but 2
not from (E1). As for natural science, it is required that every particular law could be deduced from the more general laws with logical validity. So it is inevitable to conclude that dialectic law is not a kind of the law of nature, and natural dialectic is not a natural science, and furthermore dialectical materialism could not be classified as a kind of logic in the narrow sense. Kurosaki proposed, instead, that Dialectic should be regarded as a way of looking at things, which is especially required when we consider the problems of development. In other words Dialectic is a view of the world regarding it as development. Each law of Dialectic is a proposition representing such a world view, and Dialectic as a system of such laws is a methodology of inquiry, which would provide anticipations required to resolve the problems we have to cope with in the process of development. 4 H. Nakano, who is a specialist in Hegel's philosophy, especially of dialectic, analyzed dialectic and explicated it as the methodology of "dialogic thinking"(3). We should highly appreciate his works on Dialectic but we must point out that he fell victim to the fallacy of simplification, when he said, 'Dialectic is neither a logic nor a law, but a "Denkenmethode" (plainly speaking, "Denkenweise")'. It would be true that the dialectical laws of natural dialectics are neither logical nor natural; however, we can claim that they are empirical universal propositions, so we do not have to hesitate to admit that they are a kind of law. It could be right that the methodology of dialogic thinking does not belong to logic in the narrow sense. But it is also apparent that it belongs to the methodology of inquiry and that in this sense it has a position in its own right within the framework of logic in the broad sense. In spite of over-simplifying the problem, Nakano's argument is very suggestive. First of all, he made clear the nature of Dialectic as a multifactorial complex. We quite agree that Dialectic contains a core factor of dialogic thinking. Nevertheless, we do not feel inclined to deny the possibility that the logic of dialogue becomes a part of logic in the narrow sense. In fact it seems that the logic of dialogue advocated by D. Lorenzen and R. Rescher showed that possibility. 5 "Dialogic thinking" could be regarded as a process of "surmounting" contradiction at various levels. As showed in Nagai's early paper, logical contradiction could be classified into four groups (4). Here we should like to add another classification from a different perspective. We rename logical contradiction "genuine contradiction", and to contrast with it, we shall introduce "pretended contradiction". As far as genuine contradiction is concerned, two ways could be seen as the process of surmounting it. The first is when one person violates the law of contradiction of propositional logic (the law of semantical contradiction), making a judgement that p (the statement is true) and non-p (the statement is not true). In this case we must make a choice between p and non-p alternatively, for whatever reason, either logical or empirical. Once the decision of choice is made, the process of surmounting contradiction will be completed. The second case would be found in the case that statement p and non-p are both provable according to the rules of a certain theory. Such a case would be seen as the contradiction of syntactical sense. The only possibility for us to get out of the contradiction in this case is to modify the rules of proof within the theory. 3
The process of surmounting "pretended contradiction" is different. Distinguished advocates of Dialectic in history, Socrates and Hegel, tackled this kind of contradiction. As we have seen, in "genuine contradiction", p and -p are incompatible. So an alternative judgement is demanded between the two. However, in "pretended contradiction", the opposite two must be compatible. In fact, this compatibility is a necessary condition for "Aufheben", a key concept of Dialectic, to work. A typical case of Socrates' Dialectic could be described as a dialogue between two persons. That is, a person X1 recognizes that A. But X1 is not confident of that. X1 starts a dialogue with X2. Suppose X2 denies that A and asserts that non-a. X1 understands that X2's claim would be part of the process to seek for the truth, for he himself is still wondering whether A or not. However, he does not think that the total negation of A leads to true recognition, so is unwilling to accept non-a as true unconditionally. He might try to refute X2's assertion by the use of, for instance, reductio ad absurdum. But if we draw contradiction from the presupposition that non-a, we can not conclude that A is true, though we can make sure that non-a is not true, because the relation between A and non-a is only "pretended contradiction". We would regard this stage of Dialectic as "negative" or "fighting". On the other hand, the next stage would be characterized as "affirmative" or "cooperative". Both X1 and X2 recognize that neither A nor non-a is true, and start their dialogue cooperatively toward true recognition. As a result, "pretended contradiction" being resolved, they could reach B as a synthesis. This process is so-called "Aufheben". Therefore, it is necessary that the contradiction is "pretended", if the second stage of dialectic functions as "Aufheben". 6 It is known that R. Carnap took a negative attitude toward Dialectic through his life. However, his concept "explication" seems suggestive. We suppose the concept implies the possibility of interpreting Dialectic as "the logic of philosophical reflection". We also think Hegel already held this factor within his concept of Dialectic. It would be better to start by talking about Carnap's "explication" in some detail. I should like to quote a paragraph from Logical Foundations of Probabilities: A problem of explication is characteristically different from ordinary scientific (logical or empirical) problems, where both the datum and the solution are, under favorable conditions, formulated in exact terms (for example, 'What is the product of 3 and 5?', 'What happens when an electric current goes through water?'). In a problem of explication the datum, viz., the explicandum, is not given in exact terms, if it were, no explication would be necessary. Since the datum is inexact, the problem itself is not stated in exact terms; and yet we are asked to give an exact solution. This is one of the puzzling peculiarities of explication. (Pp.3-4) The problem he is considering here is that which we call "the paradox of explication". According to Carnap, explication is an analysis in a broad sense. So it does not have to require the relation of identity between "explicandum" and "explicatum", which an analysis in a narrow sense usually requires and consequently falls victim of "the paradox of analysis". The thing explication requires is only the relation of "similarity" between the two, though, it does not seem that it can avoid a more fundamental paradox, that is, "the paradox of explication". This paradox is connected with the vagueness and preciseness of intention of sign 4
(including non-linguistic sign as well as linguistic expressions). The intention of sign is deemed to be determined by a test. The subject of the test is asked about every logically possible object of a sign whether it is an instance of the intention of the sign. The degree of the vagueness or preciseness of the intention of sign depends on the answers given by the subject. In proportion as the subject could answer clearly with "yes" or "no" for each object, the intention of the sign will be precise, vice versa. Considering the relation between explicandum and explicatum, the latter is more precise than the first or the first is vaguer than the latter ex hypothesi. However, strange to say, in order to judge whether an explicatum is appropriate to explicate a particular explicandum, we must already know the intention of the explicandum, on which the judgement will have to be made. That is, explicandum must be no less precise than explicatum. This is the paradox of explication. This argument seems to show that the statement of explication must inevitably contain a kind of circular argument. As far as the logic of individual science is concerned, no circular argument is permitted, because individual science should be a linear-deductive system. On the other hand, logic as philosophy, which we distinguished from logic as individual science, would be characterized as a cyclic-non-deductive system, to which it does not matter if it comprises circular argument. As we have seen, it is clear that the process of explication is inseparably related to cyclic self-reference, which individual sciences categorically refuse to contain within their systems. In fact Carnap himself refused a self-referential theory and constructed a hierarchical structure in his semantics in order to avoid semantical antinomy. From a philosophical point of view, however, it does not matter if the system is self-referential or not. Of course, philosophy does not have to be self-referential. It could be compatible with a linear deductive theory. But to make a clear contrast with individual sciences, it would not be inappropriate to mention a cyclic non-deductive aspect as a most important characteristic of philosophy. Explication is the process, activity or procedure of constructing an analytical theory characterized as cyclic non-deductive and self-referential. It is apparently incompatible with individual sciences. However, it is also apparent that there is no obstacle for us to regard it as a part of logic as philosophy. We have tried to show the possibility that explication could be given a position as logic. If our argument is accepted, our attempt to explicate "explication" would be applicable to the attempt to interpret dialectic, to be exact, an element of Dialectic, as the logic of philosophical reflection. And if so, we suppose, it would also be possible to say that Dialectic could be given a unique position in the classification of logic we have presented at the beginning of this paper. (*) This paper is based on S. Nagai's unpublished paper "Benshouhou no Honshitu". However, the paper had been revised and restructured through discussion between the two authors and newly formulated in English by N. Takato as an introduction to the historical development of the philosophy of science in Japan. NOTES (1) Takeo Sugihara, 'The Philosophical Status of Formal Logic', Tetugakukenkyu, Vol.43, No.5 1966. Also see his Logic of Time, Waseda University Press, Tokyo, 5
1976. (2) The paper appeared in Studies in the Philosophy of Science, Vol.1, No.1, 1961. (3) Hajime Nakano, Dialectic: For Free Thinking, Chuoukouron Sha, Tokyo, 1973. (4) See Shigeo Nagai, 'The Law of contradiction and the Existence of Contradiction', Bunkakagaku Kiyo, No.2, 1960. Authors: * * * * * Shigeo Nagai, a past President of the Philosophy of Science Society, Japan, died in 2005. Naoki Takato is Professor of Philosophy at University of Hyogo, Japan 6