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Concerning the analysis of initial principles and conceptions of formal logic

The Journal of The Institute for The Comparative Study of History, Philosophy and The Sciences, vol. 5. no. 2. September, 1967; Reprinted from The Proceedings of the Philosophical Institute of The Bulgarian Academy of Science, Volume XII, 1966; Translated by Mrs. Sophie Bray in collaboration with Miss A. Durco and Mr. A. G. E. Blake.
G. P. Schedrovitsky

1. FORMULATION OF THE QUESTION. THE THEORY OF MENTATION AND LOGIC

Today, in the most various domains of social production there is being brought to the surface the problem of investigating the process of mentation. This appears to be necessary for the development of the methodology of scientific research; for the elaboration of effective methods of education (general and professional); for the construction of machines modelling aspects of human activity, etc. Tendencies towards many-sided and detailed investigation in the domain of mentation became so obvious that they prompted the Natural Scientist, G. Thomp­son to write that "our century is significant in the sense that it initiates the science of mentation" (The Foreseeable Future, Russian Trs., Moscow, 1958, p.161). And, indeed, by all appearances, it will not be an exaggeration to say that, during the next decades, mentation will become established as one of the most important subjects of scientific research and model construction.

Mentation, as a special subject, is being examined from various aspects by Logic, Psychology and Linguistics. However, the achieve­ments of these sciences in exposing the structure of mentation and its mechanisms cannot be considered satisfactory: they are in obvious dis­proportion to the practical demands made upon them. In particular, the automation of certain processes of mental work which is applied in cybernetics (for example, mechanical translation, mechanization of information retrieval and such like) stumble not so much upon the technical problems, as upon the absence of models of those thinking processes which are to be automated. Similarly, in Pedagogy, the working out of the new systems of teaching, which have become necessary because of the developments in Production that are now taking place, is retarded through the lack of a clear understanding of the nature and mechanisms of thinking, the capacity for which must be formed among the pupils.

Naturally, in these conditions, an exceptionally important problem arises: to examine the methodological foundations of all the above-mentioned Sciences and to ascertain the causes hindering their advance in the investigation of mentation. This problem is equivalent to another: to decide the question of the character of those principles and concep­tions which must become the point of departure in the theory of mentation.

One of the factors in solving this general problem will be an investigation to discover whether the principles and conceptions under­lying the basis of formal Logic (including also the contemporary mathe­matical or so-called "symbolical" Logic) might serve this aim.

The necessity of such an investigation is prompted also by the fact that, at present, there are the most diverse appraisals of what is the subject of formal Logic among its own representatives. R. Carnap, for instance, asserts point-blank that the relationship of formal Logic to mentation is no different from that of Political Economy or Biology, and that in no circumstances can Logic be considered as a science about mentation (27, 6). Other logicians, including Soviet researchers, still defend the thesis that formal Logic studies mentation.

In addition, the situation becomes aggravated by the fact that from the side of Psychology, a well-founded criticism is constantly heard against the assertion that mentation is the subject of study by formal Logic. It is pointed out, in particular, that mental activity always has the character of being directed at a goal, stipulated by a problem and by the relationship of the problem to the fundamental cognizable data; but all this is not taken into consideration in the conceptions of formal Logic.

Thus, the situation concerning the appraisal of the subject and of the significance of formal Logic is rather complicated, while practical needs press for the clarification of this question. Therefore, it deserves the most concentrated attention and a thorough theoretical discussion.

2. INITIAL NOTION CONCERNING THE CONSTRUCTION OF MENTATION

We shall begin this discussion by introducing a hypothesis about the construction of mentation which, in our view, allows us to resolve a great number of the antinomies that were disclosed in the course of the development of the preceding theories about mentation. Thus, this hypothesis is, in some sense, a result of the history of the science of mentation and arises as a result of our endeavours to appraise it; but, prior to the exposition of our point of view regarding the methodological limitations of preceding theories, it is necessary to begin with the hypo­thesis for, without it, our way of reasoning will not be understood.

The substance of the hypothesis consists in the supposition that mentation appears to be, so to speak, a "double-plane" movement, i.e. a simultaneous movement in the "planes" of that which is being denoted and that which denotes. This supposition bears witness to certain common intuitive notions. The process of real thinking, which is indissolubly bound with communication, begins with the eduction of a definite "state of affairs" in actuality (in some situations such a state of affairs might be the language itself, or the actions, thoughts and feelings of other people, and the like) and "the transmission" of the educed actuality begins with its description in language. Further, in constructing and expressing propositions, a man bases his approach upon a "discernment" of certain elements and interconnections per­taining to this actuality, i.e. upon "eduction" of the domain of that which is being denoted. In this way, not only the initial separate pro­positions are constructed, but also the complex chains of propositions constituting the discourse.

In precisely the same way, the understanding of linguistic expres­sions spoken by another person is impossible without the "turning of thought" towards the domain of that which is being denoted and without a peculiar "re-establishing" of those elements and interconnections of the domain which have been denoted in the corresponding linguistic expressions.

A special analysis shows that an analogous situation also exists in those cases when we deal with the most abstract discourses which, one would assume, do not admit of exemplification in the domain of material things. Let us take, as an example, Geometry. In it we deal with signs of different kinds: diagrams, verbal descriptions and logico-arithmetical correlations.  One might ask: where are the denoters and the domain of that which is being denoted in this case? However, a more thoughtful analysis shows that the geometrical signs are far from being uniform. In relation to the verbal descriptions and logico-arithmetical correlations the diagrams appear in the role of objects ; and inversely, the logico-arithmetical correlations denote the content which is being educed in the course of definite activities with the diagrams (transformations), whilst the verbal descriptions are nothing else but the descriptions of these activities (33,34). But we have a similar state of affairs in any part of Mathematics, Physics or Chemistry (12). Let us assume we have determined certain mutually corresponding values of the pressure and volume of a mass of gas (PI, P2, P3…, VI, V2, V3…) and afterwards find an analytical form of interdependence between the pressure and the volume: V=f{P). In this case we act in a definite manner with regard to PI, P2, P3…, VI, V2, V3…; we compare them in the same way as we compare things, and the arrived at formula V = f(P) stands to the signs P and V in a relationship very similar to that of P and V themselves to the actual gas. For the sake of simplification, we, at the moment, put aside the question of relating the formula V=f(P) directly to the actual mass of gas: this process appears to be an auxiliary one of a secondary nature (3,4,13,35). Thus, in general, the effectual process of mentation incorporates as an important (and, apparently, as the most important) component a certain "movement" in the domain of that which is being denoted-the ascer­taining of its elements, relationships and interconnections. And, besides, it is quite impossible to assume that the process of mentation is limited by its movement on one plane only. It is always a simultaneous movement on two planes, and its distinguishing feature is that the movement on one plane is possible only owing to the movement on the other plane and as a matter of fact by way of it.

But it follows from all these assertions that in graphic representa­tion of the processes of mentation, or of their products (knowledge), we must have recourse to two-planes schemes of the kind:

[1]

A fact which was insufficiently considered in traditional Logic.

The representation of mentation in the form of such two-planed figures, in conjunction with the additional considerations that each plane is composed of a multitude of units and that among the units of these two planes there are relationships of denotation or "substitution", allows us to apply, in the description of mentation, the category of "form-content" in that meaning of it which was worked out by K. Marx in "Capital" in his analysis of the structure of relations of production in the bourgeois society.* (7). According to this approach, the substituted element of such a structure (in our scheme to be found on the left) can be determined as content, whereas the substituting element (the one to the right in the diagram) can be determined as form. In applying these definitions to the scheme [1] representing mentation, it will look as follows:

[2]

Here it is important to note that this scheme represents only one aspect-or to be more precise one component-of what is usually called "mentation" – namely, its objective character, independent of individuals and apparently existing as a "culture". In order to be able to distinguish this partial formation from the complete entirety of "mentation", we call it – just for the sake of convention – "linguistic mentation". In our view, precisely this structure is the specific subject of logical analysis. (18)(19)(20).

Presenting in this way the processes of "linguistic mentation" and their product (knowledge) we came across the necessity to define the symbolic form, the connection (=meaning) and, the most important, the content of mentation: each of these questions requires special investiga­tion. We have no possibility here to appraise, more or less in detail, the first two questions (we would recommend, to those who are interested, the above-mentioned articles). We are justified by the consideration that, in the given context, it is important for us to underline and to work out only the one postulate: that linguistic mentation may be represented as a two-planed formation and that both its planes-the one of content and the one of symbolic form – are indissolubly connected one with the other and cannot be considered separately. At the present moment, it is not so important to realize what exactly is represented by the line connection (= meaning) and what, in this structure, must be called a symbolic form.

3. THE BASIC PROBLEM OF THE THEORY OF MENTATION

 The most difficult problem to solve, and the most important for research on the structure of "linguistic mentation", is the one of its content. In order to educe and to study the primary patterns of the structure of knowledge, we must, first of all, educe and study the primary patterns of the content of knowledge, and only after that examine as to how and in which symbolic forms they are expressed. In other words, we must deduce the primary patterns of symbolic forms and of structures of knowledge from the primary patterns of content. But to do this is not so easy. The difficulty lies, first of all, in the fact that the content of linguistic expressions as such is never given to the investigator of linguistic mentation. It always manifests itself in a certain symbolic form (this, by the way, is indeed the primary character of linguistic mentation, which allows us to apply to it the category of "form-content"). Although, as we have already said, a thinking man proceeds from a "discernment" of definite states of affairs in actuality; that which he has "discerned" and educed as a content of his knowledge is always expressed in a definite symbolic form; and this "discernment" itself, as well as the eduction, are not possible without a corresponding expression which takes place simul­taneously. But this means if a logician and a psychologist wish to deduce from the patterns of content the patterns of symbolic forms and of structures of knowledge, they should, first of all, in proceeding from symbolic forms, fixed on "the surface", expose, and reconstruct this very content and its patterns. Thus, a research in the structure of linguistic mentation presupposes a complex twofold movement: firstly, from form towards content; and then, inversely, from content towards form. As a consequence of this analysis, the content of linguistic mentation must – in its character and structure – appear as being different from symbolic form and, at the same time, as determining this form; whereas a form – being different from content – must, at the same time, appear as that which expresses this content.

The method of such (specifically dialectical) research were worked out for the first time by Hegel and Marx (30). Formal logic was unable to work out these methods and, for the reconstruction in the domain of the content of mentation, made use of a special principle which we conventionally call "the principle of parellelism of form and content". Its main point is based on the supposition that (1) to every element of symbolic form (or that which denotes) of linguistic expressions there is a strict correspondence defined, of an obligatory substantial element of content (or that which is being denoted): and (2) the method of linking elements of content into more intricate complexes corresponds exactly to the method of linking elements of symbolic form. These two features, are combined in the term "parallelism".*

4. TWO ASPECTS OF INVESTIGATING LINGUISTIC DISCOURSES

In order to understand the circumstances which, in the first place, originated the principle of parallelism as a principle in the practice of research, and which afterwards led to a rational formulation of this principle, it is necessary to take into consideration the following.

A.  From the very beginning, a linguistic discourse appears to any investigator as a series of interconnected propositions which, in their turn, are composed of words. Like words in a sentence, sentences in a discourse are interconnected in a definite manner, and should these interconnections be changed – for example by transposing words in a sentence or sentences in a discourse – then "the sense" of sentences and discourses will be either altered or will disappear completely. Consequently, it follows that "the sense" of propositions and discourses is, in some measure, conveyed by the connections between elements of linguistic expressions (propositions and discourses) and, should we wish to investigate the nature of this "sense"  (i.e.   the  nature  of  the  meaning and  content  of  linguistic expressions), then we must study these connections and their nature.

B.   On the other hand, it is no less obvious that any separate word in these propositions, as well as separate propositions within discourses, have their own definite "sense", irrespective of their position within a proposition or, correspondingly, within a discourse ; and, also, are inde­pendent of the connections between words and propositions. Thus, it follows that "the sense" of propositions and discourses must in some way be composed out of "the sense" of the separate elements of the proposi­tions and the discourses, and, if we wish to investigate the nature of this "sense" – i.e. the nature of the meaning and content of linguistic expressions – we must investigate the nature of these elementary "senses".

Thence, there are in view two aspects in the investigation of "sense" in linguistic expressions – for the sake of convenience, let us call them respectively aspect A and aspect B – and, should a researcher wish to analyse the nature of the integral "sense" in linguistic expressions, he must, of course, take into consideration both these aspects and examine them, in an uncompromising manner, in their connexion with one another. The method of examining both theseaspects jointly, as one, forms one of the procedures of the method of ascending from the abstract to the concrete, but it was hardly ever applied to the analysis of "sense" in linguistic expressions (14). Instead of this, logicians and psychologists from the very beginning have divided these two aspects of investigation and attempted to examine them separately from one another.

Besides, it became clear that attempts to investigate the significance of linguistic discourse according to aspect B encountered, from the very start, questions which could not be resolved by using traditional methods. These, above all, are questions regarding the nature of "the general" in the meaning and content of linguistic expressions. So, this way of research became virtually closed to the early investigators in linguistic mentation.

On the other hand, it became obvious that in aspect A (the aspect concerning the structure of sense), complex linguistic expressions, con­trariwise, can be analysed and delineated easily enough, and that within comparatively wide limits this delineation does not depend upon research regarding the nature of the meanings and contents of their elements according to aspect  B.

To a certain extent, this fact seems to be paradoxical. The truth is that linguistic expressions considered as such, i.e. from the aspect of their "material", appear either as successions in time of sounds and movements, or as spatial combinations of symbolic forms. To divide these successions of sounds and movements, as well as combinations of symbolic forms, into separate meaningful units so as to present them as definite structures of sign expressions, is possible only by proceeding from their meaning or, more exactly, from that which they denote, that is, their content. Strictly speaking, only the presence of that which is being denoted, or content, transforms these sounds, movements and graphic symbolic forms into signs, whilst a definite order and sequence in the process of denoting creates a structure of linguistic expressions. But this means, in particular, that only the understanding of its content {corres­pondingly, the meaning of signs) gives to man a possibility of exposing the structure of linguistic expressions. In other words, in analysing linguistic expressions according to aspect A (i.e. in terms of their structure) the investigator cannot take a single step without reference to the "sense" (i.e. meaning and content) of the elements of complex linguistic expressions. But, as this "sense" is already clear to everyday awareness and is firmly fixed and defined in the common usage of a language, the division of complex linguistic discourses into elements, as well as the study of their mutual relationships and connec­tions, can  take place  irrespective of investigations into that which represents the nature of "senses" (meaning, contents) of these elements. It is quite sufficient "to know" that such sense exists and "to under­stand" it. To sum up, investigation of the sense structure of complex linguistic discourses, i.e. a research according to aspect A, is possible on the basis of: (1) establishing of "sense" (meaning, content) of each element of linguistic expression and (2) an abstraction from research on the nature of this sense (of meaning, of content). Such an approach is characteristic of traditional Logic, beginning with Aristotle and ending with the very latest "mathematical" trends. This approach forms "a practical basis" for the principle of parallelism.

5. THE SUBJECT MATTER OF "LOGIC AS SUCH" AND THE SUBJECT MATTER OF "THE THEORIES OF LOGIC"

Investigation of the structure of complex linguistic expressions used to be accomplished on the basis of the above approach belonging to traditional Logic.

Now, to complete the picture, it is important for us to note that this approach has by no means embraced the whole domain of dis­courses existing in Science and in everyday life. From their diversity Aristotle had isolated one narrow group of so-called "necessary" deduc­tions, and depicted this group in various kinds of "syllogisms". Beyond the domain which was thus educed, there remained (and, basically, still remain): firstly, all expressions containing descriptions of various actions upon objects and phenomena, interactions and alterations in objects themselves and such like,* i.e. all discourses, so to speak, not bound by necessity; secondly, a whole series of "necessary" conclusions which were constructed on the basis of propositions dealing with relation­ships, connections, and on the basis of arithmetical correlations, etc.

It is also necessary to emphasize that the eduction of the structure of "syllogistic" propositions and descriptions of the mechanics of their formal transformation was not dependent upon the analysis of structure in the domain of content. It was sufficient-on the basis of understanding the sense of various linguistic expressions – to distinguish the relationship of "inherence" or "inclusion" among all other relationships which are encountered in propositions of a language, and thereupon, in orientating oneself on this relationship preserved everywhere, to compare the initial and the final propositions for revealing elements undergoing change.

With such a comparison it is not difficult to see that this transformation of a pair of propositions into one is simply a "discarding" or "eliminating" of the mediating term. And this becomes especially apparent if one writes out the propositions in a line: A-------B, B-------C, indeed, it was the way in which they were written out by Aristotle and, therefore, it is not by accident that the "the eliminated" term is called by him "the medial".

The formulae of constructions of linguistic expressions and rules of their transformation fixed by Aristotle formed a core of "Logic as such".

All its further development according to the method of analysis and eduction of complex linguistic discourses comes, basically, to the following:

(a)    In analysing the structure of Aristotle's syllogisms, the Stoics came to the conclusion that linguistic discourses, corresponding to them, contain not only connections between terms, but also connections between  propositions  and,  accordingly, can  be presented not only in the symbolic form of a syllogism, but also in another form of deduction (with connections of implica­tion, conjunction, disjunction and so on). This analysis initiated the so-called "logic of propositions" and, eventually, the so-called "prepositional calculus".

(b)   Galen, and later A. De Morgan, C. Pierce and others educed and investigated a special structure of propositions, regarding relationships which conform to rules of transformation different from those in syllogisms.

(c)    F. Bacon and J. S. Mill made evident some discourses on causal connections which they erroneously alloted to the so-called "inductive methods". G. Reichenbach, A. Burks and others tried to educe specific logical features of these dis­courses (23, 31).

(d)   Beginning with the works of G. Boole on the Algebra of Logic and by endeavours of G. Frege, D. Peano, B. Russell and others, a new symbolic description of the structure of linguistic discourses was worked out, whereby it became possible to define more accurately a whole series of structures and to build up various logico-mathematical calculations.

The formulae belonging to all these lines regarding the construction of linguistic expressions, as well as the rules of their transformation, constitute the subject matter of "Logic as such". In comparison with the state of affairs in Aristotle's time, the subject of Logic, indisputably, has considerably widened its boundaries ; nevertheless, at the present time, a large majority of linguistic forms still remain entirely outside of these boundaries, such as for example, the languages of geometrical diagrams and chemical formulae, the languages of Arithmetic, Algebra, Differen­tial Calculus and many others.

The eduction of all the above enumerated schemes regarding con­structions of linguistic expressions and rules of their transformations, as well as the eduction of syllogistic schemes, was based on the under­standing of "sense" in corresponding complex linguistic expressions and their elements. But, at the same time, there instantly appeared a whole series of points in which it became evident that the understanding of "sense" alone proved to be insufficient, and a certain analysis of the "nature" and structure of meaning and content in separate linguistic expressions was required. In other words, in a series of points, the analysis of the structure of linguistic discourses according to aspect A proved to be organically bound with their analysis according to the aspect B.

One of the reasons for reverting to the aspect B was the necessity of giving a justification to the educed structures of complex linguistic discourses and to the rules for transforming one set of propositions into another; to find their basis ; to prove that, indeed, these structures are "necessary".

The reference to a definite structure of objective reality, expressed in these discourses, became the most prevelent method of this justifi­cation. In comparison to other methods of justification, such as apriorism and conventionalism, this method has, naturally, appeared to be the most scientific one.

The other reason for reverting to the aspect B was the need to make evident the differentiation between true and false propositions. A mere observance of the "necessary" structure of discourse could not as yet guarantee that the knowledge obtained in the end would correspond to a real state of affairs. For this purpose, it was necessary that those initial propositions, or "premises" – from which, with the help of "necessary" transformations, we educe new propositions – should also correspond to reality. It was imperative to have a certain criterion in order to select from all feasible propositions those which, in fact, would correspond to the real state of affairs. And here too, a reference to a definite structure of reality – in fact to a definite structure of content in linguistic expressions–became again the most prevalent basis for the differentiation and selection of truth from falsehood.*

A discussion on this line of questions has led to the appearance side by side with the subject of "Logic as such", of another particular subject: the "Theory of Logic", or, if it is permissible to say so, "the grounding of Logic". Strictly speaking, in the grounding of Logic various trends – ontologic, psychologic, theoretico-cognizable or logico-semantic – were established which depended upon what procedures were used in formulating questions, as well as upon what means were used to solve these questions. Indeed, "the principle of parallelism" was per­ceived and formulated in connection with a discussion of this "meta-logical" line of questions.

Here it is important to note that a simple reference to the structure of reality is unable to give a true support either to the "indispensability" of educed structures of discourse, or to the "truth-value" of any separate propositions. The character of these structures is determined not so much by the construction and character of reality itself – although it, too, forms one of the components by being instrumental in its influence on structures of linguistic discourses – as by the place and role of these linguistic discourses and their elements – propositions – within human social activity and in the process of communication between people. Therefore, the foundation in any structure of discourse lies not so much in the direct reference to a certain structure of objective reality reflected in these discourses, as in the explanation of the role of language, hence of linguistic discourses, in the process of human productive activity and communication. I think, in this sense only, are we to understand the well known Marxist statement that practicability is the criterion of verity in any discourse, and this understanding should, in our view, become, indeed, the basis in approaching investigation into the various phenomena of linguistic mentation. The analysis propounded by us of structure in the process of correlation (15) is an attempt – so far being rather crude and simplified – to carry out this kind of investigation.

From the outset, in Logic there existed a particular difference between the problem of justifying the "necessary" character in certain structures of linguistic discourses and the problem of separating "true" propositions from "false" ones; and this difference has brought about their division. The solution of the first problem is connected with the analysis of schemes of transformation of linguistic structures which, being schemes of activity, do not immediately make substitutions for anything in the domain of actuality. They do not depend upon the specifically individual contents of the transformed propositions and the terms within them, or upon specific attributes of those objects which are being compared. The solution of the second problem is connected with the analysis of definite connections of terms, which directly depend upon the concrete objective content of terms and, consequently, upon specific   indications   of   those   objects which are being compared.

This methodological difference has also set up certain distinctions in the procedures whereby, in traditional Logic, the correspondence with reality of one and the other structure was grounded. If, in the first case, the reference is to a general character of the structure of the objective world, the general character of the structure of human consciousness (apriorism) or the community of conventions, then in the second case the reference would be directed towards the concrete situations, towards concrete states of affairs and would consist in the assertion of an imme­diate relationship between the terms and the objective things to which they refer, as indicated by feeling or thoughts (24).

With respect to our suggestion of grounding the structures of various linguistic expressions on an investigation as to their place and role within the system of human productive activity, knowledge and communication, we admit that, in that approach, also, will exist a certain difference in method between specifying "the necessity" of certain structures of reason­ing and "the veracity" of certain propositions. The meaning of separate terms, as well as their connections within propositions, will be based upon references to the character of operations of thought – comparisons and references (16) –and, also, on merging of these operations in certain concrete cases (the traditional problem of induction, in particular, will be included). Structures of transformation in linguistic expressions will, con­trariwise, be based upon references to general principles of connections between the signs in linguistic expressions and, correspondingly, to general characteristics of connections between various operations in certain processes of activity – in particular, that of mentation – which are inde­pendent of any individual specific peculiarities of these operations and objects (also including signs) to which they are directed. But, in both cases, the substantiation of existing structures of linguistic discourses and their components must follow the path of investigation into the position and role of these linguistic discourses in the processes of human productive activity, knowledge and communication (22).

A research of this nature presents an exceptionally complex problem. The very formulation of this problem has become a possibility only within the last hundred years, but the methods of solving it have hitherto been scarcely worked on at all. Therefore, it is not surprising that, beginning with Aristotle and up to recent times, an overwhelming majority of investigators have chosen an entirely different approach, in particular, by the reference to the structure of objective reality reflected in linguistic discourses.

6. PRINCIPLES OF PARALLELISM OF FORM AND CONTENT OF MENTATION

But, in order to follow the path indicated above and to justify the structure of a linguistic discourse by referring to a certain construction of actuality which is reflected in this discourse (i.e. by a certain con­struction of the objective content of this discourse) it is necessary, first of all, to introduce and to define this content and, in particular, its structure. And, considering that this content does not reveal itself any­where outside and apart from symbolic form, the content must, in one way or another be made manifest in form, i.e. it must be reconstructed, and only after that shall we be able to deduce the structure of the symbolic form in linguistic expressions from the structure of their content. As we have already said, the method applied to such recon­struction is exceptionally complex. In particular, such reconstruction presupposes a recourse to specifically dialectical methods of investi­gation into complex organic objects. Without having worked out these methods and, consequently, lacking a possibility to accomplish such research; and, at the same time, faced with the problem of establishing that the structure of the symbolic forms of linguistic expressions is based upon the structure of their content: the great majority of philosophers, logicians, psychologists and linguists have simply postulated a parallelism between the content of linguistic mentation and its form (this way of solving the above problem is often described as a realization of the principle that being and thought are identical).

Already in Aristotle's work we find not only a consistent use of the principle of parallelism in practical applications, but also a suffi­ciently clear theoretical cognizance of it.

According to his view, to every term, i.e. to one most minute irresolvable unit of symbolic form there corresponds an atom* of content – to a greater or lesser degree (32, 25). The question as to how these particles of content are educed from the entire actuality does not arise with Aristotle. They are, they exist in actuality and therefore, for him they appear as given facts. Aristotle, equally, does not put the question (at any rate, within the limits of Logic), as to how the signs arise, how their matter obtains meaning, i.e. how the connection between that which is being denoted (content) and that which denotes (symbolic form) becomes established. Thus, according to Aristotle, the factual elements in a linguistic discourse appear to be a combination of the form:

(A)

(where (A) represents a term of that which denotes, and A that which is being denoted) and he considers them to be quite well-grounded and ready-made.

For our further discussions, it is important to point out that this method of examining linguistic mentation entirely  presupposes a possible comprehension of the nature of linguistic discourse itself and a possible comprehension of the entire mental activity. If the elements in the domains of content and symbolic form are set, then the processes of formation and transformation in complex expressions can only appear as a combinatorial of the simpler elements (as a con­junction of simple elements into intricate complexes, or a disjunction of intricate complexes into simpler or quite simple components; as a substitution, in intricate complexes, of some elements by others, or as a "rejection" of certain elements).

The basis of these "combinatorials" lies in the domain of content; i.e. Aristotle presupposes that all combinations are already specified there, and do not depend upon the practical and cognitive activity of man. The combining activity is manifested only in the domain of symbolic form, and it must be in concordance with combinations already existing in the domain of content, i.e. it must reproduce the latter. As to what mechanism accomplishes this dependence, and by which it is guaranteed that symbolic combinations do correspond to the combina­tions of that which is being denoted – this question is neither solved nor even raised by Aristotle. He simply described the structure of one group of combinations of signs and their transformations which is encountered on the surface of mentation – the structure of so-called "processes of correlation between formal attributive knowledge and particular objects" (14).

Whilst stressing that the verity of the ultimate product in this process depends upon the verity of the initial propositions, Aristotle does not, however, raise the question as to how these initial propositions become established, and does not solve the question of how their verity can be ascertained. He simply postulates that certain interconnections in terms correspond to certain interconnections of elements in the domain of content, and that these connections of terms, being true, can be separated from the fallacious ones. But, putting the question in this way again presupposes a theoretical taking into account of the existence of the domain of content in linguistic expressions.

Thus, as the above observations show, the assertion – not frequently met with – that Aristotle, in his logical analysis, was not taking into account the domain of content and digressed from it is erroneous. On the contrary, Aristotle did take into account this aspect of linguistic discourses and, for this purpose, worked out a definite "metaphysical" (or, as we call it nowadays, ontological) picture of the world, placing it in direct connection with the structure of the domain of symbolic form, as well as with the rules, formulated by him, of its transforma­tions. This ontological picture was an essential component in his logical theory: in it the schemes and rules of inference were justified and proven.

But there is another aspect to this matter – and this is, indeed, the most important one for us now – that neither in the case of taking as a basis the "necessity" of certain structures in linguistic discourse nor in the case of taking as a basis the "truth-value" of certain premises did Aristotle produce any actual analysis of the domain of content. The stating of the domain of content as distinct from the domain of symbolic form must be a condition and a premise of such an analysis. Aristotle did not state anything of that kind. In relying upon the understanding of "sense" in various linguistic discourses and upon a formal (commutational) juxta­position of various linguistic forms (understandable to him as to any other man) he simply separated the "true" structures of propositions from the "fallacious" ones, the "necessary" transformation of these structures from the "baseless" ones and transposed all "true" and "necessary" structures into the domain of content. This means, in particular, that structures set forth by Aristotle in the domain of content were empirically as accidental as the structures of symbolic form which he had educed. He did not really educe the structure of symbolic form in a discourse from the "necessary" content – this would have been a real guarantee for the logical schemes – he simply identified content, including its structure and elements, with structures and elements of symbolic form which (by accident) have become apparent, he simply "threw" form into content and, therefore, the latter appeared to him as nothing but a mirror image of "true" and "necessary" components in the domain of symbolic form.

Such was Aristotle's actual method of investigation. But the con­ception of it does appear in a distorted form: as a recognition of an objective, naturally existing, correlation between "true" and "necessary" structures in the domain of symbolic form on the one hand, and structures in the domain of content on the other. A distorted understanding of his work, concerning the grounding of the domain of content gives an appearance of a knowledge about a supposed objective correlation between reality and linguistic forms reflecting this reality, and becomes a theoretical principle which determines the understanding and investi­gation of the nature of linguistic mentation.

Following on from Aristotle we shall be able to detect that the principle of parallelism has been followed by all formal logicians, with­out exception.* Besides, different investigators understood in diverse ways the nature of the elements in the domain of content: Plato and Hegel, for example, held them as being specifically intellectual generalized ideal formations; Hobbes, Locke, and Hume considered them as either generalized or unitary sensual images; Wittgenstein and Russell, in the period between 1900 and 1920, like Aristotle, as "objec­tive states of affairs".* But all this diversity in conceiving the nature of content had no influence upon the carrying out of the principle of parallelism: in every case, its core remained the same and consisted of the affirmation that (1) to every element of symbolic form corresponds a strictly defined substantial hypostatized element of content, and (2) the method of combining elements of content into more intricate complexes exactly corresponds to the method of combining elements in a symbolic form.

In addition, it is important to emphasize that, whatever was said by any of the investigator-logicians, however forcibly they asserted that they proceed not from the analysis of symbolic form towards content, but, on the contrary, from the analysis of content to a determination of the character of symbolic form, the real movement in their inquiries had always, in fact, proceeded from the analysis of the structure of symbolic form in linguistic discourses towards assertions concerning the structure of their content.

7. "THE  PRINCIPLE OF PARALLELISM" – THEORETICAL BASIS OF FORMAL LOGIC

Thus, the structure in the domain of content, reconstructed on the basis of the principle of parallelism, proves to be precisely the same as the structure in the domain of symbolic form. But, if this is so – and here we approach the basic point of the whole of our discourse – if it ensues and is accepted, that there exists between the domain of content and the domain of symbolic form a complete identity with regard to the number of elements as well as to their possible combinations; then, in describing complex linguistic discourses, it is completely unnecessary to investigate the two domains (of content and of form): it is sufficient to describe the one – the domain of symbolic form – in order to describe the other by the same process. More than that: it is quite unnecessary to reconstruct, by some complicated means, the domain of content in order to then investigate it separately – considering that what is imme­diately accessible to investigation in the domain of symbolic form is exactly the same as in the domain of content.

The basis of this thesis comprises the fundamental meaning and sense of the principle of parallelism. It would seem to give a theoretical jusification to the established practice in logical inquiry whereby the scholar approaches the analysis and description of structures in complex linguistic discourses in a special way – only from the aspect of the structure of symbolic form – and carries out this description irrespective of any re-establishment and investigation of structures in the domain of content. Indeed, as we have remarked more than once, in educing the elementary and the more complex formations in linguistic discourses, as well as in educing relationships and connections underlying them, the investigator cannot take a single step without referring to their "sense". But this "sense" is as clear to the investigator as it is to any thinking man, and the understanding of it is not linked with an inquiry into the nature and structure of "the sense" itself. Thus, the principle of parallelism justified the traditional prevalent method of inquiry into the structure of complex linguistic discourses based upon: (1) the under­standing of "sense" in linguistic discourses – in their entirety, as well as in their elements; and (2) abstraction from inquiry into the nature and structure of this sense and, at the same time, from the nature and structure of the domain of content in linguistic mentation.

Just as the principle of parallelism of form and content of menta­tion justifies a separation of inquiry into the structure of complex linguistic expressions from inquiry into the nature of the content of these expressions and their elements, so it becomes the initial theoretical principles of the entirety of formal logic. More than that, this principle is, indeed, that which makes the existence of formal logic, as a special science, conceivable in general; this principle determines its subject and method.**

A statement, which is frequently put forward, that, beginning with Aristotle, Logic has only investigated types and methods of intercon­nections of signs or of thoughts – and that, in fact, this is, indeed, the traditional subject of Logic –becomes conceivable in the light of the principle of parallelism.* This same principle explains also the case –at first sight a surprising one – of how conceptualists and realists, as well as nominalists, who were in such conflict with each other regarding the question of the nature of general terms – i.e. the question concerning relationship of signs of language to reality – came to a complete agree­ment between themselves on the conception of the problems and subject of formal Logic, i.e. on points of view concerning the structures of symbolic form in linguistic expressions. Well, if the whole multitude of elements in the domain of content evince a mirror image in the domain of symbolic form, then it does not matter in the least, with regard to Logic, what one is – a nominalist, a conceptualist or a realist – nor what is to be investigated – connections of names, of "elementary thoughts" (ideas, general notions, concepts, conceptions) or units in the "objective state of affairs". Surely, one must say this: in both cases one and the same thing is being analysed – the structure of symbolic form in complex linguistic expressions (in propositions and in groups of pro­positions). But, in the one case, the results of this analysis are considered to be a knowledge about the domain of symbolic form, and the functional relationships and interconnections of elements composing it; whereas, in the other case, the results are transposed into something else, into the domain of content which is hypothetically assumed to be beyond the domain of form, and identical with it. But the core of the analysis remains the same in all cases.[*] Indeed, these circumstances must be taken as a reason for such a surprising unity in points of view among the representatives of the most diverse trends in the theory of cognition.

8. CONSEQUENCES OF THE "PRINCIPLE OF PARALLELISM"

We have examined a resultant aspect of the "principle of para­llelism" – its meaning in educing the subject of formal Logic – and, in this connection, we have pointed out those opportunities which it reveals for the logico-mathematical modelling of certain objective systems of interconnections. But, at the same time, this principle entails, from our point of view, an inadmissible simplification in understandng mentation as such. Thought processes, as well as their product, that is, knowledge, are two-planed formations. To present them in one-plane images amounts to the loss of the important features which enable them to be processes of cognition and knowledge. To put it in another way, the principle of parallelism leads not to a simplification, but to an over-simplification in the conception of mentation.

From our point of view, it is precisely due to this that many of the difficulties which were met with by formal Logic throughout its path can be expounded. All in all, they come down to five groups of problems.

A. Just as the structure of content in linguistic thinking was neither taken into consideration, nor was it fixed in an explicit form within the schemes of formal Logic, so the symbolic form was con­sidered, in fact, to be devoid of content. A manifestation of this method  of examining symbolic form, was the thesis concerning the universality of educed structures of propositions and of methods of their transformation (2). In practice, as we said earlier, many fundamental domains of contemporary mentation still remain beyond the limits of Logic ; these domains rely, not on the words of everyday speech, but on signs of another kind – numbers, quantities expressed in letters, equations, formulae of composition and structure, geometrical figures, diagrams of different sorts, etc.

B.   Restriction of the subject of Logic to the symbolic form only had also predetermined a possible understanding of the nature and mechanisms of mental activity: as the symbolic forms and their content were taken as ready-made and composed, so the mental activity could only  be a combination – by   conjunction   and  disjunction of   these elements which, from the very beginning, were set and remained un­changeable. And, accordingly, operations of thought were often considered in Logic as being isomorphous to interconnections. Besides, the chief  thing in mentation – the eduction of units of content from the general  "background" of actuality and "movement" in accordance with this content – was dropping out from the sphere of the investigation. It was surmised in all inquiries into Logic that this content was already fixed (24).

The formula: Logic investigates not mentation, but the rules of formal inference – i.e. it is not a science of mentation, but a syntax (and semantics) of language – became a natural and fully just culmination of investigation into Logic.

C.  Just as the mental activity was considered to be a combining of ready-made elements-terms and propositions – so Logic was neverable to solve the question as to how complex knowledge is formed (for example, the knowledge of causal connections, of inter-dependencies in the components of the object, and so on). The attempts to answer this question, whilst remaining on the ground of the primary concepts of formal Logic, resulted in apriorism. Hence the formula which at first (F. Bacon, R. Descartes) was put forward against the traditional Logic, as an indication of its inferiority, but which later (Professor Alexander Vyedensky, as well as the contemporary empiricists in Logic) began to be considered as being nearly the sole basis for scientific knowledge: logic investigates neither the processes of discovering any new content, northe processes of formation of knowledge, but it investigates the processes of systematization and exposition of that which is already known.

D.  The fact that Logic has neither   educed nor examined the actual process of mentation–excluded any possibility for it to investi­gate the development of thought. Neither the fixing of the structure of symbolic form as such, nor the eduction of various kinds of content as such, give the basis for the eduction of interconnections in its development. This basis can only be found in the schemes of operations of mentation (21, 17). The refusal to investigate the genesis of mentation has rein­forced still more the fallacious thesis about "the universality" in educed structures of symbolic form.

E. The absence of a genetic approach to the inquiry into menta­tion (which, as K. Marx used to say, objectively is an "organic" system developing historically and, therefore, conceivable only in the course of genetic inquiry) has, in its turn, led to a realization that formal Logic was unable to educe the structure of a complete act of mentation, its "cell",* and formal Logic considered the actually complete acts of mentation and their separate miscellaneous elements which lacked any specific attributes of wholeness–as being qualitatively equal objects of study.

9. CONCLUSION

In concluding this article, we wish to repeat once more that from which we have begun.

At the present time formal Logic (above all as a "mathematical" or "symbolic" Logic) plays a prominent role in the system of the sciences: its apparatus is applied to the most diverse spheres – that of science itself and that of production–and, therefore, it is only natural that it is being worked out with intensity. However, it is not so difficult to notice that the least success of formal Logic is achieved precisely in the sphere of its traditional subjects – methodology of science and analysis of knowledge. This situation demands the most concentrated attention ; in pointing out the successes and the achievements of formal Logic we must, at the same time, clearly expose the domains where it suffers defeat, and try to find out the cause thereof.

The boundaries of applicability of any scientific conceptions are determined by those initial abstractions upon Which they are based. In Logic this abstraction can be expressed as "the principle of parallelism". It entails those difficulties with which Logic came across in the course of its historical development, when it pretended to be a theory of mentation.

In enumerating these difficulties we have thus indicated the basic features and aspects which, in our view, must be taken into considera­tion without fail in the initial principles and concepts of the theory of mentation. Also they must certainly be taken into consideration in the initial abstractions of that kind of Logic which wishes to describe mentation. We call such Logic "content-genetic" (19).

All that has been recapitulated above does not yet exhaust all the fundamental demands which we must make on the future theory of mentation. Thus, it is necessary that Psychology and Linguistics should be examined in the same way, so that those features of mentation which are taken into account within them, as well as those which cannot be considered because of the limitations of initial abstractions, can be educed. After that it will be necessary to raise the question about the possibility of taking into account all these various features within a unified theoretical picture. And only then shall we obtain the indis­pensable plan for constructing a common "synthetic" theory of menta­tion.

REFERENCES

Note: Titles of papers and articles are given in English only. Titles of books and names of journals are represented in a Russian transliteration with an English translation in parenthesis.

1. AKHMANOV, A. S., "The Forms of Thought and Rules of Formal Logic", and "The Problem Concerning the Subject of Formal Logic". From: VoprosyLogiki (Problems of Logic) Moscow, 1955. p. 33.

2. SCHEDROVITSKY, G. P., Doklady APN RSFSR (Reports of the Academy of Pedagogical Sciences) 1961, No. 5.

3. LADENKO, I. S., "Concerning the Relationship of Equivalence and its Role in Certain Processes of Mentation".   Doklady APN RSFSR (Reports of the Academy of Pedagogical Sciences) 1958, No. 1.

4. Ibid:  "Concerning Process of Mentation Connected with the Establishment of  Relationship  of  Equivalence". Doklady  APN RSFSR  (Reports of the Pedagogical Sciences) 1958, No. 2.

5. Logicheskie Isslyedovaniya (Logical Investigations). Collected papers. Moscow, 1959.

6. LOUKASSEVITCH, J., Aristotyelyevskaya sillogistika s tochki zryeniya sovryemionnoi formalnoi logiki

   .(Aristotle's Syllogistic from the Standpoint of Modern Formal Logic) Moscow, 1959, pp. 48-51.

7. MARX, K., Capital, Vol. I. State Political Publishing 1949, pp. 41-77.

8. POVAROV,     H.     N.,     "Logic    and     Automation". From Logicheskie Isslyedovaniya (Logical Investigations) Moscow, 1959.

9. Ibid, "Logic in the Service of Automation and Technical Progress". VoprosyFilosofii (Problems of Philosophy) 1959, No. 10, p. 56.

10. Voprosy  Yazykoznaniya (Problems of Linguistics)  1957, No.   1, pp.  64-65. " (RUSSELL, B., An Inquiry into .Meaning and Truth, N.Y., 1940, pp. 437-8.

12. SAZONOV, B. V., "Contribution to the Critique of the. Neo-Positivist Analysis of the 'Natural' Language of  Science". From Dialyekticheskiy Materialism i Sovryemmionniy Positivism (Dialectical Materialism and Contemporary Positivism) Moscow, 1961.

13. SCHEDROVITSKY, G. P., "On the Analysis of the Processes in Solving Problems". Doklady APN RSFSR (Reports of the Academy of Pedagogical Sciences) I960, No. 5.

14. Ibid:  "Concerning the Structure of Attributive Knowledge". Doklady APN RSFSR (Reports of the Academy of Pedagogical Sciences) 1958, Nos. 1, 4: 1959, Nos. 1,2,4: 1960, No. 6.

15. Ibid:    „   1959, No. 4.

16. Ibid: "On Possible Ways of Investigating Mentation as an Activity". DokladyAPN RSFSR (Reports of the Academy of Pedagogical Sciences) 1957, No. 3, pp. 44-5.

17. Ibid:   "Concerning Certain Features in the Development of Conceptions". Voprosy Filosofii (Problems of Philosophy), 1958, No. 6.

18. Ibid:  "Concerning the Principles of Research in the Objective Structure of Mental Activity based upon the Notions of Content-Genetic Logic". From Problyem'yi metodologii i logiki nauk (Problems of Methodology and Logic of Sciences). Collected papers. Tomsk,  1962, pp. 85-86. See also VoprosyPsikhologii (Problems of Psychology) 1964, No. 2.

19. Ibid: "Concerning the Difference between Fundamental Notions of 'Formal' Logic and Logic of Content". In Dyetskaya i pedagogicheskaya psikhologiya (Child and Pedagogical Psychology) Moscow, 1963. A thesis of reports made at the 2nd Congress of the Society of Psychologists.

20. "The Rdle of Logical Analysis in Solving Psychological Problems in Teach­ing". In Dyetskaya i pedagogicheskaya psikhologiya (Child and Pedagogical Psychology) Moscow, 1963. (See 19 above).

21. SCHEDROVITSKY, G. P., and  LADENKO,  I.S.,"Concerning  Some Principles in the Genetic Investigation of Mentation". Tyezisy dokladov na I s'yezde Obshchestva psikhologov (Thesis in the reports at the 1st Congress of the Society of Psychologists). Publ. 1, Moscow, 1959, pp. 100-3.

22. SCHEDROVITSKY, G. P., "Concerning the Method of Semiotic Investiga­tion into Systems of Signs". From: Semiotika i vostochniye yaziki (Semiotics and Eastern Languages). Moscow, 1957.

23. SHVIREV, V. S., "On the question of Causal Implication". From Logicheskie Isslyedovaniya (Logical  .Investigations). Collected papers. Moscow, 1959.

24. Ibid:   "Concerning   the   Question   of  Ways  of  Logical  Investigation  into Mentation". Doklady APN RSFSR (Reports of the Academy of Pedagogical Sciences) 1960, No. 2.

25. SPECHTE, E. K., "U'ber die primare Bedeutung der Worter bei Aristoteles". Kant-Studien. B. 51 H.I. 1959/60.

26. DEITZ,  E.,   "Picture  Theory  of   Meaning,"  From  Essays  in   Conceptual Analysis. London, 1956.

27. STEGMULLER, B. von W., Induktive Logik und Wahrscheinlichkeit (Induc­tive Logic and Probability) 1958, pp. 31-32.

28. SYRRIUS, Sh., Opyt isslyedovaniya znacheniya logiki (Experimental Investi­gations into the Meaning of Logic) Moscow, 1948, pp. 58-60.

29. WITTGENSTEIN,   L.,   Tractatus Logico-Philosophicus,   Moscow,   1959,  pp. 38 & 47.

30. ZINOVIEV, A. A., "The Ascent from Abstraction to Concreteness based on the material from 'Capital by K. Marx". Dissertatsiya (Thesis) Moscow 1954.

31. Ibid:  "Logical Structure of Sciences about Connection". From Logicheskie Isslycdovaniya (Logical Investigations) Moscow, 1959.

32. ARISTOTLE, Metaphysics. Book 9. Chapter 10 p. 243. London 1956.

33. ROZIN, V. M., MOSKAYEVA, A. S., "Concerning the Analysis of the System   of  Comprehension   of  Type,   Euclid's 'Elements'."From Noviye Isslyedovaniya  v Pedagogicheskikh Naukakh. (New Investigations in the Pedagogical Sciences). August 1966 and IX, 1967.

34. ROZIN, V. M., "Semiotical Analysis of Signs within Mathematics." From the compedium: Semiotika i vostochniye yaziki (Semiotics and Eastern Languages) Moscow, 1967.

35. SCHEDROVITSKY, G. P., "Methodological Problems of Systems Research". From General Systems, vol. XI, 1966.


*

*"5.1410 Content and form are always found together. Content is the determining aspect, but the form, even though it is dependent on the content, is not passive – it works on the content and plays a very great role in development.

5.1411     The content is that basic and principal aspect of an object which determines its qualitative type and appears in all of its elements.

5.1412     Form is the existential mode of the content, its internal organization and its structure, which makes possible its coming to be.

5.1413     If the form is to fulfil its task as the stable element, then it cannot be constantly changing.   As a result, the constant development of the content leads to a contradiction between the form and itself." Blakeley, Thomas J., Soviet Philosophy, Dordrecht, Holland, 1964, p. 31. trs. note.

* As one can see, this principle could also be called the principle of "isomorphism of form and content in mentation", but we have intentionally rejected this term so as to avoid introducing supplementary implications which are connected with its meaning in Mathematics.

* It must be noted that similar linguistic discourses are not sharply separated from "the necessary ones" and, in particular, from syllogistic conclusions. On the contrary, they form an organic connection with the latter and–as, for example, in Geometry–they constitute an essential component in processes of deduction. They are descriptions of transformations in various figures, comparisons of signs, new constructions, etc.

* "... Thus, in truth abides 'the one' who considers that which was divided as being divided, and that which was conjoined as being conjoined, whereas in falsehood abides 'the one' whose opinion is contradictory to the factual state of affairs". (32)

* The Russian term is myel'chaushei, which literally means "smallest or minutest unit". This expression can be substituted for "atom". Trs.

*   The lack of space does not allow us to give a sufficiently empirical con­firmation of the correctness of this statement; we shall quote here only the most extreme formulations.

"3.2   An idea in a proposition can be expressed in such a way that objects of thought will correspond to elements in a prepositional symbol.

3.21    The   configuration   of   simple   symbols   in   a   propositional   symbol corresponds to configurations of objects in the state of affairs.

4.04   In an idea there should be precisely as many distinguishable components as   there   are   in   the   state   of   affairs,   which   they   represent."   Ludwig Wittgenstein (29).

"In principle, the factual and the judgmental interpretation of logic can be used in calculation interchangeably, in so far as between the facts and the judgments there is a mutual correspondence of meaning. For example in my article, "Logic and Automation" (8) written in 1957, I confined myself to a judgmental interpretation; however, at present 1 would prefer one of development." H. N. Povarov (9).

See also concerning this problem Bertrand Russell (11), A. S. Akhmanov (1), Sh. Syerrius (28) and E. K. Spechte (25) and E. Deitz (26).

* It was not infrequent that a number of such denotations were introduced – for example, a specifically mental-image conception and, side by side with this, an objective state of affairs and sensual images – but this lead to a whole range of difficulties and contradictions (10).

** There is one single point at which the traditional Logic went beyond the boundaries of the principle of parallelism: "the methods of inductive inquiry" of Bacon and Mill. But this fact does not in any way contradict the thesis which we have put forward. The working out of this part of Logic is bound up not with Aristotle's classical syllogistic reasoning and its further develop­ment in mathematical Logic, but with the so-called "methodological" trends which are being evolved in contradiction to Aristotle's teaching as well as to the principle of parallelism.

* It may be said without exaggeration that statements characterizing thus the subjects of Logic are to be found in all systematical works, without exception, and, therefore, there is no sense in singling out or referring to any of them in particular. To all appearance, Logic was the first domain of knowledge where the interconnections of elements became a particular and special subject of investigation and where, from the outset, the simplest schemes of interconnections were worked out. These schemes, presented in their strictly formal, mathematical aspect can be applied and were applied (Gavrilov, Shanon and Moore, Shestakov, Nakasima, Povarov and others) for the analysis and synthesis of systems of the simplest objective interconnections. See H. N. Povarov (9) and also articles by Povarov, Shestakov, Kharkyevitch and others (5). Apparently, these circumstances play an important role in the tendency (as it is conceived at the present time) to ontologize Logic and to present it as the most general picture and summation of interconnections in objective reality.

** "... It is beyond doubt that always, even before Rostzelin, attention was drawn to the fact that Aristotle's Organon and Porphyry's Introduction constantly speak about words only, and not of things. Realism was not embarrassed by this, for it admitted (without any criticism whatsoever) a complete accord between Logic and Grammar–an accord which was undoubtedly accepted by Aristotle ".

"…Nominalism represents an entirely different point of view: it established a substitution of words in place of ideas and grammatical operations of speech, instead of logical operations of inference…" "…Language allowed Nominalism to preserve the structure of judgement: S is P. For this, it was sufficient to assign to the difference between subject and predicate its grammatical meaning, i.e. the meaning of nominative and of attribute. Furthermore, a substitution of one domain by another was taking place, but the general economy of the system did not undergo any changes: the technique of the syllogism and the structure of judgement has remained the same. But, for this reason, Nominalism was able to lay claim that it had remained a faithful exponent and a more eager champion of Aristotle's doctrine" (28). See also (1).

* Marxist term. Trs. note.

 
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