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Some criteria for intellectuality of systems (Logical and philosophical aspects)

(elashkina@noolab.ru), 21.08.2009

.. // , 1(32). , 2007. . 102-128.

A. Yelashkina

1. Introduction

A contemporary person lives in a world where many processes (in business, scientific research, entertainment and other) are performed with the help of information technologies (IT). This influences both already ongoing processes and the way technologies evolve. Moreover, one of the main features of this fact is that changes emerge very rapidly.

Some time ago Russia was only partly included into the worldwide process, where new means better". Nowadays we participate in the rush for newness too, evidently falling behind the leaders. But how can we speak about progress in IT development and deployment, not understanding fully how human thinking interacts with software environment and what results are to be expected from that?

The object of this research is the interaction between IT and thinking. We believe that the range of problems existing in philosophy, logic and natural sciences re-emerge in this object.

The subject of this research is the border between a system with intellectual functions and a system without those. Initially, IT were planned to replace some human intellectual resources with a computer in some tasks. In the limit, it was planned to model thinking.

Thus, the main goal of this research is formulating and justification of the criteria that could be used to distinguish a system with intellect from a system without it.

In this research an old term "artificial intelligence (AI) is used when speaking about attempts to implement mechanisms of thinking on the basis of an artificially organised material environment.

2. The contemporary situation in the intellectual systems development.

Up to date there does not exist any system (neither in practice, nor in theory) which would be so close to human thinking, that it would be universally recognised as an intellectual system. Failures in creating AI lead to certain strategies, which prevail in the community of developers.

They are as follows:

1 strategy Task localisation". The algorithm domain of applicability is sharply restricted. Developers concentrate on a particular application domain, within which the problem definition of conferring intellectual functions to a system is preserved. Generally speaking, the sort of tasks is not important. It can be, e.g., recognition of objects of the same type on certain photographs from space or contextual search inside texts of close meaning. It is important that the applicability of theoretical models and algorithms is localised and boundary conditions, parameters and other data about a real situation are defined by an expert. Inside a well-defined area it is possible to perform some powerful functions that resemble intellect. A computer carries out these functions to a certain degree independently.

2 strategy Powerful algorithms". This strategy can be characterised by scepticism towards the possibility of understanding mechanisms of human thinking in general; up to the conclusion that any problem definition of creation of any thinking models is senseless. It is proposed to concentrate not on intellectual, but on very powerful algorithms, which would amplify the work of a real human intellect. The adherents of this strategy often talk about complexities with exploitation and maintenance of already existing software and hardware. Until these topical problems are not solved, it is useless to think about AI. All the resources should be used to serve the technologies that already provide assistance to a human in real processes without any qualitative changes to IT.

3 strategy Sophisticated algorithms". It is worth saying that there still are hopes to create an AI of full value increasing the complexity and originality of algorithms without changing the scientific paradigm, in which the type of contemporary used methods itself was born. The adherents of this strategy do not think that changing the fundamental notions about AI is rational. These notions themselves emerged under the natural science paradigm. It is supposed that the goal could be achieved by making a complex and original combination of different already existing means, including already made program blocks that deal with particular tasks.

4 strategy Physiological algorithms". This strategy tries to reveal mechanisms of thinking directly in the physiology of living organisms. Sometimes it is proposed to copy revealed phenomena of a real nervous systems work; sometimes up to copying chemical reactions. It is significant that the question of the logic of intellect is either not posed at all or the adherents of this strategy try to draw all logic that is inherent in intellectual systems from physiological facts. It is supposed that, in a way, there is a parallelism: the way the nervous system works is the way the intellect itself is organised.

It is our classification. Our classification does not coincide with, but does not contradict other attempts to classify different strategies in creation of intellectual programs, e.g., a classification of trends of development of intellectual systems proposed by D. Pospelov in his work 10 "hot spots" in the field of AI research"(1).

In real developments different strategies are usually combined. E.g., neural network development area adheres to physiological" strategy and achieves efficiency localising tasks.

Many linguistic models for text processing tasks exist in the framework of local tasks and sophisticated algorithms. These models include both those based on traditional linguistic analysis and those based on certain popular conceptions that both the world and the thinking could be understood from the structure of language. Many interesting developments are made in this filed, e.g., in attempts to convert a linear text into structures, schemes, etc.

The second strategy, which is oriented towards powerful algorithms, is interesting with its scepticism. Doubts in the legitimacy of the problem definition of AI making mark a new period in theoretical understanding of what does specificity of human thinking consist in. However, in the AI developers and theoreticians community this step to a doubt turns out to be the last one. Instead of rational studies and research they turn to poetry and intuition. The arguments in favour of this are that it is impossible neither to describe nor to comprehend any type of thinking, that the thinking is absolutely irrational. The possibility of precise conceptual thinking about the thinking itself is rejected.

We believe that the most topical is the fifth strategy, which is concerned in studying the specificity of thinking and tries to find a precise formulation for the criteria of intellectuality of a system.

Let us assume that there is an irrational moment in thinking. Yet, is still should be reached. We think that between this moment and all already existing algorithms of AI lies a large area for a fully constructive theoretical and practical work. Only after having this area fully examined, it would be possible to make a conscious decision about what can be done further in modelling the thinking and what is inaccessible to us in essence and why.

We would not adhere to the pragmatism of the first trend, natural sciences and formal logic paradigm of the third trend and parallelism of physiology and intellect of the fourth. Undoubtedly, the most hard step is to refuse (even for a short time period) to rely on exact sciences the thing that in the contemporary world is believed to be the most rigorous and worked out. To model the intellect, we have to do it (even if we do so only on first steps of research), because these sciences themselves are made by the human thinking, and in a certain framework at that. And if we want to understand the mechanisms of thinking, we have to think about the thinking itself first, bearing in mind the specificity of such its product as scientific knowledge.

To depict the contemporary situation more precisely, we have to state that the strategies described above are interesting only for the developers community. A general software user is not concerned with how IT works and what are the tendencies of its development. A user is concerned with functions, not technologies. Often results of work of existing software can seem so impressive to an external observer, that principal borders of its applicability are unnoticeable.

Obviously, it is not accidental. A wealth of formalised means taken from mathematics, natural sciences, accumulated throughout two thousand years, was practically completely transferred to IT only in a couple of decades, which led to an intense rise in software functionality. As a result, a user thinks that existing software is already intellectual. It seems natural to a user to propose to add a new button to the software, e.g., to take account not only of the morphology of a word, or cases, but, in addition, to recognise as close in meaning sentences from texts in a natural language automatically. This means, that a computer would somehow automatically recognise as close in meaning sentences like "somebody is sitting in a forest" and "a man made himself comfortable under a tree, or that a computer would automatically add a new, additional parameter to describe tables. It means that a program, besides parameters already put by a coder, like number of legs and "dimensions", would automatically, with the new information coming, discover the significance of the parameter colour(2).

A developer sees himself in a blind alley here. To reveal a close meaning of texts in different forms or implement an automatic addition of a new aspect of classification, which means an automatic widening of the language by which objects are described, is, on one hand, intelligible and demanded function, but, on the other hand, it is immensely far from real contemporary technological possibilities. A user scarcely sees the gap between a new button and already existing functions. Unfortunately, many theoreticians do not see the problem here, too, and propose that a coder just make an enormous synonym dictionary for different cases, that seem to be a wrong way for developers who have this experience, at least because of a catastrophic rise of the quantity of manually put parameters. Those theoreticians shift their work of studying the intellect onto a coder. A coder sees the abyss between existing technologies and that one which should provide the user with a missing button. Its overcoming would take enormous amounts of time, money and mastering new knowledge.

The most unpleasant moment for developers is the understanding of the fact that intellectual in their interior arrangement systems will at first lose in user functions, to, e.g., "powerful algorithms. Significant for a user advantages, superficial efficiency, can appear not soon, which does not add optimism to coders. That is why most developers, finding themselves in a harsh situation of implementation of an order, use the strategies described above (3).

3. What is an intellectual task?

A computer, in which a big amount of rules describing how to process a certain information, e.g., how to separate an image out of the background or how to classify into groups a stream of data, were put beforehand, can boggle the mind of a user with its results. The bases of classification, which were put by a coder directly or indirectly, can be so well detailed and fine-tuned, that it can seem that a program itself generates some new basis not foreseen by a coder.

Eventually, if we narrow our query sharply, we will find it convenient to use a very powerful machine to process a huge array of parameters (put by a human manually) which would describe a real situation. Nobody expects from a computer which knows how to classify financial data to classify just as well texts in a natural language from the Internet. At the moment we have many programs which are efficient each in its own sphere and are sometimes interconnected through interfaces.

But software developers do not take up tasks if they see that an object of the task lies in a point of intersection of different areas, or an object is changing qualitatively and new parameters of its description appear. Most frequently, a final examination is held by the analysis department, which receives data about the object both from programs and other different sources.

Firstly, we can illustrate specific characters of contemporary functioning programs and that that we see as an intellectual system using an example that follows. Lets assume that we have an image, one half of which is white and the other one is black. Lets assume that a computer gets big amounts of such images. A task for the computer is to make a distinction and to send all that is black into one place and all that is white into another one. Certainly, a coder can make a program which will provide the computer with the necessary distinction parameters in half a minute. A coder can also add a fuzzy logic, and the program will work even when there will be a fuzzy shift from white to black. A standard well-tuned neural network will distinguish and process images easily. Meanwhile, in the case of a neural network new informational objects are not generated (4) 4, as well as while using other types of algorithms, parameters of classification are not produced independently.

Compared to other far more complicated tasks, this example does not seem in the least bit intellectual. But lets suppose that the computer was not warned of the bases of classification and into how many parts it should divide the stream of data. Thus, to accomplish the distinction, the computer will have to, e.g., produce something similar to the notion of "border" (in fact, to generate a new informational object) and to learn how to draw it between different parts of the data stream. To accomplish this, superficially easiest, task without a rule put beforehand by a human, a computer has to possess what we call intellect. There are no direct instructions in the program about what is black and white, an object or a border. A particular arrangement of the environment which we model should provide a solution for the task. This arrangement should consist of special elements, connections between them, processes launched on this elements and it should be made in accordance to what we take as mechanisms of thinking.

A solution for the task described can require training by a human, but, in contrast to neural networks, input and output of the network are not simply assigned to each other, but qualitatively new informational objects, which did not exist on at the input, should appear. A network, trained to recognise something on financial flows, does not contain within itself the notion flow, and in general case, cannot apply it to a hydrodynamics task or to a task in which a flow is only a part of an integral phenomenon being explored, while for a human analogies could be obvious. A new informational object in the system should be minimally dependent on a particular type of data. That is, obtained in an artificial environment notion of border should be applicable in any situation where something can be distinguished at all.

We would like to emphasise the fact that we chose a task, having solved which, AI would superficially lose to ordinary systems. But what it would look like and what functions would be implemented in particular do not interest us. We could have chosen other simplest tasks. It is important for us, which mechanisms will be laid for their solution and how it will be organised in the interior. Independent definition of bases for classification, generating new, not set by a human, informational object is one of many necessary stages, which should be overcome while getting over the abyss between ordinary and intellectual functions.

We assert that the contemporary scientific knowledge cannot provide a corresponding to this stage logical model of the intellect; at least because it is not itself organised in such a way. It means that people, who set up sciences, were, certainly, able to think, but the mechanism of their thinking is not implied in the constructed knowledge.

4. Two types of knowledge.

Today attempts to create AI turn out to be a challenge for exact sciences, logic, philosophy, linguistics. Those who that way or another occupy themselves with the thinking have to give an answer on to what degree is their knowledge applicable for practical realisation. It should be stated that today, for the most part, computers are an artificial environment which implements Boolean function space. The thinking in a living brain does not implement Boolean space, or implements something except it. The solution of the problem of mechanisms of thinking does not consist in constructing intellect from mathematics and existing logical calculations. The solution lies in seeing mathematics, logical calculations and other knowledge as a result of thinking (5) 5. Let us investigate in what consists the specificity of bases for our subject, on which contemporary exact sciences and formalised logics are grounded.

Since as far back as Aristotle there can be seen two tendencies about conceptions concerning the thinking and the structure of knowledge, which we will call formal and dialectic.

First of them formal assumes several necessarily carried out requirements. The most important of them are:

In the bases of any knowledge are axioms, which cannot be concluded or proven from anything on principle. We here understand axioms in a broad sense as any starting positions, any foundation, any system of basic definitions, facts or descriptions which are not changed while the system is functioning.

The content of each of them is independent from the others. Axioms are specified by the author according to his external to axioms and not inherited into the system itself considerations.

On the bases of these axioms all other knowledge is concluded and deducted according to already specified and non-qualitatively changing rules. Inside one system the appearance of qualitatively new objects is impossible.

In any formal system of knowledge the implementation of basic laws of formal logic is necessary. For the present discussion the most important of them is the law of non-contradiction. Aristotle formulates this law as follows: It is impossible for the same thing to belong and not to belong at the same time to the same thing and in the same respect. In a contemporary wording it is sometimes rendered as It is impossible for a statement to be true and false at the same time.

All the natural sciences, all formal logical systems and many other fields of knowledge as well as many philosophical systems are constructed according to these principles. Any exact science is constructed upon the axioms which cannot be inferred within a science itself. These axioms are taken in a finished form and in this sense they are chosen arbitrary. Laid in the bases of sciences axioms and rules of deducing allow on the following axioms steps to make exact constructions. Within such system of knowledge contradictions are precluded.

There can be stated a paradox consisting in the fact that the most exact and rational sciences, which put in a claim for strict proving, have in their bases axioms which cannot be rationally discussed or inferred, and which often do not have a definite connection to practice. Most pioneers and big theoreticians of science put questions about the foundations of science and scientific thinking. Many great scientists show us an example of turning to philosophical knowledge, to methodology and to the history of science. Such reflections can be found in Einsteins, in Diracs, in Weil's works and in works of many other scientists.

Abovementioned features of formal systems coincide with habitual for philosophy understanding of the rational component of human thinking. This distinction is discussed in great detail in Hegels works. Understanding (Verstand, sometimes rendered as Intellect), in contrast to Reason (Vernunft) in Hegelian terms, works with finished forms and eliminates contradictions. Causes of any thought, any knowledge are not in themselves, but in something exterior to them. Everything qualitatively new appears not within the system, and even not as a result of interaction with something different with respect to it, but as a result of effects of an entirely exterior to the system force, which determines the system. E.g., new rules of computer text processing, and, in general, new notions about text generation, are put into the computer by a human, and are not a result of development of an intellectual system itself while working with texts (6) 6. On one hand, the formal logic sets rules for building formalised knowledge, but on the other hand, it is itself organised according to these rules. But it is not all thinking!

The second tendency dialectical differs from formal in every above-mentioned point.

Basic premises of dialectical systems are mutually agreed (and in this sense they are provable) one through another. Thus, they are self-consistent. Moreover, this mutual agreeing and definition of premises is done according to their content, and not by some external to this content way.

Subsequent acquisition of knowledge is generation of qualitatively new objects within the system itself, the rules can change throughout the development of the system and they are not set in a finished form beforehand.

Contradictoriness is the main condition of the possibility of mutual definition of basic premises and generation of new objects within the system. A dialectical system is a self-defining system and it does not need an external force for its development; it possesses development leverage within itself.

In Hegelian terms, dialectics belong to the sphere of Reason.

It is to be noted that the term contradiction" is too ambiguous. We can find many different types of contradictions in a logic reference book. According to purposes of this article, it is important to point out the difference between contradictions in formal and dialectic systems. A contradiction in formal systems is abstract, while in dialectical systems it is concrete. That means that within a dialectic system we take as a contradiction not just, e.g., form and non-form, where non-form is merely everything e.g., a table, red, multiplication table, a neighbour, etc. We take as a contradiction what is opposed to form concretely, not abstractly, viz. content. Sometimes to describe this concrete opposite the term own other is used. Something third, which turns out to be the unity of two concrete opposites, emerges as a result of their interaction. Formal systems prohibit both abstract and concrete contradictions in the same object at the same time in the same respect.

The question about which kind of contradictions can or cannot act as generating for intellectual functions of a systems will be tackled in this article further, although limits of an article do not allow a comprehensive study of this problem, on which big scientific volumes are written. While in this article it is important to show the general necessity to talk about dialectical contradictions in application to intellectual systems. It should be noted that in this research we do not claim any new philosophical or logical ideas. We use well-known ones, but making necessary emphases in the context of the AI developing task.

Further, when we will mention mutual definition of contradictions we will mean not abstract, but concrete contradictions.

Fig. 1. A schematic outline of axiomatic knowledge. B schematic outline of mutual definition of two basic ideas (or two informational objects).

A dialectical system with many premises could be depicted like this:

Fig. 2

From the point of view of the formal logic, all dialecticians make a mistake when they insist on the mutual definition of basic premises or ideas of a system. This mutual definition inevitably leads to a circular reasoning (7). The law of non-contradiction asserts that the same thing cannot be such and not such at the same time. A formal logician can think of a table as an entire object or as consisting of parts, but only in different propositions and in other respect, prohibiting circle reasoning and contradictions in thought. It is important that, according to a formal logician, dialectics with its abovementioned principles finds itself in the sphere of irrational, not strict. But the human thinking makes these operations regularly, in commonplace situations, no falling into mysticism or absurdity.

The fact of understanding of a text can serve as an example of mutual definition of the thought. A hypothesis about the meaning of a text in general appears at the very first step of reading its first fragment. Subsequently, this hypothesis is redefined by following reading. However, the second fragment was read taking into account the first hypothesis and now it is to be redefined and understood taking into account the second fragment. But, then, the understanding of the second fragment after the new understanding of the first should also change. And this happens with all the fragments of a text.

Following fragment redefine preceding ones and have to be redefined themselves anew. And the human thinking successfully comes out of this vicious circle of mutual definition and infinite loop of meaning genesis with a finished meaning of the entire text at that, while existing software, based on formal logics, cannot. From this integral meaning of the text one can see meanings of its fragments, conceptually important meanings in the theory of thematic-rhematic text analysis (8). It is claimed that only with the condition of mutual definition, objects (semantic fragments of a text) make up an integral system which has properties of internal unity.

It should be noted that a text is conceived contradictorily. A human views a fragment of a text simultaneously as an independent isolated meaning fragment and as a part of a whole. And the text is viewed as a whole and as consisting of parts at the same time. Only this simultaneousness allows uniting, as a result, fragments of the text into its integral meaning.

There are other classes of tasks being performed in human commonplace activities which cannot be solved by knowing of axioms, derivation of rules from axioms and procedural description of actions on principle. An analysis of a situation with many interconnections and ability of the participants of the situation to reflect can serve as an example. One of very important classes of tasks solved by the thinking is constructing new set of axioms as a new object. In the framework of a theory defined by axioms only derivation of consequences is possible. This derivation does not qualitatively change the theory; and those tasks are well tackled and solved by contemporary computer processing powers. But none of existing processing powers can overcome a vicious circle (consisting even of two elements), which human thinking overcomes continually.

It should be noted that we are reasoning in the framework of the paradigm which admits the possibility of regularities in general or, at least, not complete randomness of shifting from one state of an intellectual system to another, from one theory to a following one.

There are philosophical schools that consider this shift to be a random one. They assert that it occurs as facts which contradict the previous theory appear. Dialectics as a contradiction between a new fact and the theory is understood not as a basis of any thinking, but only as an organising moment which launches spontaneous generation of new theories. Then follows trial-and-error method. These thinkers would offer to coders to turn on a "random-number generator" for a computer to obtain a new informational object, new notion or set of terms of a language in this way, exhausting all possible combinations, which should be examined for efficiency. We believe that this version is only going away from the problem and will not provide necessary results, but nothing prevents coders to try this way.

But there still are questions: how to organise the examination of enormous amount of obtained combinations and what to consider success in this examination? It is known that many new theories initially lost to old ones in solving practical tasks. Then the complicacy of the problem is moved into the sphere of problem definition, formulating of the goals and criteria for efficiency for new, not yet tested knowledge. This shifts the intellectuality to a human, adding nothing to the sphere of AI.

But if we think that random generation of new theories is somehow stipulated by external environment, by the context they appear in, then acuteness of the problem is moved onto not concrete enough for programming notion of context. There emerge questions about what to mean by it, how to use it, how does it communicate with that part of the system which generates new knowledge. Sooner or later, we will return to the same problems or we will encounter new ones, which would be no less complicated.

The question about the presence of randomness in thinking needs undoubtedly more detailed examination and will be examined in our another research (9).

It should be admitted that there does not exist an appropriate logic-mathematical description of mutual definition of ideas or objects so far. Indeed, in an attempt to describe such a process one falls into a vicious circle, infinite loop. Defined (determinate) plays the role of defining (determinant) and vice versa. Let A define B. But A itself was defined by B, and thus A should be redefined and so on. Sometimes attempts to formalise such systems or to put it on paper in the form of signs and their combinations are undertaken, as well as other attempts to create a formal system different from formal logic.

The regularity of the appearance of these attempts is described by the author of ternary digital machines N. Brusentsov in his work The adventures of dialectics in informatics:

Throughout two odd thousand years there were made only single attempts to overcome the fatal boundedness (Ramon Llull, William of Ockham, Jan Komenský, Leibniz, Hegel, Lewis Carroll). The XX century can be characterised by a progressing protest against two-valuedness: rejecting the law of excluded middle by the mathematical intuitionism, Lewiss and, following, Ackermanns attempts to overcome paradoxes of material implications, the invention of the ternary logic by Łukasiewicz, Reichenbachs conjecture about the ternarity of the logic of microworld (quantum mechanics), general rise of research in the field of multivalued logic, after all, Zadehs fuzzy sets, fairly characterised as a challenge thrown to the European culture with its dichotomic perception of the world in a rigidly demarcated system of notions. But all this, in a way, is a kind of modernity which does not achieve the aim pursued. However, the aims themselves are far from being realised clearly" (10) .

The limits of this article do not permit a detailed discussion on the attempts to create and formalise non-standard logics, but the facts known to us show that they all failed. The abolition of the excluded third often turns out to be an easing step to the following introduction of excluded fourth. The law of non-contradiction is abolished for some cases but still is in power for others. From our point of view, attempts to formalise the mutual definition of the premises of a theory from their content fail. Probably, there is some philosophical underlying reason for that; the question is whether the logic of real objects and living thinking systems could be implemented "on paper" or it is accessible only to engineering implementation in practically functioning artificial environments.

Thus, we suppose that principles put into a system and promising to bring really intellectual functions in perspective should be of dialectic type.

How do abovementioned strategies of software developing correlate with this proposition?

Strategies from the first to the fourth belong to formal systems and to the domain of Understanding. Local efficiency presupposes not defined within a system axioms. All sophisticated algorithms are usually developed as a combination of already existing locally true theories. Making algorithms more powerful, it is not reasonable to go beyond the scope of a well tested calculation type or method, because all that lies beyond the accuracy of mathematics and formal logic cannot be thought strictly in a common sense. From this comes a conclusion that no strict thought, notion or argumentation can exist beyond the reason altogether; and everything that finds itself beyond formalised science is either called poetry, intuition or art or is placed into a bin of "bad literature".

We can characterise physiological strategy as not critical to the empirical material being processed. It is tacitly assumed that the thinking functions according to formal logic. For this reason an axiomatic system, which is already a result of thinking, is assigned to empirics. Parallelism turns out to be a consequence of that: it is supposed that elements, structures and measured forms of processes in a living neural network are, in fact, elements, structures and processes of the thought, without a significant qualitative leap. That is typical for vulgar materialism, which is often criticised by adherents of dialectical schools in philosophy. E.g., an interesting critique of vulgar materialism in understanding of the thinking can be found in E. Ilyenkovs book Dialectical logic" (Moscow, 1984) in an essay devoted to Spinoza The thinking as an attribute of substance. A good example of not trivial understanding of physiology is, e.g., the D. Marrs work Vision and informational approach to studying of perception and processing of visual images (, , Moscow, 1987).

5. The difference of mechanisms attributed to the thinking in different systems of knowledge.

One can sometimes think that adherents of two abovementioned schools (formal and dialectical) not only speak two different languages, but do not hear one another as well.

Let us, e.g., point an apple with the phrase it is an apple. A formal logician does not see a problem here at all. It is just an indicating proposition about a fact, and facts only need a description in a logically true language. But a dialectician sees even in this single phrase and preceding it act of thought a great question about the mechanism of thinking.

From the point of view of formal logic the situation is as follows: we have an abstract notion of apple, and we point out one of the representatives of the set of real apples. The abstract notion was obtained some time earlier by observing apples and cutting off insignificant characters. Significant characters build up a notion. But to see significant characters we already have to know what an apple is.

If a coder would be offered simply to show many apples to a computer for it to cut off what would be insignificant, a coder would understand that he needs to create many descriptions of significant and insignificant characters for different cases with apples. The fact is that a coder knows about apple as an abstract object and due to this reason can think out and put into a computer the rules of processing some set of particularities of particular cases.

For a formal logician in thinking there are two consecutive operations.

Fig. 3

In the first case one abstract object (the model) is tried on present object, and from those which fit the model a set is formed. In the second case, insignificant characters are cut off on a set of objects and another model object is constructed.

Many researchers (the author of this article included) tried to reach the AI this way. The coding, in the end, was constantly coming to putting into a computer endless description of prepared patterns (abstract objects) or rules of abstracting for different cases.

A dialectician does not reject the idea that there can exist two different propositions about an apple as a whole and an apple as a particular. And these propositions, of course, contradict each other. But the thought which produced as a result these propositions was one. A dialectician believes that in a single act of thought a human unites both pointers and conceives in a single object a contradiction, e.g., plurality and unity at one time, in one frame, with the same respect. It is that that formal logicians consider to be irrational and impossible to be thought of strictly or be described.

But to make the proposition it is an apple a human beforehand has to keep in thought simultaneously, not subsequently both one apple and the whole potentially infinite set of apples, which belong to the same genus of apple, because otherwise nobody could neither conceive nor name anything. How can it be that an infinite set of phenomena (all possible apples in the apple genus) can be present in a single act of thought? It is this question that should be answered. All dialecticians tried to answer this question, beginning with Plato, with the antique One-Many problem. This question cannot ever be solved improving formal logic, axiomatic in its essence, prohibiting contradictions, working on the level of propositions and not on the level of thinking by which those propositions are obtained, or using fuzzy or multi-valued logic.

Thus, our hypothesis is that a system should choose not the way of formal logic, but the way of dialectical logic to be intellectual in its essence (and not on the surface). It should allow it to have mutually defining premises and contradictory propositions at the same time.

Both oppositions of the object (an apple is simultaneously one, particular, this and many apples of the same genus) should be captured in one tact of the mechanism of thinking. Let us give here another brief explanation why.

A circle denotes an act of thought, and letters denote its contradictory moments (Fig. 4). According to dialectical point of view in the same act of thought exist both unity and plurality; the thought itself is A and its concrete, own not-A, and their unity:

Fig. 4

A formal logician affirms that it is not necessary to try to obtain the combination of contradictions in a single act, as this situation can easily be described using two propositions (different acts of thought, different "viewpoints").


Fig. 5

But what act will unite them now? Let now B denote the first act, and C denote the second act, to make the situation simpler. In reality it can correspond to translation of a sentence into another formal language.


Fig. 6.

But we come again to the same structure, where both this sentences are apart.

Fig. 7

We can continue to infinity without achieving the necessary combination. The human thought is possible only due to existence of the mechanism which combines two dialectically contradictory acts. A regress into infinity can be avoided if we assume the existence of such combining act. But this means that the scheme on the fig. 4. should be implemented necessarily: concrete contradictions should be combined in a single act, and they make a unity because each one is the own other for the other.

We have already mentioned that sometimes different attempts to leave off the acuteness of the question about the allowance or prohibition of contradictions are made. It is said that, e.g., that contradictions in propositions or in the thought are possible as a logical, rhetorical or procedural method or as a temporary impediment to finding the final unity without any contradictions. In these cases it is believed that a correct thought which would result and configure initial controversies (and the object of thinking itself) does not really contain any contradictions at all.

We would like to point out again that A and "own not-A" are not different views upon the object or projections of something single and non-contradictory on different axes or aspects of something single, e.g., a sour apple and a green apple in the simplest case; but it is the thought itself, and single at that. An apple is one and many with the same respect. A concrete, not abstract dialectical is not a simple negation of something (part/not part, motion/not motion, white/not white), but it is a mutually linked contradiction, e.g., part/whole, movement/rest, form/content. Only these contradictions are mutually defining, they are not connected by some random and exterior to their content thought. Moreover, as they are concrete contradictions, they do not exist without each other, and the thought does not exist if in its fundament do not lie concrete contradictions in their unity.

Not dialectical logic can operate qualities of objects, already obtained as a result of the interaction of contradictions. Certainly these qualities are distinct, not identical and can even be contradictory, because they can be related to different aspects of an object, e.g., to different time moments of its existence. But it is only an aggregate of characters of an object, e.g., an apple is green and round, a human is young and old. These contradictions are removed by a properly conducted reasoning, which can whether choose one true proposition or find that there in fact is no contradiction, because each one of the contradictory proposition is made, e.g., with different respect to the object.

Different propositions about an object, made with different respect to it, can apply to different parts, different time stages of the life of the object, to different logical moments of the thought about it, to different viewpoints of the people who think about the object; all this does not require dialectical understanding. Our propositions turn out to have different respect to the object. It is implicitly implied here, that in some other acts all these propositions are already combined as related to one object and the object itself somehow already is in thought; and we are only discussing its different aspects.

The difference that is present in the thought and in the object and that turns out to be the condition of their existence exists not on this level of characters of a finished object, but, e.g., in the contradiction that there are many qualities, but they all belong to one object, which, however, cannot be reduced to them.

Dialectics is the distinction and combination within a system from inner content of the objects or ideas; it is the logic of self-organisation. It is also the logic of reflexion, because the reflexion unites in a single act passive and active, the object and subject. Formal logic operates with qualities of an object somehow already united in one, and already distinguished in this one by external rules at that. The Understanding abstracts from a dialectical unity of contradictions one of its aspects without preserving the initial unity.

Another topical trend in the contemporary philosophy is worth mentioning here. Adherents of this trend affirm that almost any usual philosophical range of problems can be avoided by rendering it into some new language or improving the language. Sometimes it is assumed that, on the whole, all usual philosophical problems are historically incidental and they are only an outcome of wrong used natural language. If proposed corrections or some new language can help the thinking to escape, at least, the One/Many problem, they should be brought to technological discussion and be implemented on practice. Such language should be implemented on the material of already existing computers or on any other material, the properties of which would be chosen or created with the respect to this language. Thus, we will obtain long-expected AI. But would it be possible to say or think anything in this language, e.g., to think "an apple" without combining in one act of thought its unity and plurality? Will such language be able to solve the problem of AI (even on the example of the simple abovementioned task), thereby proving that it is in fact the genuine model of thinking?

Our arguments about the necessity of mutual definition of premises and contradictoriness of the thought as the condition of any thinking at all concern, of course, not only simple language expressions, but they have a universal character. We could use as an example of the necessity of uniting in the thought not One and Many, but other contradictions Essence/Phenomenon, Whole/Part, Subject of Thought/Form of Thought, Element/Connection. In any case, we affirm that the thinking can only think about any object only combining contradictory moments of thought in one act.

Let us try to formulate the problem definition of creating intellectual functions with respect to two above discussed tendencies. The simplest argument closest to the raised task of demarcating the border on the screen is as follows. The object of thought exists in the thought only when it has its borders and it is separated from not differentiated stream of data, it is separated from other objects from any other with respect to it. But the thought should keep both the object and what is opposed to it (other with respect to the object) to think anything at all. Cutting the object out of what is not-object, from the background, marking a border between the object and not-object is the first task of any intellectual system, and it is faced by the necessity to keep in thought both the object and the background in a single act of thought, with the same respect. It is not possible to see on the first tact the object and on the second tact the background and to combine them on the third tact, because the first tact is impossible without the second and the third. Both contradictions should exist in the though about the object with the same respect, in the same act and not in different acts. A different mechanism of thought leads us to an ill infinity or demands that this combination be done beforehand by someone else, and thus, does not assume independent generation of knowledge. A system cannot be truly intellectual using this mechanism; we will only obtain an infinite attempt to combine to contradictory propositions with aggrieving results. For our task to be solved, it is necessary to generate new objects within an intellectual system, which is possible only with the existence of the mechanism that would distinguish and combine contradictions in one tact of the work of the system.

The mechanism of uniting contradictions is needed even on the first steps of information processing on the steps of perception and conception. On this level one can be not conscious about its presence, it can be not apparent, and can unfold itself fully only on highest levels of thought; but the fact is that the dialectical mechanism works as basis. It is possible that this basis is implemented in the nervous system and it provides the possibility of any intellectual action at all even on the level of insects (11).

This is the reason why any attempts to organise in an artificial environment independent transition e.g., from a phenomenon to the standing behind it essence (this is to what, finally, come the requests for user functions of intellectual systems) by existing means of natural sciences or mathematics are a priory foredoomed to failure until the mechanism which will unite contradictions is created.

Thus, it is necessary to comply with the principles that are specified as dialectical to create an intellectual system. I.e., the mutual definition of ideas, informational objects within a system from themselves and not from exterior source should be carried out. The contradictoriness of the thought has principal significance for a system. A single act of an intellectual system should contain A and its own not-A. This system possesses an ability to develop, i.e., to create new objects within itself, including the possibility to change once obtained procedures and rules. We take such dialectical system as basic for the intellect and the thinking in general. The reason plays its important role in the thinking, e.g., it works on the level of propositions about already defined and previously existing in thought objects and their properties. Formal logic on the level of reason plays the role of the regulative that allows to make true propositions in a locally limited area.


Today the problem of AI is tackled by specialists with natural science or mathematics education, which is constructed in the framework of formal systems. Some initially humanitarian sciences are becoming more and more similar to them, e.g., sociology or linguistics. This education does not assume that it can be possible to ponder seriously beyond locally true theories, to see the subject of one's thought as constantly changing and defined not by an exterior force, but within itself. This education does not allow to see that there are laws related to mechanisms of thinking that are not less rational than natural sciences knowledge in the sphere of humanitarian, e.g., in the history of philosophy, even in the Platos world of Forms.

We do not want to reject completely the reasoning and formal logics, because they exist in the integral human thinking; moreover, the reasoning is more effective than other forms of thought applied to certain tasks. What we propose is not to attach an exclusive importance to the reason in the question of mechanisms of thought.

Appealing to dialectical thinking as a possible alternative in the AI development, we leave the generally accepted scientific and technical tradition, which, on all hands, now ensures the progress. To speak seriously about attempts to formalise dialectics in Hegelian or Platonic sense means to be, at least, not understood by the contemporary educated and technically skilled community. In such communities the motto that new is absolutely better than old is hardly put on trial. However, judging by abovementioned reasons, in the logical development of intellectual systems Platos dialectic is still to be, we still have not reached it yet.

The initially chosen object of studying, the interaction of the human thinking with the IT, and the aspect treated, ascertainment of the criteria of intellectuality of systems lead to actualisation of many old philosophical and logical problems. It follows from the abovementioned that some aspects of philosophical, logical or natural sciences problems in fact turn out to be necessarily included into the discussion of the problem. There are some questions that need to be answered touching the social reaction to the fact that the human thinking cannot be reduced to the reasoning mechanism, which absolutely dominate contemporary informational technologies.

Is it necessary to try to escape the already formed and flourishing IT paradigm? What are the restrictions imposed by the fact that existing IT support only reasoning forms of thought? In what kind of situations these technologies cease to be suitable? Could types of situations, the automation of which is topical, but which demand other, not reasoning (or not only reasoning) forms of thought, be distinguished? What approach to IT is needed for that?

For today we in a natural way have obtained in the IT development a system with a feedback between IT and human activity: the Understanding lies in the base of computers and it is the reasoning human thinking that computers support. It is natural that instruments, appropriate for solving formalised and reducible to sequential procedure tasks stimulate formulating exactly such tasks not taking into account the possible contradictoriness of situations and the fact that the situations can be multi-aspect. The class of tasks that cannot be solved using only Understanding on principle and that cannot be formalised using contemporary methods finds itself beyond the focus of attention or is reduced to reasoning forms. Humans life, relationship between people, personal problems, sophisticated activities in medicine, education, ethics, management, subject to this procedure, lose their scope, are projected onto the only accepted plane.

And there does not exist a strict border between the IT area (reasoning area of Understanding) and the area of the Reason at that. The omnipresent spreading of IT formats the human thinking according to its laws, and due to that the reason expands itself without control into all forms of life and activity; it obliges a human to think and act complying with existing norms.

One of the natural effects of such expansion is an excess attention to all that seems irrational to a human suppressed by rigid limits. The sphere of irrational is uncritically connected to freedom. A human, tired of plane procedures and prepared algorithms puts there everything that is, to his mind, more vivid, more dimensional and less determined than the reason. Everything without distinction is carried to the sphere of irrational from classics of literature, music, cinema, philosophical thought to absurd, absolutisation of spontaneity, different forms of so-called creative that come from different lords of mass consciousness. The latter is respected in the highest degree because of its maximal remoteness from the Understanding and the thinking itself and according to the principle of least action too, because it does not require serious examination and can be assimilated directly. From our point of view, such escape from the reason is only an illusion of freedom of thinking and creativity, which leaves humankind in the same situation.

The disagreement with such situation is the best stimulus to continue studying philosophical problems, finding technical solutions, making models of AI that will lead us beyond the framework of formal logics and preserve truly creative nature of human identity.


(1) 10 "hot spots" in the field of AI research" ( " " ), Intellectual systems ( "), Moscow, 1996., Vol. 1, issue 14.

(2) The examples are taken from real conversation with the Customer about the site search function of the warehouse data base.

(3) The interest in AI problem did not disappear in the developers community. This topic is widely debated on different IT forums, often provoking serious discussions. The interest in the corresponding literature, and not only purely coding-oriented literature, remains, too. E.g., the book The Emperors New Mind by R. Penrose raised considerable resonance. In this book the question about the logic of thinking is posed directly and deadlocks in its natural science description are brought out.

(4) We believe that the main essence of a neural networks work is that many different input signals are linked (after training) to many different output signals. Enormous amounts of connections between neurons are, in fact, different routes of linking the input with the output. As a network receives a signal equal to those that were already input, it unequivocally links it with a certain output. The main point is that the entering information is not processed within the network, it is not changed, analysed or generalised, its significant characters are not distinguished; it is as a whole, as it is, linked with one of numerous pretenders to a result. No new informational objects (except those which were input) are generated within the network.

(5) Cf. V. Yelashkin, Conceptual Definition of a Neural Network Model ( ), Novosibirsk, 1994.

(6) Here the author relies on her personal experience in creating software for computer text processing and on constant monitoring of information in this field.

(7) Cf. P. Gaydenko, History of Greek Philosophy in its Connection to Science ( ) about the Aristotles critique of circle proving.

(8) M. Dymarsky Problems of text generation and fictional text (" ) Saint-Petersburg, 1999, M. Dymarsky, N. Maksimova Dialogical syntax: "Not only But also principle ( : " ... "), Discourse, 1996.

(9) It is known that there are so-called wandering potentials in a human brain, which bring a certain element of chance in the response of neurons. Cf., e.g., Ivanickys work Neural informatics and the Brain (- ), Moscow, 1991. The question about the significance of these potentials seems to be of the highest importance. But their presence does not contradict at all mentioned here arguments about the logic of thinking in general and its difference from the logic of reasoning as a part of the thinking.

(10) N. Brusentsov The adventures of dialectics in informatics. ( . ). Moscow, 2000.

(11) We can mention here an old, but significant example of D. Marrs attempts to formalise the process of distinction objects from the background by the eye of a fly. An original mechanism of perceiving the borders of objects being observed was found, but the research reached a deadlock, because it required the presence of known beforehand models of objects-patterns. Judging by the fact that AI is not yet created, Marrs work is not much outdated.

(elashkina@noolab.ru), 21.08.2009
NooLab ()

.. // , 1(32). , 2007. . 102-128.