Table of Content | Содержание

Signification and the Problem of Truth1

Emilia A. Tajsin

Kazan State University of Power Engineering. Kazan, Russia. Email: emily_tajsin[at]
Received: 1 May 2023 | Revised: 16 June 2023 | Accepted: 26 June 2023


The great hopes of scientists in various fields, fr om computer science and mathematics to literature and art criticism, fr om analytical philosophy to post-structuralism, in the last third of the 20th and first quarter of the 21st centuries are assigned to semiotics, or the general theory of signs, which studies signification and its laws. Signification, or designation (denotation, signalizing, symbolization) is the widest-common procedure in scientific creativity and culture in general.

The scope of the semiotic approach and the abstractness of the categories of semiotics are such that they allow for speaking at least of the theoretical-cognitive, if not ontological, universality of its approaches and the general methodological validity of its tools. One is capable of thinking only on the basis of the semiotic mediation of reality; moreover, the essence of consciousness itself as a whole is reflective, and representative. The recognition of the great informative capacity and value of the basic semiotic concepts, as well as the extreme breadth of the subject of semiotics due to the actual or potential symbolic nature of human science and culture, the instrumental nature of signs and symbols which science, ethics, religion, and art are full of, allows us to hope that semiotics will play, in the near future, the role of a universal manifestor and communicator.


Sign; Meaning; Semiotics; Communication; Image; Reflexion; Cognition; Truth


1First published in Russian, 2017

Сигнификация и проблема истины1

Тайсина Эмилия Анваровна

Казанский государственный энергетический университет. Казань, Россия. Email: emily_tajsin@[at]
Рукопись получена: 1 мая 2023 | Пересмотрена: 16 июня 2023 | Принята: 26 июня 2023


Большие надежды ученых различных областей, от информатики и математики до литературы и искусствоведения, от аналитической философии до постструктурализма, в последней трети XX и первой четверти XXI века возлагаются на семиотику, или общую теорию знаков, которая изучает законы сигнификации. Сигнификация, или обозначение (денотация, сигнализация, символизация) — наиболее широко распространенная процедура в научном творчестве и культуре в целом.

Масштабы семиотического подхода и абстрактность категорий семиотики таковы, что позволяют говорить хотя бы о теоретико-познавательной, если не об онтологической, всеобщности ее подходов и универсальной методологической обоснованности ее инструментов. Человек способен мыслить только на основе семиотического опосредования действительности; более того, сущность самого сознания в целом рефлективна, репрезентативна. Признание большой информативности и ценности основных семиотических понятий, а также чрезвычайной широты предмета семиотики, обусловленного актуальной или потенциальной символичностью человеческой науки и культуры, инструментальной природой знаков и символов, которыми оперируют наука, этика, религия и искусство, позволяет надеяться, что семиотика сыграет в ближайшем будущем роль универсального манифестора и коммуникатора.

Ключевые слова

знак; значение; семиотика; коммуникация; образ; рефлексия; познание; истина


1Впервые опубликовано на русском языке в 2017


The term “signification” comes in the closest way fr om the English word “sign”; it is, however, pan-European: (Zeichen, signo, seño).

The subject of semiotics which is the rules and laws of functioning of symbolic systems has universal significance indeed. A person is inclined to understand any well-ordered phenomenon that becomes the object of knowledge, as meaning something. Accordingly, a person makes any fragment of reality a sign or even a symbol if s/he ascribes a certain meaning to it. Semiotics therefore, being a general scientific knowledge, tends to a kind of “arrogant imperialism” (expression used once by U. Eco), that is, the spread of its vision throughout the world. Sure such hypostasis is something superfluous; however, the explanatory power of semiotics is really great.

The main semiotic idea was born long before semiotics itself. Even in the “Memphis Theological Treatise(See: Frankfort et al., 1984), the creative word (name), thought and world were combined into a triad. Today this triad is called by the name of Gottlob Frege or the English semantics Ogden and Richards. In reality, the semiotic triangle is a symbol of the unity of the material and the ideal, and the place of the event of the meeting of these two worlds is a linguistic sign. The recognized founder of comparative historical linguistics Wilhelm von Humboldt believed that each language is the result of the interaction of three factors: the “real nature of things”, the “subjective nature of the people” and the “peculiar nature of language”. This is it, a semiotic triangle. In the sign, the interference of the subject and the object, of sensory and logical, of material and ideal, of individual and general, is carried out.

Semiotics “officially” originated in the 19th century thanks to the efforts of the American logician and philosopher Charles Sanders Peirce and the ideas of the founder of structural linguistics, the Swiss scholar Ferdinand de Saussure, who included the science of language in the general theory of signs. Charles Peirce studied the works of medieval scholasticism in scripts for a long time. After him, with a break of many decades, this huge intellectual work was done by Umberto Eco. F. de Saussure is perhaps better known, especially to philologists; however, in fairness, it should be noted that he expressed the initial idea of the need for the science of semiology, whereas Peirce has constructed it. Now we have two introductions to semiotics: “fr om linguistics”, when a sign is understood as an elementary unit of the system, and “from logic”, when a sign is understood ontically, as an independent dominant entity. Hence its fundamentally different definitions: 1) semiotics is the science of any systems of elements that signify meaning and transmit information; 2) semiotics is the science of the objects of knowledge and means that signify these objects.

The roots of semiotics, its genesis, its main topics (in fact, this is true for any European science) are philosophical. Teacher of F. de Saussure Michel Bréal, the inventor of the term “semantics” and founder of French linguistics, in the preface to “Comparative Grammar” by F. Bopp draws a line from Bopp to Friedrich Schlegel, his teacher Karl Windschmann, and then higher up to Herder and Leibniz (De Mauro, 2000).

The value status of symbolic means in the human world, the possibility of studying language as a system of signs, the relationship of semiotic objects with forms of cognition, the materialization of abstractions, the problem of meaning and interpretation, the social transforming role of symbolism, the interaction of language and thinking, and finally, the essence of truth has traditionally been the most important epistemological and general gnoseological problems. They stood at the center of cognition theories or even accomplished the philosophical systems of individual thinkers.

In Russian humanities, studies on semiotics appeared around the middle of the twentieth century, also initially in philosophy (L.V. Reznikov, Leningrad, 1964; L.V. Abramyan, Yerevan, 1965) and then in linguistics (A.G. Volkov, Moscow, 1966). Tartu School led by Yu.M. Lotman gain fame; close to it were studies of the Moscow school developed; the most famous author was Yu.S. Stepanov. Leningrad scientific works were devoted mainly to literary criticism, and Moscow ones to linguistics. Our own centers of semiotic research appeared in the 70s. in Sverdlovsk (Yekaterinburg) and Kazan. Despite all the differences between the relativistic and substantialistic approaches, they retained the main semiotic postulate: natural spoken human language is a sui generis sign system, and it occupies a central place, being a cor cordium of all other sign-symbolic systems. All other codes – computers’, informational-logical, cultural texts and forms of culture themselves, diagrams and maps, emblems, seals, phalerae and coats of arms, genetic information, animal gestures and signals, etc. – are “also languages”, standing either “below” (as biological codes), or “above” the natural language (as technical codes).

Semiotics as a science and university discipline

The 1st Congress on Semiotics was held in 1974 in Milan. Recently, a three‑volume dictionary of linguosemiotics was published, edited by (late) Thomas Sebeok (USA). Then semiotic literature, so to say, poured in full flow.

When semiotics became a university discipline, scientific literature replenished with educational. Works of the following Russian authors are known: N.I. Mechkovskaya (her first works were devoted to sociolinguistics), S.T. Makhlina (semiotics of everyday life), E.S. Nikitina (semiotics and behavior), Belarusian semiologist A.B. Solomonik (semiotics as the “alphabet of communication”); G.E. Kreidlin and M.A. Krongauz whose “Semiotics, or the ABC of Communication: a Training Manual” has withstood several editions. In 2019, a textbook was published by E.A. Tajsin on philosophical aspect of semiotics.

Observation of language, a universal signifier, is the main source of the semiotic ideas of ancient and modern scholars. Due to such an important role of its object, linguosemiotics occupies a central place among other branches – namely, technical semiotics, semiotics of literature, semiotics of culture and art. At the same time, language exists and is understood in three dimensions: syntactic, semantic and pragmatic, as Saussure pointed out. Semiotics, together with linguistics, has passed in recent times the following main stages: comparative-historical, structural-functional, nominative, and discursive-cognitive. Today, many new linguosemiotic disciplines are born: generative grammar, linguistic logic, text linguistics, semiotics of discourse, ethnography of speech, ethnopsychoconflictology, ethnopsychosociology and even linguosynergetics, etc. There are many different classifications of language signs; these are built on dozens of grounds: according to the quantum of abstraction of the base word; according to the structure of construction (linear, branching, algorithmic); by the degree of openness / closeness; by the way of creation (spontaneous or planned) etc. For a semiologist, it is especially important to have the laws of the meaning of signs and “super signs” – syntaxems (the term of the linguist V.V. Zvegintsev) in the topography of the semiotic field.

The heuristic possibilities of signification are great. The languages of science and natural spoken human language, cultural forms and the genetic code, technical devices and media, signaling situations in the animal world and refined aesthetics of elite consciousness, all kinds of ciphers and structures – all of these can be interpreted as sign systems. (T. Sebeok).

And the agitating and optimistic part ends with this statement. Serious theoretical and practical questions arise.

The main problem of semiotics, both as a science and university discipline, is the relationship between sign and meaning. It remained enigmatic to this day. How is it possible at all, to combine sound and thought, phenomena of different worlds that do not have common predicates? How strong and motivated is this relationship? Wh ere is the meaning of our reasoning localized, and if “nowhere”, then what is it? For example, many philosophers and linguists believe that a linguistic sign connects two “functives”, the signifier and the signified, and the latter is an idea (for example, G. Frege and de Saussure believed in it). From this follows the thesis of the indissolubility of the signified and the signifier. Then it is not clear: why is this connection declared “arbitrary”?

E. Benvenist believed that his teacher Saussure interpreting the essence of designation resorted in fact, unconsciously and illegally to the third term: “thing” in relation to which the sign is arbitrary. It seems that this cannot be avoided. So it is one of the deepest laws of human existence and cognition acts – namely, the semiotic situation.

Let us dwell a little longer on the limitations of the semiotic approach. It operates within the general framework of the principle of systemicity although it does not exhaust it, but, on the other hand, it includes hermeneutic insights that do not obey systemicity.

The limitations on the possibilities of applying the semiotic approach are diverse. Umberto Eco, in his famous “Theory of Semiotics”, (Eco, 1976) for example, spoke of “political” and “natural” limitations.

Political” limitations are divided into “academic” restrictions associated with the fact that semiotics has become a separate discipline relatively recently; “comradely” restrictions on the part of the adjacent sciences, which achieve important results for semiotics, so to speak, “incidentally”; “empirical” restrictions associated with the underdevelopment of the theory of signs itself. “Natural” limitations are explained by the non-sign nature of many objects.

To this we can add that there are limitations of philosophical nature, for, although the categories of semiotics in a number of cases reach the gnoseological level, but they do not reach the ontological universality. The world itself does not represent a system of signs, is not “charged” with information, contrary to profane opinion; it does not “speak” to the subject of knowledge; only a human being can give meaning to natural phenomena. Therefore, semiotics is not able to replace philosophy. Finally, a special facet through which semiotics can be considered is logic and methodology of science, – this “state in the state” of the theory of knowledge.

So: did the knowledge of some laws of signification help at least one art historian to analyze a film better, a linguist – to isolate the main language units and their correlates, to combine vocabulary and grammar, a geographer – to build a topographic map? Do scientists who came to semiotics “from different sides” really understand each other? Or, according to Heraclitus, most people don’t understand what they are encountering, and having learned, they still don’t understand, although it seems to them [they do]?

More problems: image, symbol and sign

Deeper answers are required to the questions posed, for it is not enough to indicate that signification is universal or close to that, and even to study the basic properties of sign systems of various kinds. It is necessary to reveal the regularity of the emergence and change of these systems, the causes of symbolism itself and the semantic transformation of symbolics, to show the value of this knowledge, the ability of semiotics to write a holistic scientific picture of the world, to anticipate the unfolding of the laws of human existence based on understanding of the essence of man, human thinking and practical actions, which understanding semiotics gives.

We give a concrete example of the undoubted usefulness of general scientific approaches, namely semiotic, for the examination of particular scientific research.

Let us consider some of the ideas contained in the remarkable book of someone D.N. Zamyatin “Metageography: The Space of Images and Images of Space” (Zamyatin, 2004). Its other name is imaginary geography.

Written in a postmodern style, with the use of such powerful general scientific methods of cognition as systemic structural analysis, and such fruitful disciplines as semiotics, with the goal of bringing social science closer to natural science, this monograph offers many solutions to modern problems of geopolitics and political geography, geomorphology and “geophilosophy of language”, in the field of geo-urban studies and studies of regional self-consciousness – and at the same time it gives rise to many new queries.

Images of space”, i.e. geographical images, and their specification as “the image of the locality, territory, region, country” – are of interest to the author of “imaginary geography” in several respects: substantiating the concept of a geographical image, studying its genesis and modeling, developing mechanisms for adapting this concept “in decision processes for important social problems (politics, ideology, education, socio-economic and cultural strategies)”, studying geoculture as a cumulation of geo-images. (p. 13)

It is significant in this case that in the long list of social sciences and humanities that are “responsible” for justifying the key concept for D.N. Zamyatin, linguosemiotics and, even more offensively, theory of knowledge are absent. As we can see, its absence leads to an annoying situation: though understanding the heterogeneous origin of the (geographical) image, the author, building his own text, does not consider it necessary – or he is not able – to distinguish between the image, symbol and sign.

This flaw characteristic of many modern scholars involved in postmodern discourse is explained in different ways; in particular, one can refer to neo-Kantian phenomenology, which totally excludes the “real”, “physical” object from analysis; to the “second navigation” of Platonism, which makes a Himmelmann in search of the lost eidos; to the indivisibility of the reflective-critical and objectal language in many modern cultural texts, etc. But the main explanation is just that: without taking into account the family treasure of the materialist theory of knowledge – the principle of reflection – and, on the other hand, the running “working capital” of linguosemiotics – namely, techniques and practices of symbolization, – errors are inevitable.

We give clarifications.

An image is the result and basic structural unit of reflection. Reflection is a type of interaction of systems in which they exchange matter, energy or information in such a way that one of the systems acquires similarities with the other. The image has no other generic properties except objectivity (disposition, attachment to its original) and similarity to its object (there is no property of “maximum distance” and especially “obligatory mediation”: say, the first stage of cognition, sensory perception, is characterized by immediate direct reflection of reality, observable data, sense data).

All differences in the images depend on the features and varieties of this very resemblance or similarity. The first and basic type of it is a contour geometric similarity, which the geographical images of space fully satisfy. They are congruent with objective reality, and correspond to it orographically. Also, geographical images are connected with their objects not by just one relation, — for example, by convention (as signs), but by all possible connections, starting with the genetic one and ending with the functional one. The principle of reflection in philosophy is based on these postulates. It is up to the scientist to accept or not accept it (at the risk of declaring that cognition is not able to correctly and adequately reflect reality); however, it is immutable that the author should be aware of this challenge and, most importantly, one should not mislead the reading public.

At the same time problems remain. If the subject of semiotics – namely, the laws of sign systems functioning – does have universal significance (after all, any orderly phenomenon, including natural one, is understood as a system that has a semantic content, that is, as something meaningful), — then why semiotics itself is defined as only a general scientific discipline? If it is a general scientific, and not a philosophical discipline, then its methodological, or rather practical, significance should, by definition, exceed its worldview value. Then why is it so difficult to give a concrete answer: what exactly is the practical significance, what is the benefit of applying the semiotic approach to the analysis of the phenomena of culture and being in general in comparison with other – special – approaches? Why, it remains unclear, is it better to characterize the film with the help of semiotics, and not with the help of art history? Why does postmodern fashionable analysis, namely, text deconstruction, require semiotics rather than literary criticism? How is a semiotic approach better than computer science in itself? And why is there no semiotic study that would bypass worldview issues – the origin of consciousness, the laws of knowledge, the specificity of human existence, and the like?

The nature of semiotic concepts requires research and refinement. Often these have an intuitively clear content and philosophical meaning (for example, the famous Frege triangle, also known as the Ogden-Richards triangle or the Peirce triad). In reality, however, they are very complex and need analysis using all the power of gnoseology. Thus, the dialectics of image and sign is the most important philosophical aspect of semiotics, and its solution depends on the knowledge of the dialectics of the subject and the object of cognition. The problem of conventionality of the sign is a species in relation to the dialectic of necessity and contingency, conditions of cognition, etc.

The principles of selection and combinatoriality in syntactics, the first part of semiotics, are insufficient, for example, to explain the laws of phonology; they need support from the theory of completeness and incompleteness of knowledge. The central problem of semantics, the second part of semiotics, – i.e., the nature and essence of meaning, depends on the solution of the problem of ideal. The third part of semiotics which is pragmatics, studying the relationship of signs and the world of culture, always demonstrates the fundamental dependence of its presentation on the type of scientist’s worldview.

As to an attempt to build consistent sigmatics (the fourth part of semiotics proposed by G. Klaus), responsible for the relationship of signs to objects, — it encounters methodological difficulties caused by the uncertainty of the concepts of form and content in the sense of their nonaxiomatizability. (At the same time, in the theory of music, for example, these categories are generally declared “boring,” and instead, musicologists today speak of ... “form and harmony”).

The problem of sign and meaning, broadly speaking, is the problem of correlation between material and ideal. In a semiotic situation, the ideal appears as meaning. The meaning, we announce immediately, is an abstraction, a certain qualification of the ideal. The meaning is “not given to us in sensation”. The signifier, sign “body” transporting meaning (sign vehicle) is sensed; it is usually material, except for the reproduction of a sign within memory. And the third (or rather, the first) component of the semiotic situation is the signified – named referent, denotatum, significant, nominant, representant, interpretant (etc., quantum satis), that is, a real or ideal object of designation, a thing.

What, then, is a sign? Here are scholastic definitions that are quite acceptable today. A “sign” ...designates that which leads to the knowledge of something else and is intended to mean it (“natum est pro illo supponere”) or to be added... in a statement... (“vel tali addi in propositione”) ... these are syncategories, and verbs, and those parts of speech that do not have a complete [sign] – or what should be composed of the above – this is the sentence. And with this understanding of the term “sign”, the word is not a natural sign of anything” (Ockham, 2002). This will almost literally be repeated in recent times by C. S. Peirce in his “Collected Papers”: ‘Something which stands to somebody or something in some respect or capacity’. Nevertheless, these definitions are really too general, and besides, these outstanding logicians, for an unknown reason, did not want to build definitions according to the scheme legitimized by Boethius in V A.D.

Meaning and the Ideal

The greatest difficulty in the discussion at all times was caused by the problem of the semantic side of the linguistic sign, its ideal substance. Today it cannot be said that the problem of meaning has been resolved. This term, as a rule, is introduced without definitions and is understood intuitively (the term “sign” is likewise introduced in computer science). The intrigue is that until a phase transition from the (ontological) essence of a thing with its accidents to the (gnoseological) “Schein”, from the material to the ideal, from the sensually perceived world to sensory perception, reasoning for these topics will remain speculative.

Most often, the categories “activity”, “experience” and “practice” are used for explanations. There is some sense in this. The essence of a thing is manifested only in operation, in working with an object. The very German word thing (English), Ding (German), comes from the word “ting”, veche, the general assembly of the tribe. Also, the familiar “What’s the matter?” shows us the same unity (“matter” as substance, thing, and deed). It can be assumed with a certain degree of certainty that Aristotelian “ousia” says the same: it is an entity that manifests itself in human activity. Usia → use. (The word “ousia” originally denoted the real price of property offered as a guarantor in commerce by the Greeks; this is being-in-action).

An object that cannot be processed is declared unknowable, or rather, essentially unknowable. But to the extent that the object lends itself to view, it is already known, and not only potentially knowable. To declare something unknowable is to declare that it is not amenable to processing, but still cognizable as “non‑amenable to processing” or even “non-amenable to Anschauung” in the sense of perception.

By the way, G. Frege considered intellectual intuition as an active process, denoting it by the term “grasping”. This is the only relationship connecting the sign with meaning (semantics), the sign with a person (pragmatics). In this process, thinking does not create thoughts, but enters into a relationship with something objective.

Let us recall (once sacramental) Lenin’s words: “Every mysterious, tricky, ingenious difference between a phenomenon and a thing in itself is pure philosophical nonsense. In fact, every person has seen the simple and obvious transformation of “a thing in itself” into a phenomenon, “a thing for us” millions of times. This transformation is knowledge”. (Lenin, 1967, p. 120)

If there is a transformation, then there might be a substitution, a transition from one to another... If there is no transition, then there is simply nothing to build the theory of knowledge upon; but if it exists, then why is there no simple replacement of material with spiritual? “But this is a dialectical transition! This is not a mechanical replacement, but Aufhebung, removal!” – you can fend off. Otherwise in order to be spiritually born, one would have to die naturally...

In this philosophically suspicious “transition” nothing concrete changes in content in the natural, external, material world. The ideal does not constitute another world, another corner in this world, it is not a double-ganger and not part of the sensually perceived physical reality, but no one has yet managed to define the ideal else than negatively: “ideal is not material”. And unless a scientific explanation of the “growth” of this higher form of movement from all others has not been composed, any strict knowledge of the basic cognitive relationship is also impossible. It will remain a postulate, open to critique at any time.

Semiotics intervening with theory of knowledge

We can try to line up an explanation of a different kind. For example, we could take advantage of the not-so-effectively used but perspective term “presentation”, Vorstellung, which is a form of cognition that is intermediate between the sensual and abstract, being central in its position on the “ladder” of cognitive ascent.

Otherwise, the singular is felt, otherwise the general is conceived” in the same subject, Boethius believed (Boethius, 1990, pp. 28–29). But in Vorstellung, firstly, the individual is felt “not otherwise” than the general is conceived: they are equidistant from the concrete object of perception; secondly, “Vorstellung” in Latin (and in English) is notitia, notion, which emphasizes the connection of /re/presentation with designation (language). The explanation of the ideal through presentation is threatening, however, with semiotic imperialism and “existential” materialism; but the most important ontological position is happily postulated: “matter is the subject of all changes”.

Presentation is a gnoseological correlate of the “ideal” which is an ontological attribute of consciousness. “Consciousness” implies reflection; “ideal” does not. Not the “world” exists as a “/re/presentation”, but the ideal consciousness exists “as” it; moreover, it is a /re/presentation.

There is no presentation in nature; there is only substitution. However, what has been said does not apply to signals issued by animals: this is a type of signs. Then it’s more accurate to put it this way: there is no presentation in the inanimate nature. From here follows the coincidence of the ideal and the presentative in volume, as inherent in the psyche.

This is the reason why gnoseological images are compared with signs or declared as signs (symbols, hieroglyphs, etc.), which tempts their ability to presént. But the sign is not just a presenter, it is a representant.

The unity of semiotic and philosophical problems does not exclude the possibility of at least approximately distinguishing, firstly, those that are studied mainly due to their importance for special sciences; secondly, the problems on whose solution the improvement and fruitfulness of the semiotic approach itself to various spheres of human life depends on (as well as other general scientific approaches – information-theoretical, cybernetic, system-functional, etc.); thirdly, and it is most important for us, these are problems that do not so much serve specific sciences from a “technical” point of view as they have great philosophical meaning.

Problems of the first kind can acquire universal gnoseological significance over time, and vice versa, the most general philosophical conclusions may interest a researcher who is engaged in special science. Explication of semiotic concepts, the expansion of their layer, the formation of a semiotic approach in connection with the tendency to integrate science allowed Russian scientists in the 70s of the 20th century use appropriate techniques to build general scientific information models (I.I. Grishkin), ternary description language (A.I. Uemov, A.Yu. Tsofnas), variants of system theory (Yu.A. Urmantsev, A.I. Uemov, E.M. Khakimov), etc.; undoubtedly, logicians, linguists and philosophers rely on them, too.

The essence of signification has been the subject of debate for many years.

A simple denial of the immanently symbolic nature of human existence and human consciousness makes the problems of nature and the essence of culture, the content and forms of consciousness, the specificity of language, etc. — unsolvable.

But a simple recognition of the symbolism of human culture and mentality, human ability to understand the world and its phenomena as something significant poses an old gnoseological problem: is it possible for consciousness to be an image (and not a hieroglyph or constructor) of reality, and is it not better to go to little-binding terms “reference”, “correspondence”, “correlation”, etc., speaking about the relationship of language, meaning and reality?

Therefore, both denial and recognition of the universality of symbolism are under one common question; and cardinal philosophical reflections and their results depend on this decision.

A clear positioning of the problem of truth depends on how signification is understood. Theory of truth as reference (Greek-Lat.: ferrein – to bear, to carry) is based on sigmatics – the relationship of the sign (name, utterance) and the object. Theory of truth as efficiency, or clarity providing interaction, is based on the relations of a sign and a subject, i.e., pragmatics. Theory of truth as a coordination of statements (and in general all shades of conventionalism and operationalism) is founded on the relationship of signs among themselves, i.e., syntactics. Theory of truth as correspondence studies the relationship between a sign and its meaning, namely, semantics. The research area that is studied jointly by the theory of cognition, semiotics, logic, epistemology, and to some extent psychology, which is the relationship of meaning and the object, depending on how the problem of the ideal is treated, as a result of critical reflection, ends either as a theory of coherence (epistemology, analytical philosophy), or a theory of correspondence (gnoseology).

In the latter theory truth is interpreted as a variant of reference, or, again, correlation standing in the same row with the correct, right-up-to-rules and adequate correspondence of the ideal image of consciousness to its object (notwithstanding of how much effort logic makes to contrast the formal correctness and substantive truth of the judgment).

It is right that the term “relatedness” or “co-relatedness” (reference) in itself does not yet speak of the truth of anything; it needs species specifications. Such metaphors in gnoseology and even rigorous epistemology are “correspondence” (respond, “answer”), mitstimmen (Germ. “voice”), “coincidence” (“fall”) “coordination” (“order”), “conformity” (“form”), “combination” (“bini”, two-by-two) etc. The requirement of clarity and the strictness of definition, generally speaking, should prohibit the use of metaphors... The term “adequacy”, as a gnoseological category that has a solid tradition, might be preserved; but its content should finally be described from the point of view of not so much volume and structure (“isomorphism”, for example) as intensively, with identification of such properties as resemblance and similarity as necessary explicands.

These categories have a very rich meaning, its analysis and disclosure is one of the “growth points” of gnoseology in general. In addition, the term “adequacy” should cease to be associated under the guise of explication (but in fact superficially) with coordination, correspondence, conformity, or even “isomorphism” (“form”) and model (“mode”, reduced form), because, firstly, etymologically it does not mean anything other than equalization, equivalence; and secondly, acting as a synonym for the above-mentioned relations, it becomes indefinite, replacing the “old” developed theories – those of correspondence, coherence, etc.

In Soviet-Russian literature, for obvious reasons, an equal sign was put between the theory of knowledge and the theory of reflection. At present, attempts are being made to get away from “contemplative materialism”, “inert epiphenomenalism”, “copy theory”, etc., as the theory of reflection has come to be called. The stake is mainly on the reorientation of logic and methodology of science towards the “value aspects of cognition”, “background knowledge” and sociocultural determinants. The results are still small; there are basically two of them: the transfer of emphasis from “focal” knowledge to “background” one and positing representation along with reflection, and in some cases also the transfer of emphasis from reflection to representation. On the other hand, the question “Are necessary truths true by convention?” undermining conventionalism – the basis of semiotic idealism, – objectively serves to strengthen the theory of truth as an identity.

On truth

G. Frege believed that the difference between /re/presentations (Vorstellungen) and reality is the most essential in determining truth; although, apparently, in this case there can be no complete coincidence and complete truth: “Dabei ist es gerade wesentlich, daß das Wirkliche von der Vorstellung verschieden sei” (Frege, 1993, p. 60). He wrote that it is necessary to distinguish between the expression of thought and the statement, or utterance. It is clear that reality differs from presentations, presentations – from expressing thoughts, expressing thoughts – from utterances, this all is trivial. Thanks to the ongoing conversation about “correspondence”, “conformity”, “coincidence”, “compatibility”, etc., we are entitled to talk about their imposition; the result will be agreement in some aspects and inconsistency in others. But then — nothing at all can be considered true? That which is only half‑true, that which permits gradation, is no longer true? Or is it possible to state the truth even if there is a coincidence only in a certain respect? But in which one?

Plato asked the same through the mouth of Socrates in “Cratylus”, the classical antique semiotic dialogue (Plato, 1994)1. “…how ridiculous would be the effect of names on things, if they were exactly the same with them! For they would be the doubles of them, and no one would be able to determine which were the names and which were the realities”. (432d). This thesis is better known than its argumentation, which is original and shows a magnificent presentation of the dialectic of discontinuity and continuity in the relation we are interested in: a method of approximation to (absolute) truth. “…the number ten at once becomes other than ten if a unit be added or subtracted, and so of any other number: but this does not apply to that which is qualitative or to anything which is represented under an image. I should say rather that the image, if expressing in every point the entire reality, would no longer be an image” (432b). And further on: “Then you see, my friend, that we must find some other principle of truth in images, and also in names; and not insist that an image is no longer an image when something is added or subtracted”. (433d). “…do not insist that the name shall be exactly the same with the thing; but allow the occasional substitution of a wrong letter, and if of a letter also of a noun in a sentence, and if of a noun in a sentence also of a sentence which is not appropriate to the matter, and acknowledge that the thing may be named, and described, so long as the general character of the thing which you are describing is retained…” (432е). Indeed, one legislator – the name master may turn out to be good, the other – bad, so that among the names some will be made well, others will be bad: “…when the general character is preserved, even if some of the proper letters are wanting, still the thing is signified;—well, if all the letters are given; not well, when only a few of them are given… or if not, you must find out some new notion of correctness of names, and no longer maintain that a name is the expression of a thing in letters or syllables”. (433b.)

Frege explains it to us: “Denn in einer Definition gäbe man gewisse Merkmale an. Und bei der Anwendung auf einen besonderen Fall käme es dann immer darauf an, ob es wahr wäre, daß diese Merkmale zuträfen” (Frege, 1993). (“The fact is that each time an indication of some signs is included in the definition of the true: but in each case it is necessary to be able to decide whether it is true that these signs are present”. – Author’s translation).

Does the meaning of the sentence depend on the conditions of its truth? At present, this has not been proved. While the Russian author speaks about meaning, the meaning of the word is always meant. And when we read the texts of English-speaking authors, they refer to the meaning of the sentence, the statement. This is due to the different nature of English compared to Russian: English is analytical. And therefore, the question always arises about the conditions of truthfulness in connection with the question of meaning.

It is impossible to equate the ability to realize the fulfillment and non-fulfillment of the conditions for the truth of a sentence, which is characteristic of epistemology and analytical philosophy, and the knowledge of what these conditions are. But even such a departure from conventions to objective examination is nevertheless enclosed within the framework of the analysis of truth as truthfulness of a sign, which is typical of logic and linguistic philosophy. Without questioning it – otherwise the heuristic ability of signs is being questioned! – the question must be posed differently: can a statement be true in itself, without its ideal content, its sense, were true? Sense is the substance of language; therefore, the question under study is the problem of the adequacy of the ideal and the material. And here we fall into a vicious circle.

For then we will have to examine whether it is true that the sentence, idea, thought or image coincided with something or correspond to something. In the same way, if we refuse to analyze for coincidence or correspondence, any other attempt (compatibility, isomorphism, similarity, adequacy = equivalence, etc.) will fail.

Let’s start over again

The fact that the process of cognition is a kind of unity of reflection and designation was accentuated by almost all major philosophers: Hegel and Fichte, Frege and Peirce. The worldview and methodological analysis of the true and the untrue has probably the deepest and most serious history. Aristotle stood at its source.

In 1930, M. Heidegger posed the problem exactly as we are trying to do it today: he investigated the role of /re/presentation not only in acts of cognition, which are always supplemented by notation, but in the processes of assimilating des Gesagtes to an opposing thing – der Gegenstand – as such, in its open ens, considering that what makes righteousness and correctness possible to be the essence of truth. The most important judgment is: the measure for the presenting assimilation (open as correctly open) takes (or should take upon itself) the prescription of the directing measurement for the whole process of presentation, “a measure and a stand against the confusion of opinions and reckonings(Heidegger, 1989, p. 65).

It is proposed, in a much less individualized and poeticized language, to discuss truth as representation using a term taken from the theory of speech acts: direction of fit (direction of coincidence). It allows one to simply and briefly explain the subject’s orientation to the order of things or the order of conscious states. “Truthfulness” is a characteristic of consciousness; “Understandability” is a characteristic of an object, its embeddedness in a given semantic and syntactic system in the given socio-cultural circumstances.

The first strict and consistent definitions were given in 1931 by Alfred Tarski, who linked truth with feasibility. The works of Tarski and Gödel, as well as successes of semantics and logic have demonstrated that an exact definition of truthfulness of a statement can only be given in a meta-language, in relation to which a statement subjected to verification of validity is in the domain of an object language containing statements of more complex logical types.

However, a great number of philosophers, including Frege and sometimes Heidegger himself, call true (or false) not only real joy, real certified gold and all of that sorts of things, but also judgments about them: “We call true not only an actual joy, genuine gold, and all beings of such kind, but also and above all we call true or false our statements about beings, which can themselves be genuine or not with regard to their kind, which can be thus or otherwise in their actuality” (p. 65). Ontologizing truth in general [Lichtung im Wald], Heidegger was forced to explain why then the predicate of reality does not allow us to distinguish truth from falsehood. “The true is the actual. Accordingly, we speak of true gold in distinction from false. False gold is not actually what it appears to be. It is merely a “semblance” and thus is not actual. What is not actual is taken to be the opposite of the actual. But what merely seems to be gold is nevertheless something actual. Accordingly, we say, more precisely, actual gold is genuine gold. Yet both are “actual,” the circulating counterfeit no less than the genuine gold. What is true about genuine gold thus cannot be demonstrated merely by its actuality”. (p. 92)

It turns out that neither correctness, nor coherence, nor reality in itself can be definitive properties of truth, for correctness appears when truth is already there, and it is itself determined through truth, and consistency/coherence as well as reality or actuality, characterize not only truth but also other relationships and states.

In return, Heidegger achieved an important result for those philosophers who are not concerned, like him, with the extension of the concept of the true to the thing: he shows what, in essence, resemblance is and proves that the similarity of dissimilar in nature [physei] phenomena is not only possible, but it alone makes it feasible to equate the statement about the object and the object itself.

Comparing the two gold coins (as both Frege and Heidegger did): they are in accordance with one another. They come into accord in the oneness of their outward appearance and are identical in this respect. However, the judgment about the coin, say, “This coin is round,” is also consistent with it; but how is such accordance possible? The coin is round, and the concept of it has no spatial character at all. The coin is, and the concept is not a means of payment; the coin is material, it is metallic, and judgment is immaterial, etc. What is consistent in them? What do they have in common, what similar? “…this accord is supposed to be a correspondence. How can what is completely dissimilar, the statement, correspond to the coin? It would have to become the coin and in this way relinquish itself entirely… The moment it did, it would no longer be able as a statement to be in accordance with the thing. In the correspondence the statement must remain — indeed even first become — what it is” (p. 95-96).

It is not enough to prove that the ideal cognitive act is a reflection, and if so, (let it be “for the total humanity”, “commonly”, “in general”, etc.) it can automatically be considered true. The falsity is also actual; the untrue image is also an image, and practice can be as much a criterion of its effectiveness as for a true image.

It has been settled long ago that “...even false, erroneous and generally lacking an objective referent knowledge can lead an activity to a preassigned result”, (Kasavin, 1990) and “sensory data, being the result of the impact of an object on the senses, its reflection, are, however, insufficient to distinguish between reality and illusions…” (Mikeshina, 1990, p. 78).

Explanations and Proposals

It is important to find out exactly what qualities, properties, and differences make an image an image, and then also a true one. The first necessary property, as is known, is objectivity. One must have the original in order to be an image, material or ideal. The second quality is similarity with this original, and not only geometric or physical, structural or external, but also both these and many other types of similarities that should be taken into account and analyzed in gnoseology. This rich category has not yet been sufficiently developed, leaving the true image to be intuitively understandable. Therefore, every study that touches on the concepts of similarity and resemblance is so important.

The area in which the concept of truth is applicable is sense, Synn, Frege argued. And in this area it is impossible to verify it by simple superposition, by combining. Frege also took an example with a gold coin: if, for example, in many cases it is possible to verify the validity of a banknote by simply combining it with a reference one, then an attempt to verify the truth of a gold coin by overlaying it on a banknote can only cause a smile. But Frege does not go further – to the study of the essence of similarity; he limits himself to putting truth in logic, and the latter offers in its turn its own set of verification rules.

On the other hand, the conclusions drawn by Heidegger seem to lead away from truth as a human dimension of /re/presentation to an ontologized truth, leaving the sphere of the subjective in general and interpreting truth as the non‑concealment and non-obscurity of Being. However, one can agree that when a certain relation becomes presentation, it thereby becomes in essence a similarity (in a non-essence, though, it can remain a non-similarity). Truth is an ideal image and resemblance of nature (first navigation), of eidetic essence (second navigation), and of human relations (third navigation). The first condition of truth is the first condition of imagery – it is the presence of another, des Entgegens.

These thoughts were developed by I.S. Narsky: there is a specific, namely dispositional, character of the relationship of sensations and objective properties about which they (sensations) inform. Objects have a disposition in the form of the quality to generate sensations, and sensations – and psyche in general – have a disposition of “living through” objects. In a vague form, this was anticipated even by Anaxagoras: he believed that sensations arise due to the opposite, because “the like does not affect the like”. I.S. Narsky pointed out how wrong Hegel and Berkeley were: one – believing that thinking can know only that which is related to it, i.e. thoughts, the other – believing that cognition is bound only to “ideas”, for “ideas” are similar only to “ideas”, and cognition is possible only wh ere there is a similarity. But it is important that almost all scientists recognize the property of similarity, or resemblance, as the second main condition or circumstance of the truth of knowledge. And Heidegger is right in asserting the possibility of similarity of things different by the nature.

Objectivity is a generic property of the reflection relationship in general. Similarity is a quality of a true image.

Truth, surely, is subjective, and this is manifested in many ways; First of all, it belongs to the subject and does not exist outside of it. Symbolic instrumental knowledge, “hypothetical-selective, creatively-projective, interpretative activity”, etc. – all this is subjective (and L.A. Mikeshina is absolutely right in this) (Mikeshina, 2002, p. 31). Not only constructivization, categorization, relationships and expectations inherent in higher cognitive situations, but also the physiological limitations of perceptions and sensations by the capabilities of the nervous system itself are superimposed on the reflection ratio of the object, making the image subjective. This is pretty clear. Another question is more complicated: how is the existence of a true image possible? And what can be recognized as a guarant of the truth of reflection?

For example, how can the image in the mirror be wrong? Suppose we have an uneven mirror surface. But the laws of optics will not change when a curved-surface mirror shows us a different image than a flat, smooth, “correct” one. This will be a true image cast off by the “wrong” mirror. Their difference is a subjective matter, a question of interpretation, of the purpose of using the image. Schein, appearance, is also a phenomenon that does not violate the laws of nature and does not go beyond them. To consider it as a deception on the part of the object or a mistake on the part of a person, to call it in an untrue image in cognition is impossible in any absolute way. It’s just that the beam glides longer on an uneven surface. Schein is a phenomenon reflected not in the shortest way from the external and “shaped” to the internal in essence, but in a long, complicated and indirect way.

The “untrue” image, therefore, was obtained “not by the right person”, “not rightly” or “not on the right place”. “The measure of all things”, a human, establishes the existence or non-existence of a specific reference of an object and a “mirror”, as well as the “curvature” or “plane” of its surface, guided by intuition, convention, tradition, fruitfulness, efficiency, etc.; there are many auxiliary criteria of truth.

A special case is an image on a mirror with a flat surface, which does not represent the entire object, but some part of it. It can be qualified as a true image (in analysis operations), as the only available, and therefore useful and acceptable model, or as a deception, a “figure of default”, insufficient and untrue.

Not only in different sciences, but also in philosophy itself there is pluralism in understanding of truth. As a category, it is the prerogative of the theory of knowledge and logic; other types of cognition use this term loosely, and other forms of social consciousness have their analogues of truth: utility, convention, faith, provability, evidence, post-truth etc.

Truth, in gnoseological aspect, is characterized by coincidence, conformity, or congruency, on the basis of the existing similarity of image and object; in the aspect of worldview – by objectivity, genetic “secondarity”; in methodological aspect – by normativity, correctness (rule); in axiological one – by value (verity, justice); in praxeological – by utility and reliability. In general, in science, truth is reliability, in art it is typification, in religion – faith, in politics – contract, in economics – profit, etc.

Non-truth in gnoseological terms is a mismatch, dissimilation of an image and its object; in the aspect of worldview it is fantasy, mysticism; in methodological terms it is error, i.e. method error, or falsehood; in axiology it is harm, injustice; in praxeology – insecurity and inefficiency, etc. Epistemologically, truth is the principle of knowledge; non-truth is a violation of the principle, but it arises from the essence of truth (in M. Heidegger). Deviations from the truth have various reasons, including the one pointed out by F. Bacon: people like lies. Therefore, all various deviations must receive different explanations.

The criteria of truth in different areas of knowledge, in culture in general, should vary greatly.

Reflection and presentation, the ideal and the true, all have their own history; and the criterion (criteria) of truth also has got it.

Apparently, the adequacy of lower-order mental images should be deduced from their biological relevance.

The sensations and perceptions were “correct”, useful and served the continuation of the genus in the cases when they reflected the repeated, non-random, necessary connections (properties, relations) of things. They were remembered, preserved together with the evolving genus, and were “closer” to the object, because the more often the encounters with the object came in, the clearer, more reliable, and more correct the image was.

Wilhelm Dilthey’s idea that there was initially a criterion of truthfulness seems interesting: it is a feeling of pleasure, the shortest way to analyze the biological relevance of sensations, confirming the correctness of reflection of the vital properties of a thing. (Dilthey, 1924, pp. 84–85) But long before Dilthey it was John Locke who defined pleasure and pain as the basic regulators of mental life: “I can produce in myself both pleasure and pain, which is one great concernment of my present state. This is certain: the confidence that our faculties do not herein deceive us, is the greatest assurance we are capable of concerning the existence of material beings” (Locke, 1894).

Accepting this point of view, it can be said that the sensory images that arise in a normal, healthy body are, in principle, true. A mistake of feeling is a system dysfunction, a disease in which the psychics changes pathologically: for example, with the drastic loss of a sense of pain.

Sensations and perceptions reflect the order of things and reveal their properties; but they also testify to the existence of a lurking essence of things vital to the living body. The heretical thought for the theory of reflection – that sensations are signs – is periodically revived in different thinkers, from Helmholtz to Dilthey, from I.S. Narsky and A.A. Zinov’ev to modern young philosophers.

One can still make an attempt to give logical definition of truth. We take the liberty to characterize truth in a traditional way.


By nature, truth is ideal. Truth is a characteristic of knowledge, not of things. It is an ideal image, and as such it has the properties of presentation and objectivity inherent in any relation of reflection. Ideality is a generic property of consciousness in the ontological aspect; in the gnoseological aspect, such is truthfulness.

Generic property of truth is ideal presentation of the object, in both senses of the term “ideal” (Plato’s and modern), and in both meanings (Latin and Russian), of the word “presentation”. Generic formal traits of truth, therefore, are resemblance to an object, similarity to it, and ideal presentation. Species’ definitive property of truth is presentation of the order of qualia and relations,ordo et coherentia” of things and in things. A non-true image is a non-essence; but it is, nevertheless, presentation, likeness, reflection, and interaction. The materiality of the object of knowledge is determined in / by practice.

Accidental properties of truth are transported traits, necessary or contingent, external or internal, obvious and non-obvious, substantive and formal, etc.

To this logical attempt, we have to add gnoseological characteristics.

Not every relation is presentation, but every presentation which is there, is ideal in nature. “Truth” is human dimension of representation. This is the most complete and perfect, that is, a meaningful characteristic of cognition.

Measure of the depth of truth is the degree of presentation of the knowable entity revealed in cognition.

Measure of the completeness of truth is the presentation of the revealed generic characteristic of the object of knowledge.

Measure of preciseness is morphism.

Essence of truth is ideal presentation and transfer (transporting, transference) of order, i.e. following of things, properties and relations, events and actions of one beside the other and one after another; deepening congruent similarity of knowledge to the essence of things.

Truth combines process and performance (result) with an emphasis on relatively complete knowledge, namely, sustainable presentation. Subjectively experienced, truth is a feeling of pleasure from the discovered, open, perceived, and appropriated order.

Deviations from truth have different reasons and therefore must receive separate characteristics. Some of the attributes of truth mentioned here apply to non-truth; others do not apply. But in the main, non-truth is not an attribute of the ideal. Consciousness is in general a true image, and this is not a truism.

Absolutely true knowledge is the knowledge of essence. Understanding of absolute truth as exhaustive completeness and content completion, and yet as an extremely precise knowledge which coincides with the object in its entirety, is rather sophisticated, but not scientific. I think it came to us as a legacy of religious world-picture, wh ere the central explanatory abstraction, “the first championship of perfection” was the “Biggest”, i.e., God. (It has, of course, cognitive and historical and cultural value, — but not logical).

Relatively true knowledge is knowledge of large meaningful content; it is a particular judgment about holistic picture fragment, and it can also be understood geometrically, as all that is non-absolute – namely, in the range from 0 to 1, except these boundary numbers.

The concreteness of truth is caused not only by the dependence on the conditions of existence of this knowledge, but, first of all, by the dependence on the independent existence of objects. This is what its disposition and reference mean; more precisely, this is what makes the existing opinion about truth as a relation, possible. However, in general, consciousness is exactly such a dependent side of the disposition, that is, it is objectified, generated by independently existing objects. Otherwise, by not independently existing, but created by people; in this case it does not matter much.

Finally, it is necessary to specifically emphasize the power of mathematical signification, which is able to end disputes for a long period with the help of its recognized and real rigor. Here we propose a method of approaching (absolute) truth, suitable for any field of activity and having the socio-humanitarian meaning of gnoseological and especially epistemological optimism, which affirms the reality of the existence of (absolute) truth and the possibility of its achievement.


What is truth? There is ancient irony in the question; as if thousands of years we’ve been asking: Does there exist such thing as Absolute Truth (which I doubt since I put the question), whereas I’m (absolutely) sure in existence of such a thing as Relative Truth – since it is evident?

Realistically speaking, truth is an abstract image, isolating one characteristics of right (adequate) knowledge: to be “pünktlich”, it is accurate, precise reflection of an object of cognition. This accurate knowledge is a result of intellectual work, striving to harmonize the ideal reflection and its referent, to adjust the gnoseological image to the original outer thing or quality or relation. So it is right to speak of true (or false) knowledge, coinciding and “agreeing” and coordinating and corresponding and conjoining and becoming congruent and uniting with its target object.

Which unity we traditionally call Truth in the great and primordeal meaning of a word.

Now we’ve come up to the “number of truth”, or the method of finding it with mathematical means. The method of quantitative description of truth is harmonic series. Any path (and a method is a path) can be represented as a geometric place of points. We use special literature here (Vygodsky, 1977).

To obtain the “number of truth” we should make use of mathematical theory of rows, or series, of numbers, U1, U2, U3,… Un,… They are summed up as follows:

S1 = U1

S2 = U1+U2

S3 = U1+U2+U3

Sn = U1+U2+U3+… Un

If the series is unlimited by some finite number, it has got no definite general sum Sn. Then the row is divergent, or dispersing, like in 1 + 2 + 3 + 4 + … + n +…

Here S1 = 1, S2 = 3, S3 = 6, … Sn = n(n+1)/2, …

If Sn is a limited finite number, the series is concentrating, or meeting; e.g.,

1 + 1/2 + 1/4 + 1/8 + … + (1/2)n+1 + … – is not dispersing, but meeting and concentrating on one certain number:

S1 = 1, S2 = 11/2, S3 = 13/4, … Sn = 2·(1/2)n-1, … here limSn = 2 (by n → ∞); it might be reckoned as a target or rather Aristotelian “telos” of the whole series.

If the series has no lim it at all it is called indefinite: e.g.,

1 – 1 + 1 – 1… + (–1)n+1 + …

The utmost judgment runs as follows.

The series in which the general member Un → 0 can both disperse and meet (concentrate):

S2 = 1 + 1/2 = 3·1/2,

S4 = S2 + (1/3 + 1/4) > 1/2 + (1/4 + 1/4) = 4·1/2,

S8 = S4 + (1/5 + 1/6 + 1/7 +1/8) >1/2 + (1/8 +1/8 +1/8 +1/8 ) = 5·1/2,

S16 = S8 + (1/9 + 1/10 + … + 1/16) > 6·1/2 etc.

S1 = 1, S2 = 1/2, S3 = 5/6, S4 = 7/12, S5 = 47/60, S6 = 37/60…

Every even number S2, S4, S6... moves right and every odd number S1, S3, S5... moves left, and in the end they meet in the certain S-point. Bingo. The goal. The absolute true knowledge about concrete object found. The prosaic symbol S (0.693 ...) here is a sign for truth, a cognitive goal, the achievement of which, as mathematics testifies, is quite possible.

We should remember though, that point S2n and point S2n+1 infinitely come close together: S2n+1 S2n = 1/2n+1 → 0 by n → ∞. The process of cognition is really endless. But the model itself of seeking and finding the target-object seems valid. Number 0,693 is a guarant of the real possibility of finding the point; so, you seek – and you will find.

Such is the model of knowledge of truth, the construction of which was possible with the help of mathematical signification. And this can be presented as PHILOSOPHICAL TRUTH IN MATHEMATICAL TERMS.


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1 After Plato, Aristotle expresses two main semiotic ideas: language is a semiotic system; word and sentence are signs.