1. INTRODUCTION TO
    FORMS OF IDEAS MANAGEMENT
    (ABSTRACT CONCEPTS).
    TYPES OF LOGICAL CONCLUSION.

1.1.It is traditionally believed that the discovery of a new pattern is an example of inductive (heuristic) thinking, largely due to intuition.

With the development of such sciences as philosophy, logic, cognitive psychology, the psychology of creativity, as well as the study of various teaching methods and the operation of artificial neural networks, it became possible to better understand the forms of thought processes at various stages of creativity.

(Reference: Cognitive science, cognitive science (lat. cognitio "knowledge") is an interdisciplinary scientific direction that combines the theory of knowledge, cognitive psychology, neurophysiology, cognitive linguistics, non-verbal communication and the theory of artificial intelligence. Refers to transdisciplinary research, interdisciplinary science , cognitive science).

At various stages of solving a problem, methods can be used, which are various forms of managing methods of cognition, logical conclusions, ideas (abstract concepts).

3.2. Deduction, Deductive logic (deduction is a type of logical inference - from the general to the particular, where consequences are deduced from accepted hypotheses ('something' must be));

The doctrine of how to acquire reliable knowledge was systematized by Aristotle (384-322 BC) in the form of the science of knowledge, deductive logic or "Classical Logic".

Aristotle owns the doctrine of scientific proof, set forth in his work "Organon" - a universal instrument of true knowledge.

Deduction (derived from the Latin word: deductio - conclusion).

Deduction is a logical and methodological procedure by which the transition from GENERAL to PARTICULAR is carried out in the process of reasoning. (Rational form of thinking).

A logically correct conclusion from already existing knowledge or from already existing thoughts) in the process of reasoning - from the accepted hypothesis the Consequence is deduced: “SOMETHING” must be. The general underdevelopment of the experimental sciences (empirical knowledge) of that time prevented us from recognizing such a method of knowledge as incomplete induction as the main one. Usually, it is believed that Aristotle recognized only complete induction, and underestimated the incomplete one. (See Fig. 1.)

Deduction is a logically correct conclusion from already existing knowledge or from already existing thoughts, which is often used in standard education and activities little related to creativity.
(For example, the executor works according to unambiguously specified: in education - training programs; in production - technological maps; in administrative and bureaucratic activities - a system of legislative acts and official instructions; in paramilitary structures - service regulations, instructions, orders; ...).

      Figure 1. Fresco by Raphael Santi "The School of Athens".
                  The central figures are:
                  Plato pointing to the sky and Aristotle pointing to the earth.

1.3. Induction ,
JOHN FREDERICK WILLIAM HERSHEL ON INDUCTION (1792–1871) ,
Mill's Methods Of Induction (1806–1873) ,

Induction - targeting, suggestive, prompting, this is a type of logical inference - from the particular to the general, empirical testing of hypotheses or consideration of hypotheses and measuring the degree of their agreement with the facts ('something' really exists, probabilistic logic, confirmation logic).

      The first person to note the important role of empirical knowledge of the surrounding world and gave reasoned criticism to the speculative philosophical methods and theories of his time, was an English philosopher and natural scientist, a Franciscan monk (since 1257), professor of theology at Oxford - Roger Bacon (1214-1292).
      His work "Opus majus" (1268) expresses the idea of the uselessness of abstract dialectic, the need to study nature through observation using mathematical calculations.

     Roger Bacon distinguished two types of experience (empiricism):
      a) Real, life experience, which can only be acquired in the process life;
      b) Experience is evidence obtained through the external senses. It concerns only material objects.
     But, Roger Bacon argued, there is also spiritual experience, which can only be known by select people through a mystical state, through inner illumination. This idea anticipated the emergence of ideas about heuristic illumination and the role of intuition in science.

Figure 2. Roger Bacon in a portrait by Ernest Borda in his observatory
at Merton College, Oxford, and, a statue of Roger Bacon in Oxford.

Further, the inductive method of knowledge, inductive logic (Francis Bacon's Method) - was introduced by the English philosopher, historian, publicist, statesman, founder of empiricism and English materialism Francis Bacon (1561-1626), in his essay "The Great Instauration" and "New Organon" (1620).

Dissatisfied with the state of the sciences of his time, Bacon attempted to update the way of studying nature, which would not only make the existing sciences and arts more reliable, but also made it possible to discover new ones, still unknown to mankind.

He contrasted the dogmatic deduction of the scholastics with the inductive method based on a rational analysis of experimental data.

"The New Organon" became the second part of the extensive work "The Great Restoration of Sciences", which, according to Bacon's idea, should consist of six parts. However, the author has finished only the first two parts.

Figure 3. Francis Bacon in a portrait by John Vanderbank and a statue to Francis Bacon at the US Library of Congress..

Subsequently, a huge contribution to the development of inductive methods was made by such scientists as (See Fig. 4):
John Herschel, John Stuart Mill, William Whewell, Augustus de Morgan, William Stanley Jevons, Pierre-Simon de Laplace.

Figure 4. From left to right:
JOHN FREDERICK WILLIAM HERSHEL (1792-1871), JOHN STUART MILL (1806-1873), William Whewell (1794-1866),
Augustus de Morgan (1806-1871), William Stanley Jevons (1835-1882) , Pierre-Simon de Laplace (1749-1827).

Induction (from Latin inductio - prompting (targeting)) is a term widely used in science.

Induction is a logical inference that assumes that a major premise follows between two separate facts, the minor premise and the conclusion.

Since a rule is an axiom or general principle, induction is the inference of the existence of a general principle between two separate facts.

It is usually unclear whether a general principle obtained by induction is true.

To confirm its correctness, tests from a variety of angles are necessary of vision.

The essence of inductive analysis of facts boils down to the fact that through the study of various kinds of RELATIONSHIPS phenomena ("Processes") in a real-life or thought experiment, to discover their true causal relationships and dependencies on each other.

The main task of the science of nature (similarly - technical or non-technical system) is to study the causal relationship of phenomena ("Processes"), and not just their material composition - the number and properties (parameters) of "Objects".

In inductive logic, the task is to find general forms of phenomena ("Processes"), and not their specific differences.

In this teaching, Francis Bacon adheres to the philosophy of Aristotle and by the forms of phenomena ("Processes"), he means those general laws or typical relations of phenomena, to the discovery of which all experimental science strives.

The inductive method is used when there are no GENERAL algorithmic solutions.

The inductive method is a method of research and presentation, in which from the observed PARTICULAR facts one proceeds to the allocation of principles, GENERAL provisions of the theory, the establishment of regularities.

Induction is a type of GENERALIZATION associated with anticipating the results of observations and experiments based on experience data (PARTICULAR data).

In induction, the data of experience (PARTICULAR data) "suggest" the GENERAL, therefore inductive GENERALIZATIONS are usually considered as experimental truths or empirical laws.

Induction is a term widely used in science. Induction - (introduction, targeting, from particular to general, empirical testing of hypotheses put forward or consideration of hypotheses and measuring the degree of their agreement with the facts. “SOMETHING” really exists, probabilistic logic is used, confirmation logic is used.

      The inductive method is used when there are no GENERAL algorithmic solutions.
      The inductive method is a method of research and presentation, in which one moves from the observed SPECIAL facts to the selection of principles, GENERAL provisions of the theory, the establishment of patterns.
      Induction is a conclusion from facts to some hypothesis (general statement, patterns).
      Inductive conclusions are built on the basis of experimental data. Depending on the completeness and completeness of the experience underlying the generalizations, a distinction is made between complete and incomplete induction.

      Full induction - when the generalization refers to a finitely visible field of facts.
      The conclusion of the full induction gives certain knowledge.
      In full induction the conclusion is connected with necessity, not with some probability, and follows from premises.
      Thus, this "full induction" is a kind of deductive reasoning, although in its external form, in the course of thought it resembles incomplete induction.
      Incomplete induction - when the generalization refers to an infinitely or finitely - boundless field of facts.
      The conclusion of incomplete induction gives probabilistic knowledge.

      Incomplete induction - the incompleteness of the inductive generalization is expressed in the fact that not all, but only some elements, or parts of the class are examined.
      In inductive logic, the task is to find general forms of phenomena ("Processes"), and not their specific differences.
      The probability of a conclusion in a given scheme, therefore, can range from very small to almost complete certainty.
      Due to this fact, in incomplete inductive logic, special methods for estimating the probability of conclusions are developed.

      General knowledge, in comparison with the totality of disparate knowledge about individual objects of a class, is valuable in that it can suggest that there is some connection between the objects of the class and the attribute, and thus stimulate further knowledge.

      Incomplete induction is divided into two types:
      a) Incomplete "popular" induction enumerative (through enumeration of similar cases) , (induction by simply listing similar cases, generalization is carried out on an insignificant basis), in the absence of a contradictory case, is not reliable, so the greater the number of premises, the higher the probability of the conclusion.
      Popular induction is the first step in the development of scientific knowledge. Science begins with empirical research, classification, identification of stable connections, relationships and dependencies.
      The first generalizations in science are due to the simplest inductive conclusions through a simple enumeration of recurring features.
      They perform an important heuristic function of initial assumptions, conjectures and hypothetical explanations that need further verification and clarification.
      In conditions where only some representatives of the class are studied, the possibility of a hasty generalization is not ruled out.
      Erroneous conclusions in the conclusions of popular induction may appear due to non-compliance with the requirements for accounting for contradictory cases, which make the generalization untenable.
      Of the many phenomena, he fixes only those that turn out to be predominant in experience, and builds a hasty generalization on their basis.

      b) Scientific induction (incomplete) (the transition to general knowledge is made on the basis of identifying the necessary features (generalization is carried out on an essential basis) and the necessary connections between objects and phenomena of nature and society).

      The probability of conclusions of scientific induction depends not so much on the number of subjects considered, but on the correctness of the principles of selection, on how accurately the factors influencing the presence and change of the trait under study are taken into account, how scientific the induction is:

      Scientific induction is characterized by the search for causal relationships between phenomena and the desire to discover the essential features of objects that are combined into a class.
      Scientific induction is called inference, in which a generalization is built by selecting the necessary and eliminating random circumstances.

      Scientific induction (incomplete) is divided into:

      * Incomplete scientific induction "selective" - (induction on a representative sample) (from the Latin - "I choose") - in it, the conclusion about the attribute belonging to a class of objects is based on the study of samples methodically selected from different parts of this class (subset).
      This is a special kind of enumerative incomplete induction, which is induction through the selection of facts that exclude random generalization.

      * Incomplete scientific induction "through the study of a single representative of a certain class" - (eliminative induction on a typical representative) (from Latin - exclude) - typical representatives are selected for premises, thus items that are fundamentally different from one another.
      Elimination induction, or Eliminative induction (exclusion of different cases) is a system of inferences in which conclusions about the causes of the phenomena under study are built by detecting supporting circumstances and excluding circumstances that do not satisfy the properties of a causal connection.
      This is a conclusion about the belonging of a feature to a class of objects, based on the study of typical samples without taking into account their individual characteristics.
      It is built not only on the basis of the study of a number of phenomena or objects included in a certain class, but also on the basis of the study of a single representative of the specified class.
      In this case, when reasoning about the belonging or absence of a certain feature of an object, its individual properties that distinguish it from other objects of the same class should not be used.
      The cognitive role of eliminative induction is the analysis of causal relationships.
      Causal is such a connection between two phenomena, when one of them - the cause - precedes and causes the other - the action.
      Modern logic describes five methods for establishing causal relationships:
      (1) similarity method,
      (2) difference method,
      (3) combined method of similarity and difference,
      (4) concomitant change method,
      (5) residual method.

      The method of mathematical induction and transfinite induction uses complete induction for infinite countable and uncountable sets of objects, respectively.

The core of mathematical induction is: dispersion , correlation , regression and variational analysis.

      From a formal point of view, the essence of the method of mathematical induction is to get rid of the words "and so on ad infinitum."
      Deduction often includes the so-called mathematical induction, which is widely used in mathematics.
      The conclusion of mathematical induction is composed of two premises and a conclusion.
      The first of the premises says that the property under consideration is inherent in the first object of the series under consideration.
      The second premise states that if an arbitrary object of a given series has this property, then the object immediately following it also has it.
      The conclusion states that the property is inherent in each item in the series.

Figure 5. Scheme of the classical representation of the connection between theory, empiricism, induction and deduction. (When refuting inductive conclusions, the researcher returns again to empiricism, to experiments.).

Table 1. Human activity that activates creative, imaginative (eidetic) and inductive thinking.

Human activity that activates creative, imaginative (eidetic) thinking.

1.4. Adduction - FUTURE LOGIC (bringing, attracting, attaching, attachment, this is a type of logical inference - when deduction is attached (joined) to induction when deduction is attached (connected) to induction);

Inference based on incomplete INDUCTION leads to PROBABILISTIC CONCLUSION.
And inference based on full INDUCTION leads to DEDUCTION (forms a pattern), and unambiguously determines the algorithms.

1.5. Traductive reasoning, (moving, analogia (other-Greek. analogia - correspondence, similarity)), this is a type of logical inference - from the singular to the singular, from the particular to the particular, from the general to the general. Traductive reasoning is an analogy. ('Something' should be like some kind of analog)).

      According to the nature of the premises and the conclusion, traduction can be of three types:
      • Conclusion from single to single;
      • Conclusion from particular to particular;
      • Conclusion from general to general.

1.6. Abduction, Abductive reasoning, (syllogism, a kind of reductive inference, withdrawal, a class of plausible reasoning, search and justification, explanatory hypotheses or the study of facts and the construction of a hypothesis explaining them (assumes that 'something' can be));

      In the history of logic, the idea of abduction in the form of apagogy (proof by contradiction, reduction to absurdity, detection of contradiction) goes back to Aristotle.
      In modern times, abduction was first considered by the founder of pragmatism and semiotics Charles Sanders Peirce (1839 - 1914) , who has been using the term systematically since 1901.
      The term "abduction" was used by Bateson to refer to the third scientific methodology (along with induction and deduction) Gregory Bateson (1904 - 1980). He calls this type of thinking "roundabout", lateral. This is when we think about one thing by thinking about something else, such as through stories, poetry, and similar thought concepts.
      Abduction has a wide field of scientific and applied use, including in artificial intelligence systems.
Georgy Ivanovich Ruzavin (1922–2012) — Soviet specialist in the logic of philosophy and methodology of science, Doctor of Philosophy, professor, academician, writes:
… abduction is used to discover empirical laws that establish the necessary regular connections between observed properties and the relationships of phenomena. …

     Abduction is a widely used inferential process in everyday reasoning.
     It consists of finding explanations for observed facts.
      Abduction is a form of non-monotonic inference, since the explanations found can be cancelled out during the inference process.
      In fact, explanations that are consistent with one state of the knowledge base may not be consistent with it after new knowledge is added.
      The existence of different explanations for the same effect is the main feature of abductive inference, and choosing the most "preferred" of them is an important task.

      Promising areas of application of abduction are:

      • Diagnostics. For example, in medical diagnosis, candidates for abductive explanations are possible diseases, and observations are symptoms of diseases.
In fault diagnosis, a set of clauses describes the normal behavior of a system, and the task is to find a set of explanations of the form "some component A is not OK" that explains why the system does not function normally.
      • Graphic object recognition. In this case, explanations are objects of recognition, and observations are descriptions of the image in the visual field.
      • Natural language processing. Abduction can be used in natural language processing to interpret ambiguous sentences.
Here, abductive explanations are different ways of understanding such sentences.
      • Planning. In planning problems, planned actions can be interpreted as explanations of the target state that must be achieved.
      • Knowledge acquisition. Knowledge acquisition can occur as an addition to the knowledge base not of the data itself entering the system, but of its abductive explanations.

1. INTRODUCTION TO FORMS OF IDEAS MANAGEMENT (ABSTRACT CONCEPTS). TYPES OF LOGICAL CONCLUSION.

1. INTRODUCTION TO
FORMS OF IDEAS MANAGEMENT
(ABSTRACT CONCEPTS).
TYPES OF LOGICAL CONCLUSION.