Analysis and synthesis, induction and deduction

2. INDUCTION AND DEDUCTION METHODS

Rational judgments are traditionally divided into deductive and inductive. The question of the use of induction and deduction as methods of cognition has been discussed throughout the history of philosophy. Unlike analysis and synthesis, these methods were often opposed to each other and considered in isolation from each other and from other means of cognition.

In the broad sense of the word, induction is a form of thinking that develops general judgments about single objects; it is a way of moving thought from the particular to the general, from less universal knowledge to more universal knowledge (the path of knowledge "from the bottom up").

Observing and studying individual objects, facts, events, a person comes to the knowledge of general patterns. No human knowledge can do without them. The immediate basis of inductive reasoning is the repetition of features in a number of objects of a certain class. A conclusion by induction is a conclusion about the general properties of all objects belonging to a given class, based on the observation of a fairly wide set of single facts. Usually inductive generalizations are considered as empirical truths, or empirical laws. Induction is an inference in which the conclusion does not follow logically from the premises, and the truth of the premises does not guarantee the truth of the conclusion. From true premises, induction produces a probabilistic conclusion. Induction is characteristic of the experimental sciences, it makes it possible to construct hypotheses, does not provide reliable knowledge, and suggests an idea.

Speaking of induction, one usually distinguishes between induction as a method of experimental (scientific) knowledge and induction as a conclusion, as a specific type of reasoning. As a method of scientific knowledge, induction is the formulation of a logical conclusion by summarizing the data of observation and experiment. From the point of view of cognitive tasks, induction is also distinguished as a method of discovering new knowledge and induction as a method of substantiating hypotheses and theories.

Induction plays an important role in empirical (experimental) cognition. Here she is performing:

one of the methods for the formation of empirical concepts;

the basis for the construction of natural classifications;

One of the methods for discovering causal patterns and hypotheses;

One of the methods of confirmation and substantiation of empirical laws.

Induction is widely used in science. With its help, all the most important natural classifications in botany, zoology, geography, astronomy, etc. were built. The laws of planetary motion discovered by Johannes Kepler were obtained by induction on the basis of Tycho Brahe's analysis of astronomical observations. In turn, the Keplerian laws served as an inductive basis in the creation of Newtonian mechanics (which later became a model for the use of deduction). There are several types of induction:

1. Enumerative or general induction.

2. Eliminative induction (from the Latin eliminatio - exclusion, removal), which contains various schemes for establishing cause-and-effect relationships.

3. Induction as reverse deduction (movement of thought from consequences to foundations).

General induction is an induction in which one moves from knowledge about several subjects to knowledge about their totality. This is a typical induction. It is general induction that gives us general knowledge. General induction can be represented by two types of complete and incomplete induction. Complete induction builds a general conclusion based on the study of all objects or phenomena of a given class. As a result of complete induction, the resulting conclusion has the character of a reliable conclusion.

In practice, it is more often necessary to use incomplete induction, the essence of which is that it builds a general conclusion based on the observation of a limited number of facts, if among the latter there are none that contradict inductive reasoning. Therefore, it is natural that the truth obtained in this way is incomplete; here we obtain probabilistic knowledge that requires additional confirmation.

The inductive method was already studied and applied by the ancient Greeks, in particular Socrates, Plato and Aristotle. But a special interest in the problems of induction manifested itself in the 17th-18th centuries. with the development of new science. The English philosopher Francis Bacon, criticizing scholastic logic, considered induction based on observation and experiment to be the main method of knowing the truth. With the help of such induction, Bacon was going to look for the cause of the properties of things. Logic should become the logic of inventions and discoveries, Bacon believed, the Aristotelian logic set forth in the work "Organon" does not cope with this task. Therefore, Bacon wrote the New Organon, which was supposed to replace the old logic. Another English philosopher, economist and logician John Stuart Mill extolled induction. He can be considered the founder of classical inductive logic. In his logic, Mill gave a great place to the development of methods for studying causal relationships.

In the course of experiments, material is accumulated for the analysis of objects, the selection of some of their properties and characteristics; the scientist draws conclusions, preparing the basis for scientific hypotheses, axioms. That is, there is a movement of thought from the particular to the general, which is called induction. The line of knowledge, according to supporters of inductive logic, is built as follows: experience - inductive method - generalization and conclusions (knowledge), their verification in the experiment.

The principle of induction states that the universal propositions of science are based on inductive inferences. This principle is invoked when it is said that the truth of a statement is known from experience. In the modern methodology of science, it is realized that it is generally impossible to establish the truth of a universal generalizing judgment with empirical data. No matter how much a law is tested by empirical data, there is no guarantee that new observations will not appear that will contradict it.

Unlike inductive reasoning, which only suggests a thought, through deductive reasoning, one deduces a thought from other thoughts. The process of logical inference, as a result of which the transition from premises to consequences is carried out based on the application of the rules of logic, is called deduction. There are deductive inferences: conditionally categorical, dividing-categorical, dilemmas, conditional inferences, etc.

Deduction is a method of scientific knowledge, which consists in the transition from certain general premises to particular results-consequences. Deduction derives general theorems, special conclusions from the experimental sciences. Gives certain knowledge if the premise is correct. The deductive method of research is as follows: in order to obtain new knowledge about an object or a group of homogeneous objects, it is necessary, firstly, to find the nearest genus, which includes these objects, and, secondly, to apply to them the appropriate law inherent in to the whole given kind of objects; transition from knowledge of more general provisions to knowledge of less general provisions.

In general, deduction as a method of cognition proceeds from already known laws and principles. Therefore, the method of deduction does not allow obtaining meaningful new knowledge. Deduction is only a method of logical deployment of a system of provisions based on initial knowledge, a method of identifying the specific content of generally accepted premises.

Aristotle understood deduction as evidence using syllogisms. Deduction was praised by the great French scientist René Descartes. He contrasted it with intuition. In his opinion, intuition directly sees the truth, and with the help of deduction, the truth is comprehended indirectly, i.e. through reasoning. A clear intuition and the necessary deduction is the way to know the truth, according to Descartes. He also deeply developed the deductive-mathematical method in the study of natural sciences. For a rational method of research, Descartes formulated four basic rules, the so-called. "rules for the guidance of the mind":

1. That which is clear and distinct is true.

2. The complex must be divided into private, simple problems.

3. Go to the unknown and unproven from the known and proven.

4. Conduct logical reasoning consistently, without gaps.

The method of reasoning based on the conclusion (deduction) of consequences-conclusions from hypotheses is called the hypothetical-deductive method. Since there is no logic of scientific discovery, no methods that guarantee the receipt of true scientific knowledge, scientific statements are hypotheses, i.e. are scientific assumptions or assumptions whose truth value is uncertain. This provision forms the basis of the hypothetical-deductive model of scientific knowledge. In accordance with this model, the scientist puts forward a hypothetical generalization, various kinds of consequences are deduced from it, which are then compared with empirical data. The rapid development of the hypothetical-deductive method began in the 17th-18th centuries. This method has been successfully applied in mechanics. The studies of Galileo Galilei and especially Isaac Newton turned mechanics into a coherent hypothetical-deductive system, thanks to which mechanics became a model of science for a long time, and for a long time they tried to transfer mechanistic views to other natural phenomena.

The deductive method plays a huge role in mathematics. It is known that all provable propositions, that is, theorems, are deduced in a logical way using deduction from a small finite number of initial principles provable within the framework of a given system, called axioms.

But time has shown that the hypothetical-deductive method was not omnipotent. In scientific research, one of the most difficult tasks is the discovery of new phenomena, laws and the formulation of hypotheses. Here the hypothetical-deductive method rather plays the role of a controller, checking the consequences arising from hypotheses.

In the modern era, extreme points of view on the meaning of induction and deduction began to be overcome. Galileo, Newton, Leibniz, while recognizing experience and, therefore, induction as a major role in cognition, noted at the same time that the process of moving from facts to laws is not a purely logical process, but includes intuition. They assigned an important role to deduction in the construction and testing of scientific theories and noted that in scientific knowledge an important place is occupied by a hypothesis that cannot be reduced to induction and deduction. However, it was not possible to completely overcome the opposition between inductive and deductive methods of cognition for a long time.

In modern scientific knowledge, induction and deduction are always intertwined with each other. Real scientific research takes place in the alternation of inductive and deductive methods. The opposition of induction and deduction as methods of cognition loses its meaning, since they are not considered as the only methods. In cognition, other methods play an important role, as well as techniques, principles, and forms (abstraction, idealization, problem, hypothesis, etc.). For example, probabilistic methods play a huge role in modern inductive logic. Estimating the probability of generalizations, searching for criteria for substantiating hypotheses, the establishment of complete reliability of which is often impossible, requires increasingly sophisticated research methods.

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Moscow State Technical University

named after N. E. Bauman

Faculty of Engineering Technologies

Homework

on the course "Methodology of scientific knowledge"

Deduction as a method of science and its functions

Completed by a student

groups MT 4-17

Guskova E.A.

Checked by: Gubanov N.N.

Moscow, 2016

Introduction
1.
2. Deductive method of R. Descartes
3. Verification in modern science
4. Abduction method
List of used literature

Introduction

Among the general logical methods of cognition, the most common are deductive and inductive methods. It is known that deduction and induction are the most important types of inferences that play a huge role in the process of obtaining new knowledge based on derivation from previously acquired ones.

Deduction (from lat. deductio - inference) is a transition in the process of cognition from general knowledge about a certain class of objects and phenomena to knowledge of a particular and individual one. In deduction, general knowledge serves as the starting point of reasoning, and this general knowledge is assumed to be "ready", existing. Note that deduction can also be carried out from the particular to the particular or from the general to the general. The peculiarity of deduction as a method of cognition is that the truth of its premises guarantees the truth of the conclusion. Therefore, deduction has a great power of persuasion and is widely used not only to prove theorems in mathematics, but also wherever reliable knowledge is needed.

Induction (from Latin inductio - guidance) is a transition in the process of cognition from private knowledge to general; from knowledge of a lesser degree of generality to knowledge of a greater degree of generality. In other words, it is a method of research, knowledge, associated with the generalization of the results of observations and experiments. The main function of induction in the process of cognition is to obtain general judgments, which can be empirical and theoretical laws, hypotheses, and generalizations. Induction reveals the "mechanism" of the emergence of general knowledge. A feature of induction is its probabilistic nature, i.e. given the truth of the initial premises, the conclusion of the induction is only probably true, and in the final result it may turn out to be both true and false. Thus, induction does not guarantee the achievement of truth, but only "leads" to it, i.e. helps to find the truth.

In the process of scientific knowledge, deduction and induction are not used in isolation, apart from each other. One is impossible without the other.

1. The birth of the deductive method

The foundations of deductive logic were laid down in the works of ancient Greek philosophers and mathematicians. Here you can name such names as the names of Pythagoras and Plato, Aristotle and Euclid. It is believed that Pythagoras was one of the first to reason in the style of proving this or that statement, and not simply proclaiming it. In the works of Parmenides, Plato and Aristotle, there were ideas about the basic laws of correct thinking. The ancient Greek philosopher Parmenides for the first time expressed the idea that at the basis of truly scientific thinking lies some kind of unchanging principle ("single"), which continues to remain unchanged, no matter how the thinker's point of view changes. Plato compares the one with the light of thought, which continues to remain unchanged as long as there is thought itself. In a more rigorous and concrete form, this idea is expressed in the formulation of the basic laws of logic by Aristotle. In the works of Euclid, the application of these techniques and laws to the mathematical sciences reaches the highest level, which becomes the ideal of deductive thinking for centuries and millennia in European culture. Later, the formulations of deductive logic were more and more refined and detailed in the Stoics, in medieval scholasticism.

Aristotle is rightfully considered the founder of logic as a deductive science. For the first time, he systematizes the basic methods of correct thinking, summarizing the achievements of contemporary ancient Greek mathematicians. The logic set forth in the Organon was seen both as an instrument for reaching truth through right thinking and as a science preparing the ground for various other sciences.

According to Aristotle, true knowledge can be obtained through logical proof. Considering the inductive method, in which one moves from the particular to the general, Aristotle concluded that such a method is imperfect, believing that the deductive method, in which the particular is derived from the general, provides more reliable knowledge. The fundamental tool of this method is the syllogism. The following is a typical example of a syllogism:

All people are mortal (big premise).

Socrates is a man (minor premise).

So Socrates is mortal (conclusion).

Aristotle believed that the main discoveries in geometry had already been made. It is time to transfer its methods to other sciences: physics and zoology, botany and politics. But the most important tool of geometry is the logical method of reasoning, which leads to correct conclusions from any correct premises. This method Aristotle outlined in the book "Organon"; now it is called the beginning of mathematical logic. However, logic alone is not enough to justify physical science; experiments, measurements and calculations are needed, like those carried out by Anaxagoras. Aristotle did not like to experiment. He preferred to guess the truth intuitively - and as a result, he was often mistaken, and there was no one to correct him. Therefore, Greek physics consisted mainly of hypotheses: sometimes brilliant, but sometimes grossly erroneous. There were no proven theorems in this science.

In the Middle Ages, Aristotle's logic attracted much attention as a tool for deductively proving theological and philosophical propositions. The syllogism of Aristotle remained in force for about two thousand years, having undergone almost no changes during this time.

Thomas Aquinas, combining Christian dogmas with the deductive method of Aristotle, formulating five proofs of the existence of God on the basis of the deductive method.

1. Proof One: Prime Mover

Proof by motion means that any moving object was once set in motion by some other object, which in turn was set in motion by a third, and so on. Thus, a sequence of "engines" is built, which cannot be infinite. In the end, we will always find an "engine" that drives everything else, but is itself not driven by something else and is motionless. It is God who turns out to be the root cause of all movement.

2. Proof Two: The First Cause

Proof through a producing cause. The proof is similar to the previous one. Only in this case is not the cause of the movement, but the cause that produces something. Since nothing can produce itself, there is something that is the root cause of everything - this is God.

3. Proof Three: Necessity

Every thing has the possibility of both its potential and real existence. If we assume that all things are in potentiality, then nothing would come into being. There must be something that contributed to the transfer of the thing from the potential to the actual state. That something is God.

4. Fourth Proof: The Highest Degree of Being

Proof from the degrees of being - the fourth proof says that people talk about different degrees of perfection of an object only through comparisons with the most perfect. This means that there is the most beautiful, the noblest, the best - that is God.

5. Proof Five: The Goal Setter

Evidence through target reason. In the world of rational and non-rational beings, the expediency of activity is observed, which means that there is a rational being that sets a goal for everything. For nothing known to us appears to be intentionally created unless it is created. Accordingly, there is a creator, and his name is God.

The deductive method is always present in the concepts of mystical, religious theories. It is characterized by the presence of a concept that is not disclosed, in fact, in the necessary details, and therefore causes different ideas in different people. This is the reason why everyone understands religious ideas in their own way, everyone has their own god in their soul.

2. Ddeductiveth methodR. Decamouth

In modern times, the credit for transforming deduction belongs to René Descartes (1596-1650). He criticized medieval scholasticism for its method of deduction and considered this method not scientific, but belonging to the field of rhetoric. Descartes dreamed of linking all sciences into one whole, into a system of knowledge about the world, growing from a single principle, an axiom. Then science would turn from a collection of disparate facts and very often contradictory theories into a logically coherent and integral picture of the world. Instead of medieval deduction, he offered a precise, mathematicized way of moving from the self-evident and simple to the derivative and complex.

“By method,” writes Descartes, “I mean precise and simple rules, the strict observance of which always prevents the acceptance of the false as true—and, without unnecessary expenditure of mental strength, but gradually and continuously increasing knowledge, contributes to the fact that the mind achieves true knowledge of everything that is available to it. R. Descartes outlined his ideas about the method in his work “Discourse on the Method”, “Rules for the Guidance of the Mind”. They are given four rules.

First rule. To accept as true everything that is perceived clearly and distinctly and does not give rise to any doubt, i.e. quite self-evident. This is an indication of intuition as the initial element of knowledge and rationalistic criterion of truth. Descartes believed in the infallibility of the operation of intuition itself. Errors, in his opinion, stem from the free will of a person, capable of causing arbitrariness and confusion in thoughts, but not from the intuition of the mind. The latter is free from any kind of subjectivism, because it clearly (directly) realizes what is distinct (simply) in the object itself.

Intuition is the awareness of the truths that have “surfaced” in the mind and their correlations, and in this sense it is the highest form of intellectual knowledge. It is identical to the primary truths, called innate by Descartes. As a criterion of truth, intuition is a state of mental self-evidence. From these self-evident truths the process of deduction begins.

Second rule. Divide every complex thing into simpler components that are not amenable to further division by the mind into parts. In the course of division, it is desirable to reach the most simple, clear and self-evident things, i.e. to what is directly given by intuition. In other words, such an analysis aims to discover the initial elements of knowledge.

It should be noted here that the analysis that Descartes speaks of does not coincide with the analysis that Bacon spoke of. Bacon proposed to decompose objects of the material world into "nature" and "form", while Descartes draws attention to the division of problems into particular questions.

The second rule of Descartes' method led to two equally important results for the scientific research practice of the 18th century:

1) as a result of the analysis, the researcher has objects that are already amenable to empirical consideration;

2) the theoretical philosopher reveals the universal and therefore the simplest axioms of knowledge about reality, which can already serve as the beginning of a deductive cognitive movement.

Thus, Cartesian analysis precedes deduction as a stage preparing it, but distinct from it. The analysis here approaches the concept of "induction".

The initial axioms revealed by Descartes' analyzing induction turn out to be, in their content, not only elementary intuitions that were previously unconscious, but also the desired, extremely general characteristics of things that in elementary intuitions are "accomplices" of knowledge, but have not yet been singled out in their pure form.

Third rule. In cognition, thought should go from the simplest, i.e. elementary and most accessible things for us to things more complex and, accordingly, difficult to understand. Here deduction is expressed in the derivation of general propositions from others and the construction of some things from others.

The discovery of truths corresponds to deduction, which then operates with them to derive the truths of derivatives, and the identification of elementary things serves as the beginning of the subsequent construction of complex things, and the found truth goes on to the truth of the next still unknown one. Therefore, the actual mental deduction of Descartes acquires constructive features inherent in the embryo of the so-called mathematical induction. He anticipates the latter, being here the predecessor of Leibniz.

Fourth rule. It consists in enumeration, which involves making complete enumerations, reviews, without losing anything from attention. In the most general sense, this rule focuses on achieving the completeness of knowledge. It assumes:

Firstly, the creation of the most complete classification possible;

Secondly, approaching the maximum completeness of consideration leads reliability (persuasiveness) to evidence, i.e. induction - to deduction and further to intuition. It is now recognized that complete induction is a special case of deduction;

Thirdly, enumeration is a requirement for completeness, i.e. accuracy and correctness of the deduction itself. Deductive reasoning breaks down if it jumps over intermediate propositions that still need to be deduced or proven.

In general, according to the plan of Descartes, his method was deductive, and both his general architectonics and the content of individual rules were subordinated to this direction. It should also be noted that the presence of induction is hidden in Descartes' deduction.

In the science of modern times, Descartes was a propagandist of the deductive method of cognition because he was inspired by his achievements in the field of mathematics. Indeed, in mathematics the deductive method is of particular importance. It can even be said that mathematics is the only properly deductive science. But the acquisition of new knowledge through deduction exists in all natural sciences.

deduction aristotle logic

3. Hypothetical-deductive method

Currently, in modern science, the hypothetical-deductive method is most often used. This is a method of reasoning based on the derivation (deduction) of conclusions from hypotheses and other premises, the true meaning of which is unknown. Therefore, the hypothetical-deductive method receives only probabilistic knowledge.

Hypothetical-deductive reasoning was analyzed in the framework of ancient dialectics. An example of this is Socrates, who in the course of his conversations set the task of convincing the opponent either to abandon his thesis, or to clarify it by deriving consequences from it that contradict the facts.

In scientific knowledge, the hypothetical-deductive method was developed in the 17th-18th centuries, when significant progress was made in the field of mechanics of terrestrial and celestial bodies. The first attempts to use this method in mechanics were made by Galileo and Newton. Newton's work "The Mathematical Principles of Natural Philosophy" can be viewed as a hypothetical-deductive system of mechanics, the premises of which are the basic laws of motion. The method of principles created by Newton had a great influence on the development of exact natural science.

From a logical point of view, the hypothetical-deductive system is a hierarchy of hypotheses, the degree of abstractness and generality of which increases as they move away from the empirical basis. At the very top are the hypotheses that have the most general character and therefore have the greatest logical force. Hypotheses of a lower level are derived from them as premises. At the lowest level of the system are hypotheses that can be compared with empirical reality.

According to the nature of the premises, all hypothetical conclusions can be divided into three groups.

first group make problematic conclusions, the premises of which are hypotheses or generalizations of empirical data. Therefore, they can also be called properly hypothetical inferences, since the truth value of their premises remains unknown.

Second group consists of inferences, the premises of which are assumptions that contradict any statements. By putting forward such an assumption, a consequence is deduced from it, which turns out to be clearly inconsistent with obvious facts or firmly established provisions. Well-known methods of such inferences are the method of reasoning from the contrary, often used in mathematical proofs, as well as the method of refutation known in ancient logic - reduction to absurdity (reductio ad absurdum).

ThirdI am a group not much different from the second, but in it the assumptions contradict any opinions and statements taken on faith. Such reasoning was widely used in ancient disputes, and they formed the basis of the Socratic method, which was discussed at the beginning of this chapter.

Hypothetical reasoning is usually resorted to when there are no other ways to establish the truth or falsity of certain generalizations, most often of an inductive nature, that can be linked into a deductive system. Traditional logic was limited to the study of the most general principles of hypothetical reasoning and almost completely ignored the logical structure of the systems used in the developed empirical sciences.

A new trend that has emerged in the modern methodology of the empirical sciences is that it considers any system of experimental knowledge as a hypothetical-deductive system. It is hardly possible to fully agree with this, because there are sciences that have not reached the necessary theoretical maturity and which are still limited to separate, unrelated generalizations or hypotheses, or even simple descriptions of the phenomena presented. In developed hypothetical-deductive systems, mathematical methods are often used.

Often in logic, hypothetical-deductive systems are considered as meaningful axiomatic systems that allow the only possible interpretation. However, such a formal analogy does not take into account the specific features of the deductive organization of experimental knowledge, which are abstracted from in the axiomatic construction of theories in mathematics. To illustrate this thesis, consider, for example, the difference between Euclid's familiar geometry as a formal mathematical system, on the one hand, and geometry as an interpreted, or physical system, on the other. It is known that before the discovery of non-Euclidean geometries, Euclidean geometry was considered the only true doctrine of the properties of the space around us, and I. Kant raised such a belief even to the rank of an a priori principle. The situation after the discovery of new geometries by Lobachevsky, Bolyai and Riemann, although gradually, but radically changed. From a purely logical and mathematical point of view, all these geometric systems are equally valid and valid, because they are consistent. But as soon as they are given a certain interpretation, they turn into some specific hypotheses, for example, physical ones. Only a physical experiment can check which of them better reflects reality, say, the physical properties and relationships of the surrounding space. From this it becomes clear that the experimental sciences, in order to systematize and organize all the material accumulated in them, tend to build interpreted systems, where concepts and judgments have a certain meaning associated with the study of a specific empirical field of objects and phenomena of the real world. In mathematical research, one abstracts from such a specific meaning and meaning of objects and builds abstract systems, which can subsequently receive a completely different interpretation. No matter how strange it may seem, but the axioms of Euclid's geometry can describe not only the properties and relationships between geometric points, lines and planes that are familiar to us, but also many relationships between various other objects, for example, relationships between color sensations. It follows from this that the difference between the axiomatic systems of pure mathematics and the hypothetical-deductive systems of applied mathematics, natural sciences and the empirical sciences in general arises at the level of interpretation. If for a mathematician a point, a straight line and a plane simply mean initial concepts that are not defined within the framework of a geometric system, then for a physicist they have a certain empirical content.

Sometimes it is possible to give an empirical interpretation of the initial concepts and axioms of the system under consideration. Then the whole theory can be considered as a system of deductively connected empirical hypotheses. However, most often it turns out to be possible to empirically interpret only some of the hypotheses obtained from the axioms as a consequence. It is this kind of hypotheses that turn out to be connected with the results of the experiment. So, for example, already Galileo in his experiments built a whole system of hypotheses in order to verify the truth of high-level hypotheses with the help of hypotheses of a lower level.

The hypothetical-deductive system can thus be viewed as a hierarchy of hypotheses, the degree of abstraction of which increases as one moves away from the empirical basis. At the very top are hypotheses, the formulation of which uses very abstract theoretical concepts. That is why they cannot be directly compared with experimental data. On the contrary, at the bottom of the hierarchical ladder are hypotheses, the connection of which with experience is quite obvious. But the less abstract and general the hypotheses are, the smaller the range of empirical phenomena they can explain. A characteristic feature of hypothetical-deductive systems lies precisely in the fact that in them the logical power of hypotheses increases with an increase in the level at which the hypothesis is found. The greater the logical force of the hypothesis, the greater the number of consequences that can be deduced from it, which means that the greater the range of phenomena it can explain.

And above what has been said, we can conclude that the hypothetical-deductive method has received the greatest application in those branches of natural science in which a developed conceptual apparatus and mathematical research methods are used. In the descriptive sciences, where isolated generalizations and hypotheses predominate, establishing a logical connection between them encounters serious difficulties: firstly, because they do not single out the most important generalizations and facts from a huge number of others, secondary ones; secondly, the main hypotheses are not separated from the derivatives; thirdly, logical relationships between separate groups of hypotheses have not been identified; fourthly, the number of hypotheses is usually large. Therefore, the efforts of researchers in such sciences are aimed not so much at unifying all existing empirical generalizations and hypotheses by establishing deductive relationships between them, but at searching for the most general fundamental hypotheses that could become the basis for building a unified system of knowledge.

A variation of the hypothetical-deductive method can be considered a mathematical hypothesis, which is used as the most important heuristic tool for discovering patterns in natural science. Usually, hypotheses here are some equations that represent a modification of previously known and verified relationships. By changing these ratios, they make up a new equation expressing a hypothesis that refers to unexplored phenomena. In the process of scientific research, the most difficult task is to discover and formulate those principles and hypotheses that serve as the basis for all further conclusions. The hypothetical-deductive method plays an auxiliary role in this process, since it does not put forward new hypotheses, but only checks the consequences arising from them, which thereby control the research process.

The axiomatic method is close to the hypothetical-deductive method. This is a method of constructing a scientific theory, in which it is based on some initial provisions (judgments) - axioms, or postulates, from which all other statements of this theory must be derived in a purely logical way, through proof. The construction of science on the basis of the axiomatic method is usually called deductive. All concepts of the deductive theory (except for a fixed number of initial ones) are introduced by means of definitions formed from a number of previously introduced concepts. To one degree or another, deductive proofs characteristic of the axiomatic method are accepted in many sciences, but the main area of its application is mathematics, logic, and also some branches of physics.

4. Abduction method

The methods of induction analyzed above and the traditional forms of deductive reasoning cannot be considered as optimal means of discovering new ideas, although both F. Bacon and R. Descartes were convinced of this. On this circumstance at the end of the XIX century. drew the attention of the American logician and philosopher Charles S. Pierce, the founder of pragmatism, who stated that the logic and philosophy of science should be engaged in a conceptual analysis of the emergence of new ideas and hypotheses in science. To this end, he proposed to supplement the general logical methods of induction and deduction by the method of abduction as a specific way of searching for explanatory hypotheses. The terms "deduction", "induction" and "abduction" come from the root "lead" and are translated, respectively, "induction", "induction", "reduction". C. Pierce wrote: “Induction considers theories and measures the degree of their agreement with the facts. She can never create any idea at all. No more than that can be done by deduction. All ideas of science arise through abduction. Abduction consists in examining facts and constructing a theory to explain them." In other words, according to Peirce, abduction is a method of searching for hypotheses, while induction, being a probabilistic inference, according to the philosopher, is a method of testing existing hypotheses and theories.

Induction in traditional logic is considered as a conclusion from the particular to the general, from individual facts to their generalization. The result of induction may be the establishment of the simplest empirical hypotheses. Peirce, on the other hand, is looking for a means by which hypotheses are created that make it possible to reveal the internal mechanism underlying the observed facts and phenomena. Thus, abduction, like induction, refers to facts, but not in order to compare and generalize them, but in order to formulate a hypothesis based on them.

At first glance, it seems that abduction does not differ from the hypothetical-deductive method, since it also includes the statement of a hypothesis. However, it is not. The hypothetical-deductive method begins with a predetermined hypothesis, and then consequences are derived from it, which are tested for truth. Abduction, on the other hand, begins with the analysis and accurate assessment of established facts, after which a hypothesis is chosen to explain them. Peirce formulates methodological requirements for abductive hypotheses.

They must explain not only empirically observed facts, but also facts that are directly unobservable and verifiable indirectly.

They must be confirmed, and not only by observed facts, but also by newly revealed facts.

List of usedliterature

1. Alekseev P.V., Panin A.V. Philosophy. M.: TEIS, 1996.

2. Novikov A.M., Novikov D.A. Methodology. M.: SIN-TEG, 2007.

3. Novikov A.M., Novikov D.A. Methodology. Dictionary of the system of basic concepts. M.: SIN-TEG, 2013.

4. Philosophy and methodology of science. Under. ed. IN AND. Kuptsova. M.: ASPECT PRESS, 1996.

5. Dictionary of philosophical terms. Scientific edition of Professor V.G. Kuznetsova. M., INFRA-M, 2007, p. 74-75.

6. Ababilova L.S., Shlekin S.I. The problem of scientific method. - M., 2007.

7. Ruzavin G.I. Methodology of scientific research: Proc. allowance for universities. - M.: UNITI-DANA, 1999. - 317 p.

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Induction(from Latin inductio - guidance, motivation) is a method of cognition based on a formal logical conclusion, which leads to a general conclusion based on particular premises. In other words, it is the movement of our thinking from the particular, the individual to the general.

Induction is widely used in scientific knowledge. Finding similar features, properties in many objects of a certain class, the researcher concludes that these features, properties are inherent in all objects of this class. For example, in the process of experimental study of electrical phenomena, current conductors made of various metals were used. Based on numerous individual experiments, a general conclusion was formed about the electrical conductivity of all metals.

Induction used in scientific knowledge (scientific induction) can be implemented in the form of the following methods:

1. The method of single similarity (in all cases of observing a phenomenon, only one common factor is found, all others are different; therefore, this single similar factor is the cause of this phenomenon).

2. The method of a single difference (if the circumstances of the occurrence of a phenomenon and the circumstances under which it does not occur are similar in almost everything and differ only in one factor that is present only in the first case, then we can conclude that this factor is the cause of this phenomena).

3. Combined method of similarity and difference (is a combination of the above two methods).

4. The method of concomitant changes (if certain changes in one phenomenon each time entail some changes in another phenomenon, then the conclusion follows about the causal relationship of these phenomena).

5. Method of residuals (if a complex phenomenon is caused by a multifactorial cause, and some of these factors are known as the cause of some part of this phenomenon, then the conclusion follows: the cause of another part of the phenomenon is the remaining factors included in the general cause of this phenomenon).

The founder of the classical inductive method of cognition is F. Bacon. But he interpreted induction extremely broadly, considered it the most important method of discovering new truths in science, the main means of scientific knowledge of nature (all inductivism). However, induction cannot be considered in isolation from other methods of cognition, in particular, from deduction.

Deduction(from lat. deductio - derivation) is the receipt of private conclusions based on the knowledge of some general provisions. In other words, it is the movement of our thinking from the general to the particular, the individual. For example, from the general position that all metals have electrical conductivity, one can make a deductive conclusion about the electrical conductivity of a particular copper wire (knowing that copper is a metal). If the initial general propositions are an established scientific truth, then the true conclusion will always be obtained by the method of deduction. General principles and laws do not allow scientists to go astray in the process of deductive research: they help to correctly understand the specific phenomena of reality.

The acquisition of new knowledge through deduction exists in all natural sciences, but the deductive method is especially important in mathematics. Operating with mathematical abstractions and building their reasoning on very general principles, mathematicians are forced most often to use deduction. And mathematics is, perhaps, the only proper deductive science.

In the science of modern times, the prominent mathematician and philosopher R. Descartes was the propagandist of the deductive method of cognition. Inspired by his mathematical successes, being convinced of the infallibility of a correctly reasoning mind, Descartes one-sidedly exaggerated the importance of the intellectual side at the expense of the experienced in the process of knowing the truth. Descartes' deductive methodology was in direct opposition to Bacon's empirical inductivism.

But, despite the attempts that have taken place in the history of science and philosophy to separate induction from deduction, to oppose them in the real process of scientific knowledge, these two methods are not used as isolated, isolated from each other. Each of them is used at a corresponding stage of the cognitive process.

Moreover, in the process of using the inductive method, deduction is often “hidden” as well. Emphasizing the necessary connection between induction and deduction, F. Engels urged scientists: “Instead of unilaterally exalting one of them to the skies at the expense of the other, one should try to apply each in its place, and this can only be achieved if one does not lose sight of mind their connection with each other, their mutual complement to each other.

General scientific methods applied at the empirical and theoretical levels of knowledge. Analysis and synthesis. Under analysis understand the division of an object (mentally or actually) into constituent particles for the purpose of their separate study. Some material elements of the object or its properties, attributes, relations, etc. can be used as such parts.

Analysis is a necessary stage in the cognition of an object. Since ancient times, analysis has been used, for example, for the decomposition into components of certain substances. In particular, already in ancient Rome, analysis was used to check the quality of gold and silver in the form of so-called cupellation (the analyzed substance was weighed before and after heating). Gradually, analytical chemistry was formed, which can rightly be called the mother of modern chemistry: after all, before using a particular substance for specific purposes, it is necessary to find out its chemical composition.

Analysis occupies an important place in the study of objects of the material world. But it is only the first stage of the process of cognition. If, say, chemists were limited only to analysis, i.e. isolation and study of individual chemical elements, then they would not be able to know all those complex substances, which include these elements.

To comprehend an object as a single whole, one cannot limit oneself to studying only its constituent parts. In the process of cognition, it is necessary to reveal the objectively existing connections between them, to consider them together, in unity. To carry out this second stage in the process of cognition - to move from the study of individual component parts of an object to the study of it as a single connected whole - is possible only if the method of analysis is supplemented by another method. – synthesis .
In the process of synthesis, the constituent parts (sides, properties, features, etc.) of the object under study, dissected as a result of the analysis, are joined together. On this basis, further study of the object takes place, but already as a single whole. At the same time, synthesis does not mean a simple mechanical connection of disconnected elements into a single system. It reveals the place and role of each element in the system of the whole, establishes their interrelation and interdependence, i.e. allows you to understand the true dialectical unity of the object under study.

Analysis and synthesis are also successfully used in the field of human mental activity, i.e. in theoretical knowledge. But here, as well as at the empirical level of cognition, analysis and synthesis are not two operations separated from each other. In essence, they are, as it were, two sides of a single analytical-synthetic method of cognition.

Analogy and modeling are general scientific methods used at the empirical and theoretical levels of knowledge. Under analogy similarity, the similarity of some properties, features or relationships of objects that are generally different is understood. The establishment of similarities (or differences) between objects is carried out as a result of their comparison. Thus, comparison underlies the method of analogy.

If a logical conclusion is made about the presence of any property, attribute, relationship of the object under study on the basis of establishing its similarity with other objects, then this conclusion is called inference by analogy. The course of such a conclusion can be represented as follows. Let there be, for example, two objects: A and B. It is known that the object A has properties Р 1 , Р 2 , ..., Р n , Р n+1 . The study of object B showed that it has properties Р 1 , Р 2 , ..., Р n , coinciding, respectively, with the properties of object A. Based on the similarity of a number of properties (Р 1 , Р 2 , ..., Р n), both objects, an assumption can be made about the presence of property P n + 1 in object B.

The degree of probability of obtaining a correct conclusion by analogy will be the higher: 1) the more common properties of the compared objects are known; 2) the more essential the common properties found in them; and 3) the deeper the mutual regular connection of these similar properties is known. At the same time, it must be borne in mind that if the object, in relation to which a conclusion is made by analogy with another object, has some property that is incompatible with the property, the existence of which should be concluded, then the general similarity of these objects loses all meaning. .

There are different types of inferences by analogy. But what they have in common is that in all cases one object is directly investigated, and a conclusion is made about another object. Therefore, inference by analogy in the most general sense can be defined as the transfer of information from one object to another. In this case, the first object, which is actually subjected to research, is called model , and another object, to which the information obtained as a result of the study of the first object (model) is transferred, is called original (sometimes - a prototype, sample, etc.). Thus, the model always acts as an analogy, i.e. the model and the object (original) displayed with its help are in a certain similarity (similarity).

Modeling is understood as the study of a simulated object (original), based on the one-to-one correspondence of a certain part of the properties of the original and the object (model) that replaces it in the study, and includes building a model, studying it and transferring the information obtained to the simulated object - the original.

Depending on the nature of the models used in scientific research, there are several types of modeling.

1.Mental (ideal) modeling. This type of modeling includes a variety of mental representations in the form of certain imaginary models. For example, in the ideal model of the electromagnetic field by J. Maxwell, the lines of force were represented as tubes through which an imaginary fluid flows, which does not have inertia and compressibility.

2.Physical modeling. It is characterized by a physical similarity between the model and the original and aims to reproduce in the model the processes inherent in the original. At present, physical modeling is widely used for the development and experimental study of various structures (dams of power plants, irrigation systems, etc.), machines (the aerodynamic properties of aircraft, for example, are studied on their models blown by an air flow in a wind tunnel), for a better understanding some natural phenomena, etc.

3.Symbolic (sign) modeling. It is associated with a conditionally sign representation of some properties, relations of the original object. A special and very important type of symbolic (sign) modeling is mathematical modeling. Relationships between various quantities that describe the functioning of the object or phenomenon under study can be represented by the corresponding equations. The resulting system of equations, together with the known data necessary for its solution (initial conditions, boundary conditions, values of the equation coefficients, etc.), is called the mathematical model of the phenomenon.

4. Mathematical modeling can be used in special combination with physical modeling. This combination, called real-mathematical(or subject-mathematical) modeling, allows you to explore some processes in the original object, replacing them with the study of processes of a completely different nature (which, however, are described by the same mathematical relationships as the original processes). Thus, mechanical vibrations can be modeled by electrical vibrations based on the complete identity of the differential equations describing them.

5. Numerical simulation on a computer. This type of modeling is based on a previously created mathematical model of the object or phenomenon under study and is used in cases of large amounts of calculations required to study this model.

4.1.6. Inductive-deductive method (analysis)

Both psychic life as a whole and its constituent elements of content fall apart into pairs of oppositions. On the other hand, it is the existence of mutually opposed poles that makes it possible to restore lost connections. Ideas, tendencies, feelings bring to life their direct opposites.

K. Jaspers

Induction - it is the movement of knowledge from particular to general statements. Induction underlies any action, any analysis, because a particular criminal act is subject to the influence of inductive reasoning.

Based on one object and its features, the criminalist must:

1. Build a bridge between the particular and the possible general, where does the quotient enter.

For example, the corpse of a man with his throat cut was found... Subject version: the killer may be a person for whom throat cutting is a common occurrence. This is a person who overcomes the fear of profuse bleeding ... This is a person prone to extreme cruelty ... This is a native of the village, used to slaughtering cattle ... The intended object must pass through the connection filter ...

2. Build inductive reasoning including individuality, reflecting the subjectivity of the personality of the performer:

typicality of characteristics (ascending to regularities of manifestations);
regularity of connections between the discovered fact and the studied set (representative array);
features of the conditions for the appearance of a single fact (phenomenon);
own readiness to perceive a single fact and connect it with a known (established) regular set.

The signs used in inductive reasoning should:

be significant;
reflect the individuality of the object;
should already be included in the group of previously identified regularities.

Induction must act in a duet with deduction, this is a paired phenomenon that cannot be alone.

Deduction - it is the movement of knowledge from the general to the particular. It is the discovery of the effect in the cause.

As soon as a person perceives a forensically significant object, inductive activity immediately turns on, but at the same time, competing and ahead of the final conclusion, a deductive process is born. Deduction loads the consciousness of the investigator with knowledge about the general, known, classified, from which it is possible to draw counter conclusions about the individual ...

The consciousness of the investigator is picked up by induction and deduction and is confronted with the need to choose behavior with taking into account the current situation and established patterns of the past. In the field of forensic consciousness, the layer of induction mixes with the layer of deduction, giving rise to a reaction in which the following stages are distinguished:

indicative;
executive;
control.

Inductive-deductive processes are intellectually rationalized (they are in search of optimal forms), but excited by emotional-volitional components. Moreover, emotional components often outstrip rational processes and manifest themselves in actions before inductive-deductive mechanisms offer a balanced solution to consciousness.

Inductive-deductive processes involve:

1. Formulation of the goal.

2. Intellectual and motor actions.

3. Monitoring the performed action through feedback channels in accordance with the goal.

The inductive-deductive method inevitably refutes any procedure performed by the investigator.

The deductive method in application to investigative practice can have the following types: genetic and hypothetical-deductive.

When using the genetic method not all initial data are set and not all objects of objective activity are entered. The investigator has the opportunity to gradually introduce all new initial data for subsequent deduction, i.e. first, private knowledge about the object under study is derived (which does not differ in complexity and variety of elements), and then the investigator more and more “complicates” the object (for example, the scene of an incident), so that from a larger number of objects combined into a system - the “scene”, to derive new private conclusions-versions about the origin of the traces, about the dynamics of the crime, about the identity of the criminal or about his personal characteristics.

Hypothetical-deductive method It is characterized by the fact that not so much established facts (evidence) are used as initial data, but rather hypotheses-versions built on various grounds. For example, the investigator builds a series of versions:

a) on the objective side of the composition of the crime under investigation (i.e. on the mechanism of the crime);

b) according to its subjective side (i.e., according to the subjective attitude of the offender to the crime being committed, according to his emotional state before, at the time and after the commission of the crime), which are reflected in the traces of the crime; according to the subject of the crime, i.e. on the personality of the perpetrator.

The totality of the constructed and tested versions forms a general version, a hypothesis about the crime as a whole. The father of the deductive method is considered R. Descartes, he formulated the following four rules , which can be used in forensics.

1. It is necessary to carry out the division of a complex problem into simpler ones sequentially up to those. until further indecomposable ones are found.

2. Unsolved problems should be reduced to solved ones. In this way, solutions to simple problems are sought.

3. From solving simple problems, one should move on to solving more complex ones until a solution to the problem is obtained, which was the initial one during the dismemberment and is the final one in this process.

4. After obtaining a solution to the original problem, it is necessary to review all the intermediate ones to make sure that no links are missing. If the completeness of the solution is established, then the study ends; if a gap is found in the solution, then additional research is required in accordance with the listed rules.

If Rene Descartes were an investigator, he would certainly have been successful in solving complex and intricate crimes. The rules proposed by Descartes for dealing with complex problems sound very modern, especially when it comes to deadlock situations. Inductive methods are successfully used to establish and analyze connections (necessary and accidental, external and internal).

When analyzing causal relationships, five types of inductive methods are used (according to I.S. Ladenko).

1. Single match method. It is used in such conditions when the set of circumstances preceding the phenomenon contains only one similar circumstance and differs in all the others. At the same time, the conclusion is made: this is the only similar circumstance that is the cause of the phenomenon under consideration. Analyzing the initial data of the investigative situation, the investigator has the opportunity to find one, but the most important circumstance that has a major impact on the behavior of the interrogated. At the same time, similarities are found in similar investigative situations, for which the investigator can look at typical models of crimes or systems of typical versions set forth in the works of N.A. Selivanova, L.G. Vidonova, G.A. Gustova and others.

2. Single difference method it is used when two cases are considered, in one of which the phenomenon “a” takes place, and in the other it does not; the preceding circumstances differ only in one circumstance - "with". At the same time, the investigated phenomenon “a” is possible if the circumstance “c” is present. If these logical constructions are translated into forensic language, then this can be illustrated by the following example.

For example, on the road there was a collision of a car with a motorcycle, when the driver of the latter, in violation of the rules, changed lanes into the lane of the car. The injured motorcyclist claimed that the accident occurred due to the speeding by the driver of the car and failure to maintain proper distance. Experimental actions of the investigator and expert calculations showed that rebuilding motorcycle "c" in front of a closely approaching car in any situation causes collisions "a", regardless of all other circumstances. Incident - "a" - can occur only under the only condition "c" - rebuilding the motorcycle.

3. The combined method of similarity and difference. The bottom line is that the conclusions drawn by the single similarity method are tested by the single difference method.

4. Accompanying change method is used when it is necessary to establish the cause of changes in the observed phenomenon "a". At the same time, the previous circumstances are reviewed, it is established that only one of them changes, and all the others remain unchanged. On this basis, it is concluded that the change in the observed phenomenon is caused by the changing antecedent circumstance "a". In relation to investigative practice, this method can be used in the analysis of conditions, for example, a traffic accident, when among the many factors influencing the dynamics of the incident, those that make up the cause of the accident are identified.

5. Residual method is used when a complex phenomenon is being investigated, from which a series of components-consequences are distinguished, each of which has its own cause (established). Those consequences that are discovered and do not have established causes become the subject of close research. Simply put, from a complex phenomenon, the investigator extracts everything that is clear to him, that has its own reason, leaving in the balance that which has no reason, does not have a logical explanation. It is this unexplored that is the subject of investigation. The method of residuals helps the investigator to narrow the sector of the search for the unknown, to limit uncertainty, to direct the search exactly where the complex of consequences is grouped, the causes of which are unclear.

The information base of induction methods can be of a combined nature, i.e. include elements of all five named types of induction (not to mention the fact that induction can be combined with deduction).