An inference is a logical operation, as a result of which a new statement is obtained from one or more accepted statements (premises) - a conclusion (consequence).
Depending on whether there is a connection between the premises and the conclusion logical consequence, there are two types of inferences.
In deductive reasoning, this connection is based on a logical law, due to which the conclusion follows with logical necessity from the premises accepted. As already noted, the distinguishing feature of such an inference is that it always leads from true premises to a true conclusion.
Examples of deductive reasoning include:
If a given number is divisible by 6, then it is divisible by 3.
This number is divisible by 6.
This number is divisible by 3.
If helium is a metal, it is electrically conductive.
Helium is not electrically conductive.
Helium is not a metal.
The line separating the premises from the conclusion replaces the word "therefore".
In inductive reasoning, the connection between premises and conclusions is not based on the law of logic, but on some factual or psychological grounds that are not purely formal. In such a conclusion, the conclusion does not follow logically from the premises and may contain information that is not present in them. The veracity of the premises does not therefore mean the veracity of the assertion inductively derived from them. Induction gives only probable, or plausible, conclusions that require further verification.
Reasoning can serve as examples of induction:
Argentina is a republic; Brazil is a republic; Venezuela is a republic;
Ecuador is a republic.
Argentina, Brazil, Venezuela, Ecuador are Latin American states.
All Latin American states are republics.
Italy is a republic; Portugal is a republic; Finland is a republic;
France is a republic.
Italy, Portugal, Finland, France - Western European countries.
All Western European countries are republics.
Induction does not give a full guarantee of obtaining a new truth from the already existing ones. The maximum that can be said is a certain degree of probability output statement. Thus, the premises of both the first and second inductive inferences are true, but the conclusion of the first of them is true, and the second is false. Indeed, all Latin American states are republics; but among the Western European countries there are not only republics, but also monarchies, for example, England, Belgium and Spain.
Especially characteristic deductions are logical transitions from general knowledge to particular. In all cases when it is required to consider some phenomenon on the basis of already known general principle and draw the necessary conclusion regarding this phenomenon, we conclude in the form of deduction (All poets are writers; Lermontov is a poet; therefore, Lermontov is a writer).
Reasonings leading from knowledge about a part of objects to general knowledge about all objects of a certain class are typical inductions, since there is always the possibility that the generalization will turn out to be hasty and unfounded (Plato is a philosopher; Aristotle is a philosopher; therefore, all people are philosophers) .
At the same time, one cannot identify deduction with the transition from the general to the particular, and induction with the transition from the particular to the general. Deduction is logical transition from one truth to another, induction - the transition from reliable knowledge to probable. Inductive inferences include not only generalizations, but also likenings, or analogies, conclusions about the causes of phenomena, etc.
Deduction plays a special role in the justification of statements. If the provision in question follows logically from the already established provisions, it is justified and acceptable to the same extent as the latter. This is actually a logical way of substantiating statements, using pure reasoning and not requiring recourse to observation, intuition, etc.
While emphasizing the importance of deduction in the process of justification, one should not, however, separate it from induction or underestimate the latter. Almost all general propositions, including, of course, scientific laws, are the result of inductive generalization. In this sense, induction is the basis of our knowledge. By itself, it does not guarantee its truth and validity. But it generates assumptions, connects them with experience, and thereby gives them a certain plausibility, a more or less high degree of probability. Experience is the source and foundation of human knowledge. Induction, starting from what is comprehended in experience, is a necessary means of its generalization and systematization.
Deduction is the derivation of conclusions that are as certain as the accepted premises.
In ordinary reasoning, deduction appears in full and detailed form only in rare cases. Most often, we do not indicate all the parcels used, but only some of them. General statements that may be assumed to be well known are generally omitted. The conclusions following from the accepted premises are not always explicitly formulated either. The very logical connection that exists between the original and derivable statements is only sometimes marked by words like “therefore” and “means”.
Often the deduction is so abbreviated that one can only guess about it. It is not easy to restore it in full form, indicating all the necessary elements and their relationships.
It is cumbersome to conduct deductive reasoning without omitting or reducing anything. A person who points out all the premises of his conclusions gives the impression of some kind of pedant. And at the same time, whenever there is doubt about the validity of the conclusion made, one should return to the very beginning of the reasoning and reproduce it in the fullest possible form. Without this, it is difficult or even simply impossible to detect a mistake.
Many literary critics believe that Sherlock Holmes was "written off" by A. Conan Doyle from the professor of medicine at the University of Edinburgh, Joseph Bell. The latter was known as a talented scientist with rare powers of observation and an excellent command of the deduction method. Among his students was the future creator of the image of the famous detective.
One day, says Conan Doyle in his autobiography, a sick man came to the clinic, and Bell asked him:
Have you served in the army?
Yes sir! - standing at attention, the patient answered.
In the mountain rifle regiment?
That's right, doctor!
Recently retired?
Yes sir!
Were you a sergeant?
Yes sir! - famously answered the patient.
Were you in Barbados?
That's right, doctor!
The students who were present at this dialogue looked at the professor in amazement. Bell explained how simple and logical his conclusions are.
This man, having shown politeness and courtesy at the entrance to the office, nevertheless did not take off his hat. Affected army habit. If the patient were retired long time, then he would have learned civil manners long ago. In posture authoritative, by nationality he is clearly a Scot, and this speaks for the fact that he was a commander. As for staying in Barbados, the visitor is sick with elephantism (elephantiasis) - such a disease is common among the inhabitants of those places.
Here the deductive reasoning is extremely abbreviated. In particular, all general assertions without which the deduction would be impossible are omitted.
The previously introduced concept of “correct reasoning (inference)” refers only to deductive reasoning. Only it can be right or wrong. In inductive reasoning, the conclusion is not logically connected with the received premises. Since “correctness” is a characteristic of a logical connection between premises and a conclusion, and this connection is not assumed by inductive reasoning, such a conclusion cannot be either right or wrong. Sometimes, on this basis, inductive reasoning is not included in the number of inferences at all.
Induction (from Latin induction - guidance, motivation) is a method of cognition based on a formal logical conclusion, which leads to a general conclusion based on particular premises. In its most general form, induction is the movement of our thinking from the particular, the individual to the general. In this sense, induction is a widely used method of thinking at any level of knowledge.
The method of scientific induction is multivalued. It is used to refer not only to empirical procedures, but also to refer to some techniques related to the theoretical level, where, in fact, it represents various forms of deductive reasoning.
Let us analyze induction as a method of empirical knowledge.
The justification of induction as a method is associated with the name Aristotle. Aristotle was characterized by the so-called intuitive induction. This is one of the first ideas about induction among its many formulations.
Intuitive induction is a thought process by which a common property or relation is singled out from a set of cases and identifiedwith each individual case.
Numerous examples of this kind of induction, used both in everyday life and in scientific practice, mathematics are given in the book of the famous mathematician D. Poya. (Intuition // D. Poya. Mathematics and plausible reasoning. - M., 1957). For example, observing some numbers and their combinations, one can come across the ratios
3+7=10, 3+17=20, 13+17=30 etc.
There is a similarity here in obtaining a multiple of ten.
Or another example: 6=3+3, 8=3+5, 10=3+7=5+5, 12=5+7 etc.
Obviously, we are faced with the fact that the sum of odd primes is always an even number.
These statements are obtained in the course of observation and comparison of arithmetic operations. It is appropriate to call the demonstrated examples of inductionintuitive, since the inference process itself is not a logical conclusion in the exact sense of the word. Here we are not dealing with reasoning, which would be decomposed into premises and conclusions, but simply with the perception, "grasping" of relations and general properties directly. We do not apply any logical rules, but we guess. We are simply enlightened by the understanding of a certain essence. Such induction is important in scientific knowledge, but it is not the subject of formal logic, but is studied by the theory of knowledge and the psychology of creativity. Moreover, we use such induction at the ordinary level of knowledge all the time.
As the creator of traditional logic, Aristotle calls induction another procedure, namely: establishing a general sentence by listing in the form of singular sentences all the cases that are subsumed under it. If we were able to enumerate all the cases, which is the case when the number of cases is limited, then we are dealing with complete induction. In this case, Aristotle's procedure for deriving a general sentence is actually a case of deductive inference.
When the number of cases is not limited, i.e. almost infinitely, we are dealing with incomplete induction. It is an empirical procedure and is induction in the proper sense of the word. This is the procedure for establishing a general sentence on the basis of several separate cases in which a certain property was observed that is characteristic of all possible cases that are similar.with observable is called induction through a simple enumeration. This is the popular or traditional induction.
The main problem of complete induction is the question of how thoroughly, legitimately such a transfer of knowledge from individual cases known to us, listed in separate sentences, to all possible and even unknown us cases.
This is a serious problem scientific methodology and it has been discussed in philosophy and logic since the time of Aristotle. This is the so-called problem of induction. It is a stumbling block for metaphysically thinking methodologists.
In real scientific practice, popular induction is used absolutely independently extremely rarely. Most often, it is used First of all, along with more advanced forms of the method of induction and, Secondly, in unity with deductive reasoning and other forms of theoretical thinking, which increase the credibility of the knowledge obtained in this way.
When a transfer is made in the process of induction, an extrapolation of a conclusion that is valid for a finite number of known members of a class to all members of that class, then the basis for such a transfer is the abstraction of identification, consisting in the assumption that in a given respect all members of this class are identical. Such an abstraction is either an assumption, a hypothesis, and then induction acts as a way to confirm this hypothesis, or the abstraction rests on some other theoretical premises. In any case, induction is somehow connected with various forms theoretical reasoning, deduction.
In an unchanged form, induction through a simple enumeration existed until the 17th century, when F. Bacon made an attempt to improve Aristotle's method in the famous work "New Organon" (1620). F. Bacon wrote: “Guidance, which occurs by a simple enumeration, is a childish thing, it gives shaky conclusions and is endangered by contradictory particulars, making decisions mostly on the basis of a smaller number of facts than it should, and only for those that are available. on the face". Bacon also draws attention to the psychological side of the fallacy of conclusions. He writes: “People usually judge new things by the example of old ones, following their imagination, which is prejudiced and stained by them. This kind of judgment is misleading, since much of what is sought at the sources of things does not flow in familiar streams.
The induction proposed by F. Bacon, and the rules that he formulated in his famous tables of “presenting examples to the mind”, in his opinion, are free from subjective errors, and the application of his method of induction guarantees the receipt of true knowledge. He states: “Our path of discovery is such that it leaves little to the sharpness and power of gifts. But it almost equalizes them. Just as for drawing a straight line or describing a perfect circle, firmness, skill and testing of the hand means a lot, if you only use your hand, it means little or nothing if you use a compass and a ruler; and so it is with our method.”
Demonstrating the failure of induction through a simple enumeration, Bertrand Russell gives the following parable. Once upon a time there was a census official who had to rewrite the names of all householders in a Welsh village. The first one he asked called himself William Williams, the second one also called himself, the third one, and so on. Finally, the official said to himself, “This is tiresome, obviously, they are all William Williams. So I will write them all down and be free.” But he was wrong, because there was still one person named John Jones. This shows that we can come to the wrong conclusions if we believe too implicitly in induction by mere enumeration.”
Calling incomplete induction childish, Bacon proposed an improved form of induction, which calls eliminative (exclusive) induction. The general basis of Bacon's methodology was the "dissection" of things and complex phenomena into parts or elementary "nature", and then the discovery of the "forms" of these "nature". In this case, by "form" Bacon understands the elucidation of the essence, the causes of individual things and phenomena. The procedure of connection and separation in Bacon's theory of knowledge takes the form of eliminative induction.
From Bacon's point of view, main reason A significant imperfection of Aristotle's incomplete induction was the lack of attention to negative cases. Negative arguments obtained as a result of empirical research must be woven into the logical scheme of inductive reasoning.
Another disadvantage of incomplete induction, according to Bacon, was its limitation to a generalized description of phenomena and the lack of an explanation of the essence of phenomena. Bacon, criticizing incomplete induction, drew attention to an essential point in the cognitive process: conclusions obtained only on the basis of confirming facts are not completely reliable unless the impossibility of refuting facts is proved.
Baconian induction is based on the recognition:
the material unity of nature;
uniformity of its actions;
universal causality.
Based on these general philosophical premises, Bacon supplements them with the following two more:
every present "nature" necessarily has a form that calls it;
in the real presence of this “form”, its inherent “nature” will certainly appear.
Without any doubt, Bacon believed that the same "form" causes not one, but several different "nature" inherent in it. But we do not find in him a clear answer to the question of whether absolutely one and the same "nature" can be caused by two different "forms". But to simplify the induction, he had to accept the thesis: identical "nature" from different forms no, one "nature" - one "form".
According to its mechanism, Bacon's induction is built from three tables: a table of presence, a table of absence, and a table of degrees of comparison. In The New Organon, he demonstrates how to reveal the nature of heat, which, as he suggested, consists of rapid and erratic movements of the smallest particles of bodies. Therefore, the first table includes a list of hot bodies, the second - cold, and the third - bodies with different degrees of heat. He hoped that the tables would show that a certain quality is always inherent only in hot bodies and is absent in cold bodies, and in bodies with different degrees of heat it is present to a different degree. By applying this method, he hoped to establish the general laws of nature.
All three tables are processed sequentially. First, properties that cannot be the desired “form” are “rejected” from the first two. To continue the elimination process or confirm it, if the desired form has already been selected, use the third table. It should show that the desired shape, for example, A, correlates with the "nature" of the object "a". So, if A increases, then "a" also increases, if A does not change, then it retains its values "a". In other words, the table must establish or confirm such correspondences. An obligatory stage of Baconian induction is the verification of the obtained law with the help of experience.
Then, from a series of laws of a small degree of generality, Bacon hoped to derive laws of a second degree of generality. The proposed new law must also be tested under new conditions. If he acts in these conditions, then, according to Bacon, the law is confirmed, and therefore true.
As a result of his search for the “form” of heat, Bacon came to the conclusion: “heat is the movement of small particles, bursting apart and going from inside to outside and somewhat upward.” The first half of the found solution is generally correct, while the second one narrows and to some extent devalues the first one. The first half of the statement allowed for true statements, such as admitting that friction causes heat, but at the same time, it allowed for arbitrary statements, for example, to say that fur is warm because the hairs that form it move.
As for the second half of the conclusion, it is not applicable to the explanation of many phenomena, for example, solar heat. These blunders indicate rather that Bacon owes his discovery not so much to induction as to his own intuition.
one). The first disadvantage Bacon's induction was that it was based on the assumption that the desired "form" can be accurately recognized by its sensory discovery in phenomena. In other words, the essence appeared to accompany the phenomenon horizontally, and not vertically. It was considered as one of the observable properties directly. This is where the problem lies. Essence is not at all forbidden to be similar to its manifestations, and the phenomenon of the movement of particles, of course, "looks like" its essence, i.e. on the real movement of particles, although the latter is perceived as a macromotion, while in reality it is a micromotion that is not caught by a person. On the other hand, the effect does not have to be like its cause: the felt heat is not like the hidden movement of particles. Thus, the problem of similarity and dissimilarity is outlined.
The problem of the similarity and dissimilarity of "nature" as an objective phenomenon with its essence, i.e. “form”, intertwined in Bacon with a similar problem of similarity and dissimilarity of “nature” as a subjective sensation with objective “nature” itself. Does the sensation of yellowness look like yellowness itself, and does it look like its essence - the “form” of yellowness? Which "nature" of movement is similar to its "form" and which is not?
Half a century later, Locke gave his answer to these questions with the concept of primary and secondary qualities. Considering the problem of sensations of primary and secondary qualities, he came to the conclusion that the primary ones are similar to their causes in external bodies, while the secondary ones are not. Locke's primary qualities correspond to Bacon's 'forms', and the secondary qualities do not correspond to those 'nature's that are not the direct manifestation of 'forms'.
The second disadvantage Bacon's method of induction was its one-sidedness. The philosopher underestimated mathematics for insufficient experimentalism and, in this regard, deductive conclusions. At the same time, Bacon greatly exaggerated the role of induction, considering it the main means of scientific knowledge of nature. Such an unjustified extended understanding of the role of induction in scientific knowledge has been called all inductivism . Its failure is due to the fact that induction is considered in isolation from other methods of cognition and turns into the only one, universal remedy cognitive process.
The third disadvantage consisted in the fact that with a one-sided inductive analysis of a known complex phenomenon, an integral unity is destroyed. Those qualities and relationships that were characteristic of this complex whole, when analyzed, no longer exist in these fragmented "pieces".
The formulation of the rules of induction, proposed by F. Bacon, existed for more than two hundred years. J. St. Millu is credited with their further development and some formalization. Mill formulated five rules. Their essence is as follows. For the sake of simplicity, we will assume that there are two classes of phenomena, each of which consists of three elements - A, B, C and a, b, c, and that there is some dependence between these elements, for example, an element of one class determines an element of another class. It is required to find this dependence, which has an objective, universal character, provided that there are no other unaccounted influences. This can be done, according to Mill, by the following methods, each time obtaining a conclusion that has a probable character.
Methodsimilarities. Its essence: "a" arises both in AB and in AC. It follows that A is sufficient to determine "a" (ie, to be its cause, sufficient condition, foundation).
Difference method:"a" occurs in ABC, but does not occur in BC, where A is absent. From this follows the conclusion that A is necessary for "a" to arise (i.e., is the cause of "a").
Combined similarity and difference method:"a" occurs in AB and in AC , but does not occur in BC. From this it follows that A is necessary and sufficient for the determination of "a" (ie, is its cause).
residual method. It is known on the basis of past experience that B and "c" and C and "c" are in a necessary causal relationship with each other, i.e. this connection has the character of a general law. Then, if in a new experiment with ABC "abs" appears, then A is the cause or sufficient and necessary condition for "a". It should be noted that the method of residuals is not purely inductive reasoning, since it relies on premises that have the character of universal, nomological propositions.
The method of concomitant changes. If "a" changes when A changes, but does not change when B and C change, then A is the cause or the necessary and sufficient condition of "a".
It should be emphasized once again that the Bacon-Millen form of induction is inextricably linked with a certain philosophical worldview, a philosophical ontology, according to which in the objective world there is not only a mutual connection of phenomena, their mutual causation, but the connection of phenomena has a uniquely defined, “rigid” character. In other words, the philosophical prerequisites for these methods are the principle of objectivity of causation and the principle of unambiguous determination. The first is common to all materialism, the second is characteristic of mechanistic materialism - this is the so-called Laplacian determinism.
In the light of modern ideas about the probabilistic nature of laws outside world, about the dialectical relationship between necessity and chance, the dialectical relationship between causes and effects, etc. Mill's methods (especially the first four) reveal their limited character. Their applicability is possible only in rare and, moreover, very simple cases. The method of concomitant changes has a wider application, the development and improvement of which is associated with the development of statistical methods.
Although Mill's method of induction is more developed than that proposed by Bacon, it is inferior to Bacon's interpretation in a number of respects.
First of all, Bacon was sure that true knowledge, i.e. knowledge of the causes is quite achievable with the help of his method, and Mill was an agnostic who denied the possibility of comprehending the causes of phenomena, essence in general.
Secondly, Mill's three inductive methods operate only separately, while Bacon's tables are in close and necessary interaction.
As science develops, new type objects, where collections of particles, events, things are studied instead of a small number of easily identifiable objects. Such mass phenomena were increasingly included in the scope of research in such sciences as physics, biology, political economy, and sociology.
For the study of mass phenomena, the previously used methods turned out to be unsuitable, therefore, new methods of studying, generalizing, grouping and predicting were developed, which were called statistical methods.
Deduction(from lat. deduction - removal) there is a receipt of private conclusions on the basis of knowledge of some general provisions. In other words, it is the movement of our thinking from the general to the particular, the individual. In a more technical sense, the term "deduction" refers to the process of logical inference, i.e. transition according to certain rules of logic from some given sentences (premisses) to their consequences (conclusions). Deduction is also called the general theory of drawing correct conclusions (inferences).
The study of deduction is the main task of logic - sometimes formal logic is even defined as the theory of deduction, although deduction is also studied by the theory of knowledge, the psychology of creativity.
The term "deduction" appeared in the Middle Ages and was introduced by Boethius. But the concept of deduction as a proof of a sentence by means of a syllogism appears already in Aristotle (First Analytics). An example of deduction as a syllogism would be the following conclusion.
The first premise: crucian carp is a fish;
second premise: crucian carp lives in water;
conclusion (conclusion): fish lives in water.
In the Middle Ages, syllogistic deduction dominated, the initial premises of which were drawn from sacred texts.
In modern times, the credit for transforming deduction belongs to R. 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. Instead of medieval deduction, Descartes offered a precise, mathematicized way of moving from the self-evident and simple to the derivative and complex.
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. Accept as true everything that perceived clearly and distinctly and does not give rise to any doubt, those. 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 not only previously unconscious elementary intuitions, 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 full enumerations, reviews, without losing anything from attention. In the most general sense, this rule focuses on achieving the completeness of knowledge. It assumes
First of all, the creation of the most complete classification possible;
Secondly, approaching the maximum completeness of the consideration leads reliability (persuasiveness) to evidence, i.e. induction - to deduction and further to intuition. It is now recognized that complete induction is a particular case of deduction;
third, 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.
Currently, in modern science, most often operates hypothetical-deductive method. 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. Depending on the type of premises, hypothetical-deductive reasoning can be divided into three main groups:
1) the most numerous group of reasoning, where premises are hypotheses and empirical generalizations;
2) premises, consisting of statements that contradict either well-established facts or theoretical principles. Putting forward such assumptions as premises, it is possible to deduce from them consequences that contradict known facts, and on this basis to convince the assumption that the assumption is false;
3) premises are statements that contradict accepted opinions and beliefs.
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, a hypothetical-deductive system is a hierarchy of hypotheses, the degree of abstraction 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.
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 way 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.
It is necessary to distinguish between objective logic, the history of the development of an object, and methods of cognition of this object - logical and historical.
Objective-logical is a general line, a pattern of development of an object, for example, the development of society from one social formation to another.
Objectively-historical is a concrete manifestation of this regularity in all the infinite variety of its special and individual manifestations. In relation to society, for example, real story all countries and peoples with all their unique individual destinies.
Two methods of cognition follow from these two sides of the objective process - historical and logical.
Any phenomenon can be correctly known only in its origin, development and death, i.e. in its historical development. To know an object means to reflect the history of its origin and development. It is impossible to understand the result without understanding the path of development that led to this result. History often jumps and zigzags, and if you follow it everywhere, you would not only have to take into account a lot of material of lesser importance, but also often interrupt the train of thought. Therefore, a logical method of research is needed.
The logical is a generalized reflection of the historical, reflects reality in its natural development, explains the need for this development. The logical as a whole coincides with the historical: it is historical, purified from accidents and taken in its essential laws.
By logical, they often mean the method of cognition of a certain state of an object over a certain period of time, abstracted from its development. It depends on the nature of the object and the objectives of the study. For example, in order to discover the laws of planetary motion, I. Kepler did not need to study their history.
As research methods, induction and deduction stand out .
Induction is the process of deriving a general position from a number of particular (less general) statements, from single facts.
There are usually two main types of induction: complete and incomplete. Complete induction - the conclusion of some general judgment about all objects of a certain set (class) based on the consideration of each element of this set.
In practice, forms of induction are most often used, which involve a conclusion about all the objects of a class based on knowledge of only a part of the objects. this class. Such inferences are called inferences of incomplete induction. They are the closer to reality, the deeper, essential connections are revealed. Incomplete induction, based on experimental research and including theoretical thinking, is capable of giving a reliable conclusion. It is called scientific induction. Great discoveries, leaps in scientific thought are ultimately created by induction - a risky but important creative method.
Deduction - the process of reasoning, going from the general to the particular, less general. In the special sense of the word, the term "deduction" denotes the process of logical inference according to the rules of logic. Unlike induction, deductive reasoning gives reliable knowledge, provided that such a meaning was contained in the premises. AT scientific research inductive and deductive methods of thinking are organically linked. Induction leads human thought to hypotheses about the causes and general patterns of phenomena; deduction allows us to derive empirically verifiable consequences from general hypotheses and in this way to substantiate or refute them experimentally.
Experiment - a scientifically set experiment, a purposeful study of a phenomenon caused by us under precisely taken into account conditions, when it is possible to follow the course of a change in a phenomenon, actively influence it with the help of a whole complex of various instruments and means, and recreate these phenomena every time when the same conditions are present and when there is a need for it.
The following elements can be distinguished in the structure of the experiment:
a) any experiment is based on a certain theoretical concept that sets the program of experimental research, as well as the conditions for studying the object, the principle of creating various devices for experimentation, methods of fixing, comparing, representative classification of the obtained material;
b) an integral element of the experiment is the object of study, which can be various objective phenomena;
c) an obligatory element of experiments are technical means and various kinds of devices with which experiments are carried out.
Depending on the sphere in which the object of knowledge is located, experiments are divided into natural science, social, etc. Natural science and social experiments are carried out in logically similar forms. The beginning of the experiment in both cases is the preparation of the state of the object necessary for the study. Next comes the experimental stage. This is followed by registration, description of the data, compilation of tables, graphs, processing of the results of the experiment.
The division of methods into general, general scientific and special methods generally reflects the current structure scientific knowledge, in which, along with philosophical and particular scientific knowledge, an extensive layer of theoretical knowledge stands out as close as possible in terms of generality to philosophy. In this sense, this classification of methods to a certain extent corresponds to the tasks associated with the consideration of the dialectics of philosophical and general scientific knowledge.
Listed general scientific methods can be used at the same time at different levels of knowledge - on empirical and theoretical.
The decisive criterion for distinguishing between empirical and theoretical methods is the attitude towards experience. If the methods focus on the use of material means of research (for example, devices), on the implementation of influences on the object under study (for example, physical dismemberment), on the artificial reproduction of the object or its parts from other material (for example, when direct physical impact is somehow impossible), then such methods can be called empirical.
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Observation is a purposeful study of objects, based mainly on the data of the sense organs (sensations, perceptions, ideas). In the course of observation, we gain knowledge not only about the external aspects of the object of knowledge, but - as the ultimate goal - about its essential properties and relationships.
Observation can be direct and mediated by various devices and technical devices(microscope, telescope, photo and movie camera, etc.). With the development of science, observation becomes more and more complex and mediated.
Basic requirements for scientific observation:
- unambiguity of intention;
- the presence of a system of methods and techniques;
- objectivity, i.e. the possibility of control by either repeated observation or using other methods (for example, experiment).
Usually, observation is included as an integral part of the experimental procedure. An important point of observation is the interpretation of its results - decoding of instrument readings, a curve on an oscilloscope, on an electrocardiogram, etc.
The cognitive result of observation is a description - fixation by means of natural and artificial language initial information about the object under study: diagrams, graphs, diagrams, tables, drawings, etc. Observation is closely related to measurement, which is the process of finding the ratio of a given quantity to another homogeneous quantity taken as a unit of measurement. The measurement result is expressed as a number.
Observation presents a particular difficulty in the social sciences and humanities, where its results depend to a greater extent on the personality of the observer, his attitudes and principles, and his interest in the subject being studied. In sociology and social psychology, depending on the position of the observer, there is a distinction between simple (ordinary) observation, when facts and events are recorded from the outside, and participatory (included observation), when the researcher is included in a certain social environment, adapts to it and analyzes events "from the inside". In psychology, self-observation (introspection) is used.
In the course of observation, the researcher is always guided by a certain idea, concept or hypothesis. He does not just register any facts, but consciously selects those of them that either confirm or refute his ideas. In this case, it is very important to select the most representative, i.e. the most representative group of facts in their interconnection. The interpretation of observation is also always carried out with the help of certain theoretical positions.
With the help of these methods, the cognizing subject masters a certain amount of facts that reflect certain aspects of the object being studied. The unity of these facts, established on the basis of empirical methods, does not yet express the depth of the essence of the object. This essence is comprehended at the theoretical level, on the basis of theoretical methods.
The division of methods into philosophical and special, into empirical and theoretical, of course, does not exhaust the problem of classification. It seems possible to divide the methods into logical and non-logical. This is expedient, if only because it allows one to relatively independently consider the class of logical methods used (consciously or unconsciously) in solving any cognitive problem.
All logical methods can be divided into dialectical and formal. The first, formulated on the basis of the principles, laws and categories of dialectics, guide the researcher to the method of revealing the content side of the goal. In other words, the application of dialectical methods in a certain way directs thought to the disclosure of what is connected with the content of knowledge. The second (formalological methods), on the contrary, orient the researcher not to revealing the nature and content of knowledge. They are, as it were, "responsible" for the means by which the movement towards the content of knowledge is clothed in pure formal logical operations (abstraction, analysis and synthesis, induction and deduction, etc.).
The formation of a scientific theory is carried out as follows.
The phenomenon under study appears as a concrete, as a unity of the manifold. Obviously, there is no proper clarity in understanding the concrete at the first stages. The path to it begins with analysis, mental or real dismemberment of the whole into parts. Analysis allows the researcher to focus on a part, property, relation, element of the whole. It is successful if it allows a synthesis to be carried out, to restore the whole.
The analysis is supplemented by classification, the features of the studied phenomena are distributed by classes. Classification is the way to concepts. Classification is impossible without making comparisons, finding analogies, similar, similar in phenomena. The researcher's efforts in this direction create conditions for induction , conclusions from particular to some general statement. It is a necessary link on the path to achieving the common. But the researcher is not satisfied with the achievement of the general. Knowing the general, the researcher seeks to explain the particular. If this fails, then failure indicates that the induction operation is not genuine. It turns out that induction is verified by deduction. Successful deduction makes it relatively easy to fix experimental dependencies, to see the general in particular.
Generalization is associated with highlighting the general, but most often it is not obvious and acts as a kind of scientific secret, the main secrets of which are revealed as a result of idealization, i.e. detection of abstraction intervals.
Each new success in the enrichment of the theoretical level of research is accompanied by the ordering of the material and the identification of subordinate relationships. The connection of scientific concepts forms the laws. The main laws are often called principles. Theory is not just a system of scientific concepts and laws, but a system of their subordination and coordination.
So, the main points of the formation of a scientific theory are analysis, induction, generalization, idealization, the establishment of subordination and coordination links. The listed operations can be developed in formalization and mathematization.
Movement towards a cognitive goal can lead to various results, which are expressed in specific knowledge. Such forms are, for example, a problem and an idea, a hypothesis and a theory.
Types of forms of knowledge.
Methods scientific knowledge connected not only with each other, but also with the forms of knowledge.
Problem is a question that should be studied and resolved. Solving problems requires enormous mental effort, associated with a radical restructuring of existing knowledge about the object. The initial form of such permission is an idea.
Idea- a form of thinking in which the most essential is grasped in the most general form. The information embedded in the idea is so significant for a positive solution to a certain range of problems that it contains, as it were, a tension that encourages concretization and deployment.
The solution of the problem, as well as the concretization of the idea, can be completed by putting forward a hypothesis or building a theory.
Hypothesis- a probable assumption about the cause of any phenomena, the reliability of which, in the current state of production and science, cannot be verified and proven, but which explains these phenomena, which are observable without it. Even a science like mathematics cannot do without hypotheses.
A hypothesis tested and proven in practice moves from the category of probable assumptions to the category of reliable truths, becomes a scientific theory.
Scientific theory is understood, first of all, as a set of concepts and judgments regarding a certain subject area, united into a single, true, reliable system of knowledge using certain logical principles.
Scientific theories can be classified on various grounds: according to the degree of generality (private, general), according to the nature of the relationship to other theories (equivalent, isomorphic, homomorphic), according to the nature of the connection with experience and the type of logical structures (deductive and non-deductive), according to the nature of the use of language (qualitative, quantitative). But in whatever form the theory appears today, it is the most meaningful form knowledge.
The problem and the idea, the hypothesis and the theory are the essence of the forms in which the effectiveness of the methods used in the process of cognition is crystallized. However, their significance is not only in this. They also act as forms of knowledge movement and the basis for the formulation of new methods. Defining each other, acting as complementary means, they (i.e., methods and forms of cognition) in their unity provide a solution to cognitive problems, allow a person to successfully master the world around him.
The growth of scientific knowledge. Scientific revolutions and changes in the types of rationality.
Most often, the formation of theoretical research is stormy and unpredictable. In addition, one important circumstance should be borne in mind: usually the formation of new theoretical knowledge takes place against the background of an already known theory, i.e. there is an increase in theoretical knowledge. Based on this, philosophers often prefer to talk not about the formation of scientific theory, but about the growth of scientific knowledge.
The development of knowledge is a complex dialectical process that has certain qualitatively different stages. Thus, this process can be viewed as a movement from myth to logos, from logos to “pre-science”, from “pre-science” to science, from classical science to non-classical and further to post-non-classical, etc., from ignorance to knowledge, from shallow, incomplete to deeper and more perfect knowledge, etc.
In modern Western philosophy, the problem of the growth, development of knowledge is central to the philosophy of science, which is presented especially vividly in such currents as evolutionary (genetic) epistemology * and postpositivism.
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Evolutionary epistemology is a direction in Western philosophical and epistemological thought, the main task of which is to identify the genesis and stages of the development of knowledge, its forms and mechanisms in an evolutionary key and, in particular, to build on this basis the theory of the evolution of science. Evolutionary epistemology seeks to create a generalized theory of the development of science, based on the principle of historicism and trying to mediate the extremes of rationalism and irrationalism, empiricism and rationalism, cognitive and social, natural science and social sciences and humanities, etc.
One of the well-known and productive variants of the form of epistemology under consideration is the genetic epistemology of the Swiss psychologist and philosopher J. Piaget. It is based on the principle of growth and invariance of knowledge under the influence of changes in the conditions of experience. Piaget, in particular, believed that epistemology is a theory of reliable knowledge, which is always a process, not a state. Its important task is to determine how cognition reaches reality, i.e. what connections, relations are established between the object and the subject, which in its cognitive activity cannot but be guided by certain methodological norms and regulations.
The genetic epistemology of J. Piaget tries to explain the genesis of knowledge in general, and scientific knowledge in particular, on the basis of the influence of external factors in the development of society, i.e. sociogenesis, as well as the history of knowledge itself and especially psychological mechanisms its occurrence. Studying child psychology, the scientist came to the conclusion that it constitutes a kind of mental embryology, and psychogenesis is a part of embryogenesis that does not end at the birth of a child, since the child is constantly influenced by the environment, due to which his thinking adapts to reality.
The fundamental hypothesis of genetic epistemology, Piaget points out, is that there is a parallelism between the logical and rational organization of knowledge and the corresponding formative psychological process. Accordingly, he seeks to explain the emergence of knowledge on the basis of the origin of representations and operations, which are largely, if not entirely, based on common sense.
Especially actively the problem of growth (development, change of knowledge) was developed, starting from the 60s. XX century, supporters of postpositivism K. Popper, T. Kuhn, I. Lakatos.
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I. Lakatos (1922-1974), a Hungarian-British philosopher and methodologist of science, a student of Popper, already in his early work "Proofs and Refutations" clearly stated that "the dogmas of logical positivism are disastrous for the history and philosophy of mathematics." The history of mathematics and the logic of mathematical discovery, i.e. "phylogenesis and ontogeny of mathematical thought" cannot be developed without criticism and the final rejection of formalism.
Lakatos contrasts the latter (as the essence of logical positivism) with a program for analyzing the development of meaningful mathematics, based on the unity of the logic of proofs and refutations. This analysis is nothing but a logical reconstruction of the real historical process of scientific knowledge. The line of analysis of the processes of change and development of knowledge is then continued by the philosopher in a series of his articles and monographs, which outline the universal concept of the development of science, based on the idea of competing research programs (for example, the programs of Newton, Einstein, Bohr, etc.).
Under the research program, the philosopher understands a series of successive theories, united by a set of fundamental ideas and methodological principles. Therefore, the object of philosophical and methodological analysis is not a single hypothesis or theory, but a series of theories replacing each other in time, i.e. some type of development.
Lakatos sees the growth of a mature (developed) science as a change in a series of continuously connected theories - and not separate, but a series (set) of theories, behind which there is a research program. In other words, not just two theories are compared and evaluated, but theories and their series, in a sequence determined by the implementation of the research program. According to Lakatos, the fundamental unit of evaluation should not be an isolated theory or set of theories, but a "research program". The main stages in the development of the latter, according to Lakatos, are progress and regression, the boundary of these stages is the “saturation point”. New program must explain what the old one could not. The change in the main research programs is the scientific revolution.
Lakatos calls his approach a historical method of evaluating competing methodological concepts, while stipulating that he never claimed to give an exhaustive theory of the development of science. By proposing a "normative historiographical" version of the methodology of scientific research programs, Lakatos, in his words, tried to "dialectically develop that historiographical method of criticism."
P. Feyerabend, St. Tulmin.
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Art. Toulmin, in his evolutionary epistemology, considered the content of theories as a kind of "population of concepts", and presented the general mechanism of their development as the interaction of intra-scientific and extra-scientific (social) factors, emphasizing, however, the decisive importance of rational components. At the same time, he proposed to consider not only the evolution of scientific theories, but also problems, goals, concepts, procedures, methods, scientific disciplines and other conceptual structures.
Art. Toulmin formulated an evolutionist program for the study of science centered on the idea of the historical formation and functioning of "the standards of rationality and understanding that underlie scientific theories." The rationality of scientific knowledge is determined by its compliance with the standards of understanding. The latter change in the course of the evolution of scientific theories, interpreted by Toulmin as a continuous selection of conceptual innovations. He considered very important the requirement of a concrete historical approach to the analysis of the development of science, the "multidimensionality" (comprehensiveness) of the image of scientific processes with the involvement of data from sociology, social psychology, the history of science and other disciplines.
The famous book by K.A. Popperatak is called: "Logic and the growth of scientific knowledge." The need for the growth of scientific knowledge becomes apparent when the use of theory does not give the desired effect.
Real science should not be afraid of refutation: rational criticism and constant correction with facts is the essence of scientific knowledge. Based on these ideas, Popper proposed a very dynamic concept of scientific knowledge as a continuous stream of assumptions (hypotheses) and their refutation. He likened the development of science to the Darwinian scheme of biological evolution. Constantly put forward new hypotheses and theories must undergo strict selection in the process of rational criticism and attempts at refutation, which corresponds to the mechanism of natural selection in the biological world. Only the "strongest theories" should survive, but they cannot be regarded as absolute truths either. All human knowledge is conjectural in nature, any fragment of it can be doubted, and any provisions should be open to criticism.
New theoretical knowledge for the time being fits into the framework existing theory. But there comes a stage when such an inscription is impossible, there is a scientific revolution; The old theory has been replaced by a new one. Some of the former supporters of the old theory are able to assimilate the new theory. Those who cannot do this remain with their former theoretical guidelines, but it becomes increasingly difficult for them to find students and new supporters.
T. Kuhn, P. Feyerabend.
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P. Feyerabend (1924 - 1994) - American - Austrian philosopher and methodologist of science. In line with the main ideas of postpositivism, he denies the existence of objective truth, the recognition of which he regards as dogmatism. Rejecting both the cumulative nature of scientific knowledge and the continuity in its development, Feyerabend defends scientific and ideological pluralism, according to which the development of science appears as a chaotic heap of arbitrary upheavals that do not have any objective grounds and are not rationally explicable.
P. Feyerabend proceeded from the fact that there are many equal types of knowledge, and this circumstance contributes to the growth of knowledge and the development of the individual. The philosopher is in solidarity with those methodologists who consider it necessary to create a theory of science that will take history into account. This is the path that must be followed if we are to overcome the scholasticism of modern philosophy of science.
Feyerabend concludes that it is impossible to simplify science and its history, to make them poor and monotonous. On the contrary, the history of science, and the scientific ideas and thinking of their creators should be considered as something dialectical - complex, chaotic, full of errors and diversity, and not as something unchanged or one-line process. In this regard, Feyerabend is concerned that science itself, its history, and its philosophy develop in close unity and interaction, because their growing separation harms each of these areas and their unity as a whole, and therefore this negative process must be put to an end.
The American philosopher considers the abstract-rational approach to the analysis of the growth and development of knowledge insufficient. He sees the limitations of this approach in the fact that, in fact, it separates science from the cultural and historical context in which it resides and develops. Purely rational theory The development of ideas, according to Feyerabend, focuses mainly on the careful study of "conceptual structures", including the logical laws and methodological requirements underlying them, but does not deal with the study of non-ideal forces, social movements, i.e. sociocultural determinants of the development of science. The philosopher considers the socio-economic analysis of the latter to be one-sided, since this analysis falls into the other extreme - revealing the forces that affect our traditions, it forgets, leaves aside the conceptual structure of the latter.
Feyerabend advocates the construction of a new theory of the development of ideas, which would be able to make clear all the details of this development. And for this, it must be free from these extremes and proceed from the fact that in the development of science in some periods the leading role is played by the conceptual factor, in others - by the social one. That is why it is always necessary to keep an eye on both these factors and their interaction.
The long stages of normal science in Kuhn's concept are interrupted by brief, however, dramatic periods of unrest and revolution in science - periods of paradigm shift. .
A period begins, a crisis in science, heated discussions, discussions of fundamental problems. The scientific community often stratifies during this period, innovators are opposed by conservatives who are trying to save the old paradigm. During this period, many scientists cease to be "dogmatists", they are sensitive to new, even immature ideas. They are ready to believe and follow those who, in their opinion, put forward hypotheses and theories that can gradually develop into a new paradigm. Finally, such theories are indeed found, most scientists again consolidate around them and begin to enthusiastically engage in "normal science", especially since the new paradigm immediately opens up a huge field of new unsolved problems.
Thus, the final picture of the development of science, according to Kuhn, takes the following form: long periods of progressive development and accumulation of knowledge within the framework of one paradigm are replaced by short periods of crisis, breaking the old and searching for a new paradigm. The transition from one paradigm to another Kuhn compares with the conversion of people to a new religious faith, firstly, because this transition cannot be explained logically and, secondly, because scientists who have adopted a new paradigm perceive the world significantly differently than before - even they see old, familiar phenomena as if with new eyes.
Kuhn believes that the transition of one paradigm and another through the scientific revolution (for example, at the end of the 19th - beginning of the 20th century) is a common developmental model characteristic of a mature science. In the course of the scientific revolution, there is such a process as a change in the "conceptual grid" through which scientists viewed the world. A change (moreover, a cardinal one) of this "grid" makes it necessary to change the methodological rules-prescriptions.
During the scientific revolution, all sets of methodological rules are abolished, except for one - the one that follows from the new paradigm and is determined by it. However, this abolition should not be a "bare negation", but a "sublation", with the preservation of the positive. To characterize this process, Kuhn himself uses the term "prescriptive reconstruction".
Scientific revolutions mark a change in the types of scientific rationality. A number of authors (V. S. Stepin, V. V. Ilyin), depending on the relationship between the object and subject of cognition, distinguish three main types of scientific rationality and, accordingly, three major stages in the evolution of science:
1) classical (XVII-XIX centuries);
2) non-classical (first half of the 20th century);
3) post-non-classical (modern) science.
Ensuring the growth of theoretical knowledge is not easy. The complexity of research tasks forces the scientist to achieve a deep understanding of his actions, to reflect . Reflection can be carried out alone, and, of course, it is impossible without the researcher independent work. At the same time, reflection is very often very successfully carried out in the conditions of an exchange of opinions between the participants in the discussion, in the conditions of dialogue. modern science has become a matter of collective creativity; accordingly, reflection often acquires a group character.
Analysis and synthesis
Analysis(gr. analysis- decomposition) is a research method, the content of which is a set of techniques and patterns dismemberment(mental or real) subject research into constituent parts. Such parts can be separate real elements of the object or its properties and relations.
Synthesis(gr. synthesis- connection) is a method of research, the content of which is a set of techniques and laws of connection of individual parts of an object into a single whole.
Synthesis - a combination (mental or real) of various elements of an object into a single whole (system) - is inextricably linked with analysis (dismemberment of an object into elements).
As can be seen from the definition of these methods, they are opposites, mutually suggesting and complementing each other.
The whole history of cognition teaches that analysis and synthesis will only then be fruitful methods of cognition when they are used in close unity.
These paired, interrelated research methods occupy a somewhat special position in the system of scientific methods.
Deduction(lat. deductio - derivation) - conclusion according to the rules of logic; a chain of inferences (reasoning), the links of which (statements) are connected by a relation of logical consequence. The beginning of deduction is axioms, postulates, or simply hypotheses that have the character of general statements (general), and the end is consequences from premises, theorems (particular). If the premises of the deduction are true, then so are its consequences. Deduction is the main means of proof.
The role of deduction in research is steadily increasing. This is due to the fact that science is increasingly confronted with such objects that are inaccessible to sensory perception (the microworld, the universe, the past of mankind, etc.).
When cognizing objects of this kind, it is much more often necessary to turn to the power of thought than to the power of observation or experiment. Deduction is also indispensable in all areas of knowledge where theoretical statements are formed to describe formal rather than real systems (for example, in mathematics).
Deduction favorably differs from other methods of research in that, if the initial knowledge is true, it gives true output knowledge.
Induction is usually understood as a conclusion from the particular to the general, when, on the basis of knowledge about a part of objects of a certain class, a conclusion is made about the class as a whole.
Induction(lat. induction- guidance) - a conclusion from private, single facts to some hypothesis (general statement). A distinction is made between complete induction, when the generalization refers to a finitely visible field of facts, and incomplete induction, when it refers to an infinitely or finitely invisible field of facts.
In a broader sense, induction is a method of cognition as a set of cognitive operations, as a result of which the movement of thought from less general provisions to more general ones is carried out. Consequently, the difference is revealed, first of all, in the directly opposite direction of the course of thought.
The immediate basis of inductive reasoning is the repetition of the phenomena of reality and their signs. Finding similar features in many objects of a certain class, we conclude that these features are inherent in all objects of this class.
In inductive research, the central place is occupied by inductive reasoning. They are divided into the following main groups:
full induction - this is such a conclusion in which a general conclusion about a class of objects is made on the basis of the study of all objects of the class. It gives reliable conclusions, so full induction is widely used as a proof;
incomplete induction- this is such a conclusion in which the general conclusion is obtained from premises that do not cover all objects of the class. There are three types of incomplete induction:
a) induction through simple enumeration, or popular induction, represents a conclusion in which a general conclusion about a class of objects is made on the basis that among the observed facts there was not a single one that contradicted the generalization;
b) induction through selection of facts carried out not on the basis of the first
facts that have come across, but by selecting them from the general mass according to a certain
principle that reduces the likelihood of random coincidences.
For example, the warehouse received understaffed computers, you can check their entire supply different ways: examine all incoming computers of the same batch, or selectively examine computers from different batches and different types. It is clear that in the second case the conclusion will be more plausible;
in) scientific induction -- a conclusion in which a general conclusion about all the objects of a class is made on the basis of knowledge of the necessary signs of causal relationships of a part of the objects of the class. Scientific induction can
give not only probable (like the other two above types
complete induction), but also reliable conclusions.
Establishing the causal connection of phenomena is a very complex process. However, in the simplest cases, the causal connection of phenomena can be established using logical techniques called methods for establishing causation, or methods of scientific induction. There are five such methods:
single similarity method - its essence lies in the fact that "if two or more cases of the phenomenon under study have only one circumstance in common, and all other circumstances are different, then this only similar circumstance is the cause of this phenomenon;
single difference method - its essence lies in the fact that if the case in which the phenomenon under study occurs, and the case in which it does not occur, are similar in everything and differ only in one circumstance, then this circumstance, present in the first case and absent in the second, is the cause of the phenomenon under study;
combined method of similarity and difference, which is a combination of the first two methods;
concomitant change method- its essence lies in the fact that if the occurrence or change of one phenomenon every time necessarily causes a certain change in another phenomenon, then both of these phenomena are in a causal relationship with each other;
residual method- if a complex phenomenon is caused by a complex cause consisting of a set of certain circumstances, and we know that some of these circumstances are the cause of part of the phenomenon, then the remainder of this phenomenon is caused by the rest of the circumstances. Even a brief description of the method of induction shows its attractiveness and strength. This power is primarily close connection with facts, with practice.
Induction and deduction are closely related and complement each other. Inductive research involves the use of general theories, laws, principles, i.e. includes the moment of deduction, and, on the contrary, deduction is impossible without general provisions obtained by induction.
Logical conclusions often become the subject of philosophical reflection, especially when it comes to epistemology. This happened with such types of cognition as induction and deduction. Both of these methods are a means of obtaining information and new knowledge. It's just that philosophers understand by induction a logical transition from the particular to the general, and by deduction - the art of deriving conclusions from theoretical positions. However, do not assume that both of these methods are opposites.
Of course, when Francis Bacon said his famous phrase that knowledge is power, he had in mind precisely the potency of induction. But the second method should not be underestimated. In the modern sense, deduction is more of a control nature and helps to verify the hypotheses obtained through induction.
What's the Difference?
The method of deduction and induction in philosophy is associated with logic, but at the same time we are talking about two different types of reasoning. When we go from one premise to another, and then to conclusions, the truth of the latter depends on the correctness of our initial foundations. This is what deduction looks like. It relies on the clarity and necessity of logical laws. If we are talking about induction, then in this case the conclusions come first from the facts - material, psychological, legal, and so on. Such conclusions are less formal than deductive ones. Therefore, the connections between the facts that follow from these conclusions are probabilistic (or hypothetical). They need further testing and verification.
How did the concept of "induction" appear in philosophy
The English thinker Francis Bacon, analyzing the state of contemporary science, considered it deplorable due to the lack of the necessary method. He proposed it in his New Organon to replace the rules of logic proposed by Aristotle. Bacon believed that four obstacles stand in the way of knowledge, which he called idols. This admixture to knowledge human nature, individual subjectivity, incorrect terminology and misconceptions based on axioms or authorities of the past. From the point of view of the English scientist, real knowledge can only come from the generalization of sensory experience. This is how induction in philosophy appeared.
Examples of its application are given by the same Francis Bacon. If we watch the lilac every year and see that it is white, then in this garden all these trees bloom in only one color. That is, our conclusions are based on the assumption that if the experiment gives us such and such data, then this will happen in all similar cases.
What is dangerous one-way method
Conclusions in inductive reasoning can be erroneous. And if we constantly rely on them and do not check them deductively, then we can move away from the real meaning of the connection between facts. But aren't we guided in our lives - subconsciously and one-sidedly - only by inductive reasoning? For example, in given circumstances, we have always adopted such and such an approach to solving a problem, and this has brought us success. So, we will continue to act in this way, without changing anything. But after all, our experience is not facts, but only our idea of them. But often we treat our concepts as a kind of axioms. This leads to incorrect conclusions.
Why induction is imperfect
Although this method at one time looked very revolutionary, as we see, one cannot rely only on it. Now it's time to talk about what is complete and incomplete induction. Philosophy offers us the following definitions.
Complete induction is an ideal situation where we are dealing with a certain number of special cases that exhaust all possible options. This means that we have collected all the facts, made sure that their number is finite, and on this basis we prove our assertion. Incomplete induction is much more common. From observation of individual facts, we draw some hypothetical conclusions. But since we do not know whether the result will be the same in all particular cases, we must understand that our conclusion is only probabilistic in nature and needs to be verified. That is why we should constantly critically evaluate our experience and supplement it with new information.
Model that limits cognition
Induction in philosophy is the deliberate simplification of complex structures in order to create an intelligible picture of the world. When we observe different phenomena, we generalize them. From this we draw conclusions about the connections between phenomena and add up a single picture from them. It allows us to make choices and prioritize, to determine what is important to us and what is not. But if we lose control of the situation and begin to replace the facts with our own opinion about them, then we will inevitably begin to adjust everything that we see to ourselves. Thus, the presence of induction alone limits knowledge. After all, as a rule, it is incomplete. Therefore, almost all universal generalizations made with its help suggest the possibility of exceptions.
How to use induction
We need to understand that the use of this method alone replaces the diversity of the world with simplified models. This gives us a kind of weapon against the limitations that induction in philosophy is fraught with. This understanding is often justified by the thesis that there are no universal theories. Even Karl Popper said that any concept can either be recognized as falsified, and therefore it should be rejected, or it has not yet been sufficiently tested, and therefore we have not yet proven that it is incorrect.
Another thinker, Nassim Taleb, reinforces this argument with the observation that any large number of white swans does not give us the right to claim that all these birds are of the same color. Why? But because one black swan is enough to smash your conclusions to smithereens. Induction thus helps us to generalize information, but at the same time forms stereotypes in our brain. They are also needed, but we can use them until at least one fact appears that refutes our conclusion. And when we see this, we should not adjust it to fit our theory, but look for a new concept.
Deduction
Let us now consider the second method of cognition, its pros and cons. The very word "deduction" means derivation, logical connection. This is the transition from broad knowledge to specific information. If in philosophy induction is the receipt of general judgments based on empirical knowledge, then deduction proceeds from information and connections between facts that are already proven, that is, existing. This means that it has a higher degree of reliability. Therefore, it is often used to prove mathematical theorems. The founder of deduction is Aristotle, who described this method as a chain of inferences, also called syllogistics, where the conclusion is obtained from premises according to clear formal rules.
Deduction and Induction - Bacon vs. Aristotle
In the history of philosophy, these two methods of cognition were constantly opposed. Aristotle, by the way, was also the first to describe induction, but he called it dialectics. He stated that the conclusions drawn in this way are the opposite of the analytical ones. Bacon, as we have seen, preferred induction. He developed several rules for gaining knowledge using this method. Causal relationships between different phenomena, from his point of view, can be established by analogy of differences, similarities, residues, as well as the presence of concomitant changes. Having absolutized the role of experiment, Bacon declared that in philosophy induction is a universal method of epistemology. Just like in any science. However, eighteenth-century rationalism and the development of theoretical mathematics challenged his conclusions.
Descartes and Leibniz
These French and German philosophers brought back the interest in the deductive method. Descartes raised the question of authenticity. He stated that mathematical axioms are obvious propositions that do not require proof. Therefore, they are reliable. Therefore, if you follow the rules of logic, then the conclusions from them will also be true. Therefore, deduction is a good scientific method if a few simple rules are followed. It is necessary to proceed only from what has been proven and verified, to divide the problem into its component parts, to move from simple to complex and not be one-sided, but to check all the details.
Leibniz also argued that deduction can be used in other branches of science. Even those studies that are carried out on the basis of experiments, he said, in the future will be carried out with a pencil in hand and using universal symbols. Deduction and induction thus divided scientists in the nineteenth century into two parties, who were for or against one method or the other.
Modern epistemology
The ability to reason logically and base one's knowledge on facts rather than assumptions was valued not only in the past. It will always come in handy in our world with you. Modern thinkers believe that in philosophy, induction is an argument based on a degree of probability. Its methods are applied depending on how they are suitable for solving the problem you are facing.
AT practical life it looks like this. If you want to go to some hotel, then you start looking at reviews about it and you see that the hotel has a high rating. This is an inductive argument. But for the final decision, you need to understand whether you have enough budget for such a vacation, whether you personally like living there and how objective the estimates were. That is, you need more information.
Deduction, on the other hand, is used in cases where the so-called validity criterion can be applied. For example, your vacation is only possible in September. A highly rated hotel closes in August, while another hotel stays open until October. The answer is obvious - you can go on vacation only where it can be done in the fall. This is how deduction is used not only in philosophy, but also in everyday life.
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