Methods of induction and deduction in philosophy. The meaning of "induction in philosophy. The formation of philosophy. Main directions, schools of philosophy and stages of its historical development
In 1831, the world first learned about the concept of electromagnetic induction. It was then that Michael Faraday discovered this phenomenon, which eventually became the most important discovery in electrodynamics.
History of development and experiments of Faraday
Until the middle of the 19th century, it was believed that the electric and magnetic fields had no connection, and the nature of their existence was different. But M. Faraday was sure of the common nature of these fields and their properties. The phenomenon of electromagnetic induction, discovered by him, subsequently became the foundation for the construction of generators of all power plants. Thanks to this discovery, mankind's knowledge of electromagnetism has stepped far forward.
Faraday did the following experiment: he closed the circuit in coil I and the magnetic field increased around it. Further, the lines of induction of this magnetic field crossed coil II, in which an induction current arose.
Rice. 1. Scheme of the Faraday experiment
In fact, at the same time as Faraday, but independently of him, another scientist, Joseph Henry, discovered this phenomenon. However, Faraday published his research earlier. Thus, Michael Faraday became the author of the law of electromagnetic induction.
No matter how many experiments Faraday conducted, one condition remained unchanged: for the formation of an induction current, it is important to change the magnetic flux penetrating a closed conducting circuit (coil).
Faraday's law
The phenomenon of electromagnetic induction is determined by the occurrence of electric current in a closed electrically conductive circuit when the magnetic flux changes through the area of this circuit.
Faraday's basic law is that the electromotive force (EMF) is directly proportional to the rate of change of magnetic flux.
The formula for Faraday's law of electromagnetic induction is as follows:
Rice. 2. Formula of the law of electromagnetic induction
And if the formula itself, based on the above explanations, does not raise questions, then the “-” sign may raise doubts. It turns out that there is a rule of Lenz - a Russian scientist who conducted his research based on the postulates of Faraday. According to Lenz, the “-” sign indicates the direction of the emerging EMF, i.e. the inductive current is directed in such a way that the magnetic flux that it creates, through the area bounded by the circuit, tends to prevent the change in flux that this current causes.
Faraday-Maxwell law
In 1873, J.K. Maxwell re-stated the theory of the electromagnetic field. The equations that he derived formed the basis of modern radio engineering and electrical engineering. They are expressed as follows:
- Edl = -dФ/dt– electromotive force equation
- Hdl = -dN/dt is the equation of the magnetomotive force.
Where E is the electric field strength in the section dl; H is the magnetic field strength in the section dl; N is the flow of electrical induction, t- time.
The symmetrical nature of these equations establishes a connection between electrical and magnetic phenomena, as well as magnetic and electrical ones. the physical meaning by which these equations are determined can be expressed in the following terms:
- if the electric field changes, then this change is always accompanied by a magnetic field.
- if the magnetic field changes, then this change is always accompanied by an electric field.
Rice. 3. Emergence of a vortex magnetic field
Maxwell also established that the propagation of an electromagnetic field is equal to the speed of propagation of light.
What have we learned?
11th grade students need to know that electromagnetic induction was first discovered as a phenomenon by Michael Faraday. He proved that electric and magnetic fields have a common nature. Independent research based on the experiments of Faraday was also carried out by such great figures as Lenz and Maxwell, who expanded our knowledge in the field of the electromagnetic field.
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guidance) - the movement of knowledge from the individual to the universal, from the special to the regular. The opposite of induction is deduction. Induction as a method of research is substantiated and developed by Bacon.
Great Definition
Incomplete definition ↓
INDUCTION
from lat. inductio - guidance), a type of generalization associated with the anticipation of the results of observations and experiments based on experimental data. In I., the data of experience “lead” to the general, or induce the general, therefore inductive generalizations are usually considered as experimental truths or empirical. the laws. In relation to the infinity of the phenomena covered by the law, the actual. Experience is always incomplete and incomplete. This feature of experience is included in the content of I., making it problematic: it is impossible to speak with certainty about the truth of an inductive generalization or about its logical. validity, since no finite number of confirming observations "... by itself can ever prove necessity in a sufficient way" (Engels F., see Marx K. and Engels F., Soch., vol. 20, p. 544) . In this sense, I. is an anticipation of the foundation (petitio principii), on which they go for the sake of generalizations, taking I. as a source of assumptions. judgments - hypotheses, to-rye are then tested or substantiated in a system of more "reliable" principles.
The laws of nature and society serve as the objective basis of I.; subjective - the cognizability of these patterns with the help of logical. or statistic. schemes of "inductive reasoning". Logic schemes are applied on the assumption that phenomena (results of observations or experiments) are not random; statistical ones, on the other hand, are based on the assumption of the “randomness of phenomena”. Statistical hypotheses are assumptions about a theoretical laws of distribution of random features or estimation of parameters that determine the expected distributions in the studied sets. The task of the statistical I. are the evaluation of inductive hypotheses as functions of sample characteristics and the acceptance or rejection of hypotheses based on these characteristics.
Historically, the first logical circuit. I. is an enumerative (popular) I. It arises when, in special cases, k.-l. regularity (for example, the repetition of properties, relationships, etc.), which allows one to build a sufficient representation. a chain of singular judgments stating this regularity. In the absence of contradictory examples, such a chain becomes a formal basis for a general conclusion (inductive hypothesis): what is true in n observed cases is true in the next or in all cases similar to them. When the number of all similar cases is equal to the number considered, the inductive generalization is a complete account of the facts. Such an I. is called complete, or perfect, since it is expressible by a deductive inference scheme. If the number of similar cases is finitely unobservable or infinite, one speaks of incomplete I. Incomplete I. is called scientific, if, in addition to the formal one, a real basis of I. is also given by proving the non-randomness of the observed regularity, for example. by indicating the cause-and-effect relationships (dynamic patterns) that generate this regularity. Schemes of inference offered by the logic of I. for "catching" cause and effect. relations are called inductive methods of Bacon - Mill; the use of these schemes presupposes, in turn, sufficiently strong abstractions, the justification of which is tantamount to the justification of an incomplete I.
The generally accepted ways of justifying the logical. I. is not yet available, just as they are not available for statistical. schemes, to-rye are justified only by the fact that they rarely give erroneous results. Since I. is comparable to decision-making under conditions of uncertainty, probabilistic criteria play a significant role in the structure of the so-called. inductive behaviour. For example, an inductive hypothesis is accepted if a fact is known that induces it with a high probability, and rejected if such a fact is unlikely. But probabilistic criteria are not the only ones. The statistics of supporting examples cannot, for example, justify the adoption of the natural sciences. laws obtained by I., the a priori probability of which is negligible. This, however, does not contradict the probabilistic approach to I., but only confirms its rule: the smaller the a priori probability of a “working” hypothesis, the greater the chances for its “non-randomness”, for the fact that it adequately reflects the state of nature. Particularly convincing of this is the possibility of including an inductive law in a known system of knowledge, of proving its compatibility with this system or its deducibility in it. Sometimes it is possible to do more - by an abstract reasoning, to show that, although a generalization is made on particular examples, its truth does not depend on these and similar examples, if only certain other reasonings are true. The latter may have a great power of persuasiveness or even be generally valid, which leads to a purely logical. substantiation of I. This is exactly the case, for example, in mathematics, where incomplete I. is checked or substantiated by the method of mathematical I.
Two examples of inductive reasoning:
The Yenisei flows from south to north; The Lena flows from south to north; The Ob and Irtysh flow from south to north.
Yenisei, Lena, Ob, Irtysh are large rivers of Siberia. All major rivers of Siberia flow from south to north.
Iron is a metal; copper - metal; potassium - metal; calcium -
metal; ruthenium - metal; uranium is a metal.
Iron, copper, potassium, calcium, ruthenium, uranium - chemical
elements.
All chemical elements are metals.
The premises of both these inferences are true, but the conclusion of the first is true and the second is false.
The concept of deduction (deductive reasoning) is not quite clear. I. (inductive reasoning) is defined, in essence, as "non-deduction" and is an even less clear concept. It is possible to indicate darker less relatively solid "core" of inductive modes of reasoning. It includes, in particular, incomplete I., inductive methods for establishing causal relationships, analogy, the so-called. "inverted" laws of logic, etc.
Incomplete I. is a reasoning that has the following structure:
S1 is P, S2 is P,
All S1, S2,..., Sn are S.
All S are R.
The assumptions of this reasoning say that objects S1, S2, ..., Sn, which do not exhaust all objects of class S, have the characteristic P and that all the listed objects S1, S2, ..., Sn belong to class S. In conclusion, it is stated that all S have the attribute P. For example:
Forged iron.
Forged gold.
Lead forging.
Iron, gold and lead are metals.
All metals are forged.
Here, from the knowledge of only some objects of the class of metals, a general conclusion is drawn that applies to all objects of this class.
Inductive generalizations are widely used in empirical argumentation. Their persuasiveness depends on the number of cases cited in support. The larger the base of the induction, the more plausible is the inductive conclusion. But sometimes, even with a sufficiently large number of confirmations, the inductive generalization still turns out to be erroneous. For example:
Aluminum is a solid body.
Iron, copper, zinc, silver, platinum, gold, nickel, barium, potassium, lead are solids.
Aluminum, iron, copper, zinc, silver, platinum, gold, nickel, barium, potassium, lead are metals.
All metals are solids.
All premises of this reasoning are true, but its general conclusion is false, since mercury is the only one of the metals that is a liquid.
Hasty generalization, i.e., generalization without sufficient grounds, is a common mistake in inductive reasoning and, accordingly, in inductive reasoning. Inductive generalizations always require a certain prudence and caution. Their persuasive power is small, especially if the base of induction is insignificant ("Sophocles is a playwright; Shakespeare is a playwright; Sophocles and Shakespeare are people; therefore, every person is a playwright"). Inductive generalizations are good as a means of finding assumptions (hypotheses), but not as a means of confirming some assumptions and arguing in support of them.
The systematic study of I. began at the beginning of the 17th century. F. Bacon. Already he was very skeptical about the incomplete I., based on a simple enumeration of supporting examples.
Bacon contrasted this "childish thing" with the special inductive principles he described for establishing causal relationships. He even believed that the inductive way of discovering knowledge he proposed, which is a very simple, almost mechanical procedure, "almost equalizes talents and leaves little to their superiority ...". Continuing his thought, we can say that he hoped almost for the creation of a special "inductive machine". Entering into such a computer all sentences related to observations, we would get at the output an exact system of laws explaining these observations.
Bacon's program was, of course, pure utopia. No "inductive machine" processing facts into new laws and theories is possible. I., leading from single statements to general ones, gives only probable, and not reliable knowledge.
It has been suggested that all "inverted" laws of logic can be attributed to schemes of inductive reasoning. Under the "inverted" laws are meant formulas obtained from the laws of logic, which have the form of an implication (conditional statement), by changing the places of the foundation and the consequence. For example, since the expression "If p and q, then p" is a law of logic, then the expression "If p, then p and q" is a scheme of inductive reasoning. Similarly for "If p, then p or q" and "If p or q, then p", etc. Similar for the laws of modal logic: since the expressions "If p, then p is possible" and "If necessary p, then p " - the laws of logic, the expressions "If p is possible, then p" and "If p, then p is necessary" are schemes of inductive reasoning, etc. There are infinitely many laws of logic. This means that there are an infinite number of schemes of inductive reasoning (inductive argumentation).
The assumption that "inverted" laws of logic are schemes of inductive reasoning runs into serious objections: some "inverted" laws remain laws of deductive logic; a number of "inverted" laws, when interpreted as I.'s schemes, sounds very paradoxical. "Inverted" laws of logic do not exhaust, of course, all possible schemes
Great Definition
Incomplete definition ↓
Induction
By their nature, induction and deduction are special cases of inference.
Inference is a logical operation, as a result of which a new statement appears from one or more accepted statements - a conclusion (conclusion).
Induction (Latin inductio - guidance) is the process of inference based on the transition from a particular position to a general one. Inductive reasoning relates particular premises to the conclusion not strictly through the laws of logic, but rather through some factual, psychological or mathematical representations.
The objective basis of inductive reasoning is the universal connection of phenomena in nature.
Distinguish between complete induction - a method of proof, in which the statement is proved for a finite number of special cases that exhaust all possibilities, and incomplete induction - observations of individual special cases lead to a hypothesis, which, of course, needs to be proven. The method of mathematical induction is also used for proofs.
History of induction
The term first appears in Socrates. But Socrates' induction has little in common with modern induction. Socrates by induction means finding a general definition of a concept by comparing particular cases and excluding false, too narrow definitions.
Aristotle pointed out the features of inductive reasoning. He defines it as an ascent from the particular to the general. He distinguished complete induction from incomplete induction, pointed out the role of induction in the formation of first principles, but did not clarify the basis of incomplete induction and its rights. He considered it as a way of reasoning, the opposite of syllogism. Syllogism, according to Aristotle, indicates by means of the middle concept that the higher concept belongs to the third, and induction by the third concept shows the belonging of the higher to the middle.
In the Renaissance, a struggle began against Aristotle and the syllogistic method, and at the same time they began to recommend the inductive method as the only fruitful one in natural science and the opposite of the syllogistic one. In Bacon, they usually see the ancestor of modern I., although justice requires mentioning his predecessors, for example, Leonardo da Vinci and others. In praising I., Bacon denies the significance of the syllogism. According to Bacon's method, it is impossible to draw a new conclusion without bringing the subject under investigation under general judgments, that is, without resorting to a syllogism. So, Bacon failed to establish I. as a special method, opposite to the deductive one.
The next step is taken by J. St. Mill. Every syllogism, according to Mill, contains; every syllogistic conclusion actually proceeds from the particular to the particular, and not from the general to the particular. This criticism of Mill is unfair, because we cannot conclude from the particular to the particular without introducing an additional general proposition about the similarity of particular cases to each other. Considering induction, Mill, firstly, asks the question of the basis or the right to an inductive conclusion and sees this right in the idea of a uniform order of phenomena, and, secondly, reduces all methods of inference in I. to four main ones: the method of agreement (if two or more cases of the phenomenon under study converge in only one circumstance, then this circumstance is the cause or part of the cause of the phenomenon under study, the method of difference (if the case in which the phenomenon under study occurs and the case in which it does not occur are completely similar in all details, with the exception of the one under investigation, the circumstance that occurs in the first case and is absent in the second is the cause or part of the cause of the phenomenon under study); method of residuals (if in the phenomenon under study part of the circumstances can be explained by certain reasons, then the remaining part of the phenomenon is explained from the remaining previous facts ) and the method of the corresponding changes (if, after the change of one phenomenon, change of the other, then we can infer a causal relationship between them). Characteristically, these methods, on closer examination, turn out to be deductive methods; e.g. the remainder method is nothing more than a determination by elimination. Aristotle, Bacon and Mill represent the main points in the development of the doctrine of induction; only for the sake of detailed development of some questions one has to pay attention to Claude Bernard ("Introduction to experimental medicine"), to Esterlen ("Medicinische Logik"), Herschel, Liebig, Wevel, Apelt and others.
DEDUCTION AND INDUCTION METHODS
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. However, these forms of thinking are also considered as special methods, methods of cognition.
The purpose of our work is on the basis of the essence of deduction and induction, to substantiate their unity, inseparable connection, and thereby show the inconsistency of attempts to oppose deduction and induction, exaggerate the role of one of these methods by diminishing the role of the other.
Let us reveal the essence of these methods of cognition.
Deduction (from lat. deductio - derivation) - the transition in the process of cognition from general knowledge about a certain class of objects and phenomena to knowledge private and single. 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, 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.
Analysis- the process of mental, and often real, dismemberment of an object, phenomenon into parts (signs, properties, relationships) with the aim of their comprehensive study. The reverse procedure of analysis is synthesis. Synthesis- this is a combination of the sides of the subject selected during the analysis into a single whole. Analysis and synthesis are the most elementary and simple methods of cognition that lie at the very foundation of human thinking.
In the process of research, it is often necessary, based on existing knowledge, to draw conclusions about the unknown. Passing from the known to the unknown, one can either use knowledge about individual facts, or, conversely, relying on general principles, draw conclusions about particular phenomena.
what is induction and deduction in philosophy
- Induction (from Latin inductio - guidance, motivation) is a formal logical conclusion that leads to a general conclusion based on particular premises. In other words, it is the movement of our thinking from the particular 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. Along with other methods of knowledge, the inductive method played an important role in the discovery of some laws of nature (universal gravity, atmospheric pressure, thermal expansion of bodies, etc.).
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 residues (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.
In fact, the above methods of scientific induction serve mainly to find empirical relationships between the experimentally observed properties of objects and phenomena.
Deduction (from lat. deductio - derivation) is the receipt of particular 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.
But the especially great cognitive significance of deduction is manifested in the case when the general premise is not just an inductive generalization, but some kind of hypothetical assumption, for example, a new scientific idea. In this case, deduction is the starting point for the birth of a new theoretical system. The theoretical knowledge created in this way predetermines the further course of empirical research and directs the construction of new inductive generalizations.
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.
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.
- These are methods of knowing the world.
Briefly:
* deduction - from the general to the particular;
* induction - from the particular to the general.And in general, there is Wikipedia.