Deduction is a special case of inference.
In a broad sense inference - a logical operation, as a result of which a new statement is obtained from one or more accepted statements (premisses) - a conclusion (conclusion, consequence).
Depending on whether there is a connection of logical consequence between the premises and the conclusion, two types of inferences can be distinguished.
AT deductive reasoning this connection is based on a logical law, whereby the conclusion follows with logical necessity from the premises accepted. Distinctive feature such an inference is that it always leads from true premises to a true conclusion.
AT inductive reasoning the connection of premises and conclusions is not based on the law of logic, but on some factual or psychological grounds that do not have a purely formal character. In such a mind-
conclusion does not follow logically from sprinkles and may contain information not found 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 requiring further verification.
Examples of deductive reasoning include:
If it rains, the ground is wet.
It's raining.
The ground is wet.
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".
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 discussed is a certain degree of probability of the statement being deduced. So, the premises of both the first and second inductive reasoning 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 countries of Western Europe there are not only republics, but also monarchies, such as England, Belgium, and Spain.
Especially characteristic deductions are logical transitions from general knowledge to a particular type:
All people are mortal.
All Greeks are people.
Therefore, all Greeks are mortal.
In all cases when it is required to consider some phenomena on the basis of an already known general rule and draw the necessary conclusion regarding these phenomena, we conclude in the form of deduction. Reasoning leading from knowledge about a part of objects (private knowledge) to knowledge about all objects of a certain class (general knowledge) are typical inductions. There is always the possibility that the generalization will turn out to be hasty and unfounded (“Napoleon is a commander; Suvorov is a commander; therefore, every person is a commander”).
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. In reasoning “Shakespeare wrote sonnets; therefore, it is not true that Shakespeare did not write sonnets” is a deduction, but there is no transition from the general to the particular. The argument "If aluminum is ductile or clay is ductile, then aluminum is ductile" is commonly thought to be inductive, but there is no transition from the particular to the general. Deduction is the derivation of conclusions that are as reliable as the accepted premises, induction is the derivation of probable (plausible) conclusions. Inductive reasoning includes both transitions from the particular to the general, as well as analogy, methods of establishing causation, confirmation of consequences, target justification, etc.
The special interest shown in deductive reasoning is understandable. They make it possible to obtain new truths from existing knowledge, and, moreover, with the help of pure reasoning, without resorting to experience, intuition, common sense, etc. Deduction gives a 100% guarantee of success, and does not simply provide one or another - perhaps a high - probability of a true conclusion. Starting from true premises and reasoning deductively, we will certainly obtain reliable knowledge in all cases.
While emphasizing the importance of deduction in the process of expanding and substantiating knowledge, one should not, however, separate it from induction and underestimate the latter. Almost all general propositions, including scientific laws, are the results of inductive generalization. In this sense, induction is the basis of our knowledge. It does not in itself guarantee its truth and validity, but it generates conjectures, connects them with experience, and thereby imparts to them a certain likelihood, 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.
All previously considered reasoning schemes were examples of deductive reasoning. Propositional logic, modal logic, the logical theory of categorical syllogism - all these are sections of deductive logic.
Ordinary deductions
So, deduction is the derivation of conclusions that are as certain as the accepted premises.
In ordinary reasoning, deduction appears in full and expanded form only in rare cases. Most often, we do not indicate all the parcels used, but only some. 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 initial and derivable statements is only sometimes marked by words like "therefore" and "means",
Often the deduction is so abbreviated that it can only be guessed at. It is not easy to restore it in full form, indicating all the necessary elements and their relationships.
“Thanks to a long habit,” Sherlock Holmes once remarked, “a chain of inferences arises in me so quickly that I came to a conclusion without even noticing the intermediate premises. However, they were, these parcels, "
To carry out deductive reasoning without omitting or reducing anything is quite cumbersome. A person who points out all the premises of his conclusions gives the impression of a petty pedant. And together with
Therefore, 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, possessing rare powers of observation and an excellent command of the method of deduction. 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 a mountain 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 suffers from 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.
Sherlock Holmes became a very popular character. There were even jokes about him and his creator.
For example, in Rome, Conan Doyle takes a cab, and he says: "Ah, Mr. Doyle, I greet you after your trip to Constantinople and Milan!" "How could you know where I came from?" said Conan Doyle in surprise at Sherlockholmes' insight. “According to the stickers on your suitcase,” the coachman smiled slyly.
This is another deduction, very abbreviated and simple.
Deductive reasoning
Deductive reasoning is the derivation of the justified position from other, previously adopted provisions. If the advanced position can be logically (deductively) deduced from the already established provisions, this means that it is acceptable to the same extent as these provisions. Justifying some statements by referring to the truth or acceptability of other statements is not the only function performed by deduction in the processes of argumentation. Deductive reasoning also serves to verification(indirect confirmation) of statements: from the checked position, its empirical consequences are deductively derived; confirmation of these consequences is evaluated as an inductive argument in favor of the original position. Deductive reasoning is also used to falsifications statements by showing that their consequences are false. Failed falsification is a weakened version of verification: failure to disprove the empirical consequences of the hypothesis being tested is an argument, albeit a very weak one, in support of this hypothesis. Finally, deduction is used to systematization theory or system of knowledge, tracing the logical connections of its constituent statements, constructing explanations and understandings based on the general principles proposed by the theory. The clarification of the logical structure of the theory, the strengthening of its empirical base and the identification of its general prerequisites is an important contribution to the justification of the statements included in it.
Deductive reasoning is universal, applicable in all fields of knowledge and in any audience. “And if bliss is nothing but eternal life,” writes the medieval philosopher I.S. Eriugena, “and eternal life is the knowledge of truth, then
bliss - it is nothing but the knowledge of the truth.” This theological reasoning is a deductive reasoning, namely a syllogism.
The share of deductive reasoning in different fields of knowledge is significantly different. It is very widely used in mathematics and mathematical physics, and only sporadically in history or aesthetics. Bearing in mind the scope of deduction, Aristotle wrote: "Scientific evidence should not be required of a speaker, just as emotional persuasion should not be required of a mathematician." Deductive reasoning is a very powerful tool and, like any such tool, should be used narrowly. The attempt to build a deductive argument in areas or audiences that are not suitable for this leads to superficial reasoning that can only create the illusion of persuasiveness.
Depending on how widely deductive reasoning is used, all sciences are usually divided into deductive and inductive. In the former, deductive reasoning is predominantly or even exclusively used. Secondly, such argumentation plays only a deliberately auxiliary role, and in the first place is empirical argumentation, which has an inductive, probabilistic character. Mathematics is considered a typical deductive science, an example of inductive sciences are natural Sciences. However, the division of sciences into deductive and inductive, which was widespread at the beginning of this century, has now largely lost its significance. It is oriented towards science, considered in statics, as a system of securely and definitively established truths.
The concept of deduction is a general methodological concept. In logic, it corresponds to the concept proof of.
The concept of proof
A proof is a reasoning that establishes the truth of a statement by citing other statements, the truth of which is no longer in doubt.
The proof differs thesis - the statement to be proved, and base, or arguments- those statements with the help of which the thesis is proved. For example, the statement "Platinum conducts electricity» can be proved using the following
true statements: "Platinum is a metal" and "All metals conduct electricity."
The concept of proof is one of the central ones in logic and mathematics, but it does not have an unambiguous definition applicable in all cases and in any scientific theories.
Logic does not claim to fully disclose the intuitive or "naive" concept of proof. The evidence forms a rather vague set that cannot be covered by one universal definition. In logic, it is customary to talk not about provability in general, but about provability within the framework of a given particular system or theory. At the same time, the existence of different concepts of evidence related to different systems. For example, proof in intuitionistic logic and mathematics based on it differs significantly from proof in classical logic and mathematics based on it. In the classical proof, one can use, in particular, the law of the excluded middle, the law of (removal) of double negation, and a number of other logical laws that are absent in intuitionistic logic.
Evidence is divided into two types according to the method of conducting it. At direct evidence the task is to find such convincing arguments from which the thesis follows logically. circumstantial evidence establishes the validity of the thesis by revealing the fallacy of the assumption opposed to it, antithesis.
For example, you need to prove that the sum of the angles of a quadrilateral is 360°. From what statements could this thesis be deduced? Note that the diagonal divides the quadrilateral into two triangles. So the sum of its angles is equal to the sum of the angles of the two triangles. We know that the sum of the angles of a triangle is 180°. From these provisions we deduce that the sum of the angles of a quadrilateral is 360°. Another example. It is necessary to prove that spaceships obey the laws of cosmic mechanics. It is known that these laws are universal: all bodies at any point in outer space obey them. It is also obvious that spaceship is a cosmic body. Having noted this, we build the corresponding deductive reasoning. It is a direct proof of the assertion under consideration.
In an indirect proof, the reasoning proceeds, as it were, in a roundabout way. Instead of looking directly
to nod arguments to derive from them a proven position, an antithesis is formulated, a denial of this provision. Further, in one way or another, the inconsistency of the antithesis is shown. According to the law of the excluded middle, if one of the contradictory statements is wrong, the second must be true. The antithesis is false, so the thesis is true.
Since circumstantial evidence uses the negation of the proposition being proved, it is, as they say, evidence to the contrary.
Suppose we need to build an indirect proof of such a very trivial thesis: “A square is not a circle”, An antithesis is put forward: “A square is a circle”, It is necessary to show the falsity of this statement. To this end, we deduce consequences from it. If at least one of them turns out to be false, this will mean that the statement itself, from which the consequence is derived, is also false. Wrong is, in particular, such a consequence: the square has no corners. Since the antithesis is false, the original thesis must be true.
Another example. The doctor, convincing the patient that he is not sick with the flu, argues as follows. If there really was a flu, there would be symptoms characteristic of it: headache, fever, etc. But there is nothing like it. So no flu.
Again, this is circumstantial evidence. Instead of a direct justification of the thesis, the antithesis is put forward that the patient really has the flu. Consequences are drawn from the antithesis, but they are refuted by objective data. This says that the flu assumption is wrong. It follows from this that the thesis “There is no flu” is true.
Proofs by contradiction are common in our reasoning, especially in dispute. When used skillfully, they can be especially persuasive.
The definition of the concept of proof includes two central concepts of logic: the concept truth and concept logical follow. Both of these concepts are not clear, and, therefore, the concept of proof defined through them cannot be classified as clear either.
Many statements are neither true nor false, they lie outside the “category of truth”, assessments, norms, advice, declarations, oaths, promises, etc. do not describe any situations, but indicate what they should be, in which direction they need to be transformed. The description is required to match
corresponded to reality. Successful advice (order, etc.) is characterized as effective or expedient, but not as true. The saying, "Water boils" is true if the water does boil; the command “Boil the water!” may be expedient, but has nothing to do with the truth. Obviously, when operating with expressions that do not have a truth value, one can and should be both logical and demonstrative. Thus, the question arises of a significant expansion of the concept of proof, defined in terms of truth. It should cover not only descriptions, but also assessments, norms, etc. The task of redefining proof has not yet been solved either by the logic of estimates or by deontic (normative) logic. This makes the concept of proof not entirely clear in its meaning.
Further, there is no single concept of logical consequence. There are, in principle, an infinite number of logical systems that claim to define this concept. None of the definitions of logical law and logical consequence available in modern logic is free from criticism and from what is commonly called "paradoxes of logical consequence".
The model of proof, which in one way or another tends to be followed in all sciences, is mathematical proof. For a long time it was thought to be a clear and undeniable process. In our century, the attitude towards mathematical proof has changed. The mathematicians themselves have broken into hostile groups, each of which adheres to its own interpretation of the proof. The reason for this was primarily a change in ideas about the logical principles underlying the proof. Confidence in their uniqueness and infallibility has disappeared. Logicism was convinced that logic was enough to justify all of mathematics; according to the formalists (D. Hilbert and others), logic alone is not enough for this, and logical axioms must be supplemented with proper mathematical ones; representatives of the set-theoretic direction were not particularly interested in logical principles and did not always indicate them explicitly; Intuitionists, for reasons of principle, considered it necessary not to go into logic at all. The controversy over mathematical proof showed that there are no proof criteria independent of
time, nor on what is required to be proved, nor on those who use the criteria. Mathematical proof is a paradigm of proof in general, but even in mathematics proof is not absolute and final.
Varieties of induction
In inductive reasoning, the connection between premises and conclusion is not based on a logical law, and the conclusion follows from the accepted premises not with logical necessity, but only with some probability. Induction can give a false conclusion from true premises; its conclusion may contain information not found in the parcels. The concept of induction (inductive reasoning) is not entirely clear. Induction is defined, in essence, as "non-deduction" and is an even less clear concept than deduction. One can nonetheless point to a relatively solid "core" of inductive modes of reasoning. It includes, in particular, incomplete induction, the so-called inverted laws of logic, confirmation of consequences, purposeful justification and confirmation of the general position with the help of an example. Analogy is also a typical example of inductive reasoning.
Incomplete induction
Inductive reasoning, the result of which is a general conclusion about the whole class of objects on the basis of knowledge of only some objects this class, is called incomplete, or popular, induction.
For example, from the fact that the inert gases helium, neon and argon have a valency equal to zero, one can generally conclude that all inert gases have the same valency. This is an incomplete induction, since knowledge of the three inert gases extends to all such gases, including krypton and xenon, which were not specifically considered.
Sometimes the enumeration is quite extensive and yet the generalization based on it turns out to be erroneous.
“Aluminum is a solid body; iron, copper, zinc, silver, platinum, gold, nickel, barium, potassium, lead are also solids; therefore, all metals are solids,” But this conclusion is false, since mercury is the only one of all metals that is a liquid.
Many interesting examples, hasty generalizations encountered in the history of science, are cited in his works by the Russian scientist V.I. Vernadsky.
Until the 17th century, until the concept of “force” finally entered science, “certain forms of objects and, by analogy, certain forms of paths described by objects, were considered, in essence, capable of producing infinite movement. In fact, imagine the shape of an ideally regular ball, put this ball on a plane; theoretically, he cannot stay still and will be in motion all the time. This was thought to be a consequence of the perfectly round shape of the ball. For the closer the shape of the figure is to a spherical one, the more accurate will be the expression that such a material ball of any size will stay on an ideal mirror plane on one atom, that is, it will be more capable of movement, less stable. The ideally round shape, it was believed then, is inherently capable of supporting once communicated movement. This way explained the extremely rapid rotation of the celestial spheres, the epicycles. These movements were once communicated to them by a deity and then continued for centuries as a property of an ideally spherical form. “How far these scientific views are from modern ones, and meanwhile, in essence, these are strictly inductive constructions based on scientific observation. And even at the present time among scientists and researchers we see attempts to revive, in essence, similar views”,
hasty generalization, those. generalization without good reason is a common error in inductive reasoning.
Inductive generalizations require a certain amount of discretion and caution. Much here depends on the number of cases studied. The larger the base of the induction, the more plausible is the inductive conclusion. Diversity and heterogeneity of these cases is also important.
But the most significant is the analysis of the nature of the connections of objects and their attributes, the proof of the non-randomness of the observed regularity, its rootedness in the essence of the objects under study. The identification of the causes that give rise to this regularity makes it possible to supplement pure induction with fragments of deductive reasoning and thereby strengthen and strengthen it.
General statements, and in particular scientific laws obtained by induction, are not yet full-fledged truths. They have to go through a long and
a difficult path until they turn from probabilistic assumptions into constituent elements of scientific knowledge.
Induction finds application not only in the realm of descriptive statements, but also in the realm of evaluations, norms, advice, and similar expressions.
Empirical substantiation of estimates, etc. has a different meaning than in the case of descriptive statements. Estimates cannot be supported by references to what is given in direct experience. At the same time, there are methods of justifying estimates that are in a certain respect similar to methods of justifying descriptions and which can therefore be called quasi-empirical. These include various inductive reasonings, among the premises of which there are estimates and the conclusion of which is also an estimate or a statement similar to it. Among such methods are incomplete induction, analogy, reference to a sample, target justification (confirmation), etc.
Values are not given to a person in experience. They do not talk about what is in the world, but about what should be in it, and they cannot be seen, heard, etc. Knowledge about values cannot be empirical; the procedures for obtaining it can only superficially resemble the procedures for obtaining empirical knowledge.
The simplest and at the same time unreliable way of inductively justifying estimates is incomplete (popular) induction. Its general outline is:
S 1 should be R.
S 2 should be R.
S n must be R.
All S 1 , S 2 ,...,S n are P.
All S must be R.
Here the first n premises are estimates, the last premise is a descriptive statement; conclusion - assessment. For example:
Suvorov must be steadfast and courageous.
Napoleon must be steadfast and courageous.
Eisenhower must be steadfast and courageous.
Suvorov, Napoleon, Eisenhower were generals.
Every commander must be steadfast and courageous.
Along with incomplete induction, it is customary to single out as a special type of inductive reasoning floor-
new induction. In her premises about each of the objects included in the set under consideration, it is stated that it has a certain property. In conclusion, it is said that all objects of the given set have this property.
For example, a teacher, reading the list of students of a certain class, makes sure that everyone named by him is present. On this basis, the teacher concludes that all students are present.
In a complete induction, the conclusion is necessary, and does not follow with some probability from the premises. This induction is thus a kind of deductive reasoning.
Deduction also includes the so-called mathematical Induction, widely used in mathematics.
F. Bacon, who laid the foundation for the systematic study of induction, was very skeptical about the popular induction, based on a simple enumeration of supporting examples. He wrote: “Induction, which is made by a simple enumeration, is a childish thing, it gives shaky conclusions and is endangered by contradictory particulars, making a decision mostly on the basis of a smaller number of facts than it should, and, moreover, only those that are available. ".
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. Induction leading from particular statements to general statements gives only probable, not certain knowledge.
All this once again confirms the idea that is simple in its basis: knowledge of the real world is always creativity. Standard rules, principles and practices
no matter how perfect they may be, they do not guarantee the reliability of new knowledge. The strictest adherence to them does not protect against errors and delusions.
Any discovery requires talent and creativity. And even the very application of various techniques, to some extent facilitating the path to discovery, is a creative process.
"Inverted Laws of Logic"
It has been suggested that all "inverted laws of logic" can be attributed to schemes of inductive reasoning. Under the "inverted laws" we mean 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, if the expression:
"If A and B, then A" is the law of logic, then the expression:
"If A, then A and B"
there is a scheme of inductive reasoning. Similarly for:
"If A, then A or B" and schemes:
"If A or B, then A."
Similar for the laws of modal logic. Because the expressions:
“If A, then A is possible” and “If A is necessary, then A” are the laws of logic, then the expressions:
"If A is possible, then A" and "If A, then A is necessary" are schemes of inductive reasoning. There are infinitely many laws of logic. This means that there are an infinite number of schemes of inductive reasoning.
The assumption that "inverted laws of logic" are schemes of inductive reasoning, however, runs into serious objections: some "inverted laws" remain laws of deductive logic; a number of "inverted laws", when interpreted as schemes of induction, sounds very paradoxical. "Inverted laws of logic" do not, of course, exhaust all possible schemes of induction.
Indirect confirmation
In science, and not only in science, direct observation of what is said in a testable statement is rare.
The most important and at the same time universal way confirmation is derivation from the substantiated position of logical consequences
actions and their subsequent verification. Confirmation of the consequences is evaluated as evidence in favor of the truth of the proposition itself. .
Here are two examples of such confirmation.
He who thinks clearly speaks clearly. The touchstone of clear thinking is the ability to communicate one's knowledge to someone else, perhaps far removed from the subject under discussion. If a person has this skill and his speech is clear and persuasive, this can be considered confirmation that his thinking is also clear.
It is known that a strongly cooled object in a warm room is covered with dew drops. If we see that a person entering a house immediately fogs up his glasses, we can conclude with reasonable certainty that it is frosty outside.
In each of these examples, the reasoning goes according to the scheme: “the second follows from the first; the second is true; therefore, the first is also, in all probability, true” (“If it’s frosty outside, the person who enters the house fogs up his glasses; his glasses really fog up; it means it’s frosty outside”). This is not a deductive reasoning; the truth of the premises does not guarantee the truth of the conclusion here. From the premises “if there is a first, then there is a second” and “there is a second”, the conclusion “there is a first” follows only with some probability (for example, a person whose glasses fogged up in a warm room could specially cool them, say, in a refrigerator, so that then suggest to us that it is very cold outside).
The derivation of consequences and their confirmation, taken by itself, is never able to establish the validity of the justified proposition. Confirmation of the consequences only increases its likelihood.
The greater the number of consequences found to be confirmed, the higher the probability of a verifiable statement. Hence the recommendation to deduce as many logical consequences as possible from the provisions put forward and requiring a reliable foundation in order to verify them.
What matters is not only the number of consequences, but also their nature. The more unexpected consequences of a proposition are confirmed, the stronger the argument they give in support of it. Conversely, the more expected in the light of those who have already received sub-
the assertion of the consequences of the new consequence, the less its contribution to the justification of the position being checked.
A. Einstein's general theory of relativity predicted a peculiar and unexpected effect: not only the planets revolve around the Sun, but the ellipses they describe must rotate very slowly relative to the Sun. This rotation is greater the closer the planet is to the Sun. For all planets except Mercury, it is so small that it cannot be captured. The ellipse of Mercury, the planet closest to the Sun, performs a complete rotation in 3 million years, which can be detected. And the rotation of this ellipse was indeed discovered by astronomers, and long before Einstein. No explanation for this rotation was found. The theory of relativity was not based in its formulation on data on the orbit of Mercury. Therefore, when the conclusion that turned out to be correct about the rotation of the ellipse of Mercury was derived from its gravitational equations, this was rightly regarded as important evidence in favor of the theory of relativity.
Confirmation of unexpected predictions made on the basis of some position, significantly increases its plausibility. However, no matter how large the number of confirmed consequences and no matter how unexpected, interesting or important they may turn out to be, the situation from which they are derived still remains only probable. No consequences can make it true. Even the simplest assertion cannot, in principle, be proved on the basis of a single confirmation of its consequences.
This is the central point of all reasoning about empirical confirmation. Direct observation of what is said in the statement gives confidence in the truth of the latter. But the scope of such observation is limited. Confirmation of consequences is a universal technique applicable to all statements. However, a technique that only increases the plausibility of the statement, but does not make it reliable.
The importance of empirically substantiating claims cannot be overemphasized. It is primarily due to the fact that the only source of our knowledge is experience. Cognition begins with living, sensual contemplation, with what is given in the immediate
nominal observation. Sensory experience connects a person with the world, theoretical knowledge is only a superstructure on an empirical basis.
However, the theoretical is not completely reducible to the empirical. Experience is not an absolute and indisputable guarantor of the irrefutability of knowledge. He, too, can be criticized, tested and revised. “There is nothing “absolute” in the empirical basis of objective science, writes K. Popper. Science does not rest on a solid foundation of facts. The rigid structure of her theories rises, so to speak, above the swamp. It is like a building erected on stilts. These piles are driven into the swamp but do not reach any natural or "given" foundation. If we stopped driving piles further, it was not at all because we had reached solid ground. We simply stop when we are satisfied that the piles are strong enough to support, at least for a while, the weight of our structure.”
Thus, if we limit the range of ways to substantiate statements by their direct or indirect confirmation in experience, then it will not be clear how it is still possible to move from hypotheses to theories, from assumptions to true knowledge.
Purpose rationale
Target inductive justification is the rationale for a positive assessment of some object by referring to the fact that with its help another object of positive value can be obtained.
For example, in the morning you should do exercises, as this helps to improve health; one must return good for good, as this leads to justice in relations between people, and so on. Goal justification is sometimes referred to as motivational; if the goals mentioned in it are not the goals of a person, it is usually called teleological.
As already mentioned, the central and most important way of empirical substantiation of descriptive statements is the derivation of logical consequences from the substantiated position and their subsequent experimental verification. Confirmation of the consequences is evidence in favor of the truth of the proposition itself. Schemes of indirect empirical confirmation:
/1/ From A logically follows B; B is confirmed in experience;
hence probably A is true;
/2/ A is the cause of B; consequence B takes place;
so probably cause A also takes place.
An analogue of the scheme /1/ of empirical confirmation is the following scheme of quasi-empirical confirmation of estimates:
(1*) From A logically follows B; B is positively valuable;
For example: “If we go to the cinema tomorrow and go to the theater, then we will go to the theater tomorrow; it's good that we'll go to the theater tomorrow; it means, apparently, it’s good that we will go to the cinema tomorrow and go to the theater. This is an inductive reasoning that justifies one assessment ("It's good that we'll go to the cinema tomorrow and we'll go to the theater") by reference to another assessment ("It's good that we'll go to the theater tomorrow").
An analogue of the scheme /2/ of causal confirmation of descriptive statements is the following scheme of quasi-empirical target substantiation (confirmation) of estimates:
/2*/ A is the cause of B; corollary B is positively valuable;
so it is likely that cause A is also positively valuable.
For example: “If it rains at the beginning of summer, the harvest will be large; ok what will be big harvest; so, apparently, it’s good that it rains at the beginning of summer. ” This is again inductive reasoning, justifying one assessment ("It's good that it rains early in the summer") by reference to another assessment ("It's good that there will be a big harvest") and some causal connection.
In the case of schemes /1*/ and /2*/, we are talking about a quasi-empirical justification, since the confirmed consequences are estimates, and not empirical (descriptive) statements.
In the scheme /2*/, the premise "A is the cause of B" is a descriptive statement that establishes the connection between cause A and effect B. If it is stated that this effect is positively valuable, the connection "cause - effect" turns into a connection "means - goal" . The scheme /2*/ can be reformulated as follows:
A is a means to B; B is positively valuable; therefore, probably, A is also positively valuable.
An argument following this pattern justifies the means by referring to the positive value of the
with their help goals. It is, one might say, a detailed formulation of the well-known and always controversial principle "The end justifies the means." The disputes are explained by the inductive nature of the purposeful justification hidden behind the principle: the end probably, but not always and necessarily justifies the means.
Another scheme of quasi-empirical target justification is the scheme:
/2**/ non-A is the cause of non-B; but B is positively valuable;
therefore, probably, A is also positively valuable.
For example: “If you do not hurry, then we will not come to the beginning of the performance; it would be nice to be at the beginning of the performance; so it looks like you should hurry up.”
It is sometimes argued that the purposeful justification of estimates is deductive reasoning. However, it is not. Target justification, and in particular, the so-called known since the time of Aristotle practical syllogism, is inductive reasoning.
The purposeful justification of estimates is widely used in various areas of evaluative reasoning, from everyday, moral, political discussions to methodological, philosophical and scientific disputes. Here is a typical example taken from B. Russell's book "History of Western Philosophy": "Most of the opponents of the Locke school," writes Russell, "admired the war as a heroic phenomenon and suggesting contempt for comfort and peace. Those who embraced the utilitarian ethic, on the other hand, tended to regard most wars as madness. This again, at least in the 19th century, brought them into alliance with the capitalists, who did not like wars because wars interfered with trade. The motives of the capitalists were, of course, purely selfish, but they led to views more in tune with the common interest than the views of the militarists and their ideologists. This passage mentions three different target arguments justifying or condemning war:
War is a manifestation of heroism and brings up contempt for comfort and peace; heroism and contempt for comfort and peace are positively valued; This means that war is also positively valuable.
War not only does not contribute to the general happiness, but, on the contrary, most seriously hinders it; general happiness is something to which one should strive in every possible way; This means that war must be categorically avoided.
War interferes with trade; trade is positively valuable; so war is bad.
The credibility of the goal justification essentially depends on three circumstances: first, how effective is the connection between the goal and the means that is proposed to achieve it; second, whether the remedy itself is sufficiently acceptable; thirdly, how acceptable and important is the assessment that fixes the goal. In different audiences, the same target justification may have different persuasiveness. This means that the goal justification refers to contextual(situational) ways of reasoning that are not effective in all audiences.
Facts as examples
Empirical data, facts can be used to directly confirm what is said in the advanced position, or to confirm the logical consequences of this provision. Confirmation of the consequences is an indirect confirmation of the proposition itself.
Facts or special cases can also be used as examples, illustrations and samples. In all these three cases, we are talking about the inductive confirmation of some general proposition by empirical data. As an example, the particular case makes generalization possible; by way of illustration, he reinforces the general proposition already established; and finally, as a model, he encourages imitation.
The use of special cases as models is irrelevant to the argumentation in support of descriptive statements. It directly relates to the problem of substantiating estimates and arguments in support of them.
Example- it is a fact or a special case used as a starting point for the subsequent generalization and to reinforce the generalization made.“Next I say,” writes the 18th century philosopher. J. Berkeley - that sin or moral corruption does not consist in external physical action or movement,
but in the internal deviation of the will from the laws of reason and religion. For killing an enemy in battle or carrying out a death sentence on a criminal is not considered sinful according to the law, although the external action here is the same as in the case of murder. Two examples are given here (murder in war and in execution of a death sentence) to support the general proposition of sin or moral corruption. The use of facts or particular cases as examples must be distinguished from their use as illustrations. Acting as an example, a particular case makes generalization possible; as an illustration, it reinforces a generalization already made independently of it.
In the case of the example, the reasoning goes according to the scheme:
“if the first, then the second; the second takes place;
so the first also holds.
This reasoning goes from asserting the consequence of the conditional statement to asserting its foundation and is not a correct deductive reasoning. The truth of the premises does not guarantee the truth of the conclusion drawn from them. Reasoning on the basis of an example does not prove the position accompanied by an example, but only confirms it, makes it more plausible. The example, however, has a number of features that distinguish it from all those facts and special cases that are used to confirm general provisions and hypotheses. The example is more convincing or more weighty than the rest of the facts and special cases. It is not just a fact, but typical fact, that is, a fact that reveals a certain trend. The typifying function of the example explains its widespread use in argumentation processes, and especially in humanitarian and practical argumentation, as well as in everyday reasoning.
The example can only be used to support descriptive statements. He is incapable of supporting judgments and assertions which, like norms, oaths, promises, etc., gravitate towards judgments. An example cannot serve as a starting material for evaluative and similar statements. What is sometimes presented as an example, designed to somehow confirm an assessment, a norm, etc., is in fact not an example, but a model. The difference between an example and a sample is significant: an example is a description, while a sample is an assessment,
rushing to a particular case and setting a particular standard, ideal, etc.
The purpose of the example is to lead to the formulation of the general proposition and, to some extent, to be an argument in support of the latter. Related to this is the selection criteria for the example. First of all, the fact or particular case chosen as an example should look clear and undeniable. It should also clearly enough express the tendency to generalization. Connected with the requirement of tendentiousness, or typicality, of facts taken as examples is the recommendation to enumerate several examples of the same type if, taken one at a time, they do not show with the necessary certainty the direction of the forthcoming generalization or do not reinforce the generalization already made. If the intention to argue with an example is not explicitly declared, the fact itself and its context should show that the listeners are dealing with an example, and not with some description of an isolated phenomenon, perceived as simple additional information. The event used as an example should be taken, if not as usual, then at least as logically and physically possible. If this is not so, then the example simply breaks off the sequence of reasoning and leads just to the opposite result or to a comic effect. Examples should be selected and formulated in such a way that they encourage a transition from the singular or particular to the general, and not from the particular again to the particular.
Requires special attention counter example. It is usually believed that such an example can only be used to refute erroneous generalizations, their falsification. However, the counterexample is often used in another way: it is introduced with the intention of preventing an illegitimate generalization and, by demonstrating its incompatibility with it, suggesting the only direction in which the generalization can go. The task of the contradictory example in this case is not to falsify some general proposition, but to reveal such a proposition.
Facts as illustrations
An illustration is a fact or a special case, designed to reinforce the audience's conviction of the correctness of an already known general proposition. An example pushes the thought to a new generalization and reinforces this generalization.
An illustration clarifies a well-known general proposition, demonstrates its meaning with the help of a number of possible applications, enhances the effect of its presence in the minds of the audience. The difference between the tasks of the example and the illustration is related to the difference in the criteria for their selection. The example should look like a fairly solid, unambiguously interpreted fact, the illustration may cause slight doubts, but on the other hand, it should especially vividly influence the imagination of the audience, stop its attention on itself. An illustration, to a much lesser extent than an example, runs the risk of being misinterpreted, since behind it there is an already known position. The distinction between an example and an illustration is not always clear cut. Aristotle distinguished two uses of an example, depending on whether the speaker has any general principles or not: “It is necessary to give many examples to the one who places them at the beginning, and who places them at the end, one for a witness worthy of faith is useful even when he is alone.” The role of special cases is, according to Aristotle, different depending on whether they precede the general position to which they refer, or follow it. The point, however, is that the facts given before the generalization are, as a rule, examples, while one or the few facts given after it are illustrations. This is also evidenced by Aristotle's warning that the listener's demands, for example, are higher than for illustrations. An unfortunate example casts doubt on the general position that it is intended to reinforce. A contradictory example can even refute this proposition. The situation is different with an unsuccessful illustration: the general position to which it is given is not questioned, and an inadequate illustration is regarded rather as a negative characterization of the one who applies it, indicating a lack of understanding by him. general principle or about his inability to pick up a good illustration. A bad illustration can have a comic effect. The ironic use of an illustration is especially effective when describing a particular person: first, a positive characterization is given to this person, and then an illustration is given that is directly incompatible with it. So, in "Julius Caesar" by Shakespeare, Antony, constantly reminding that Brutus is an honest man, cites one
after another evidence of his ingratitude and betrayal.
Concretizing the general position with the help of a particular case, the illustration enhances the effect of presence. On this basis, it is sometimes seen as an image, a living picture of an abstract thought. The illustration, however, does not set itself the goal of replacing the abstract with the concrete and thereby transferring consideration to other objects. It does analogy, the illustration is nothing more than a special case, confirming the already known general position or facilitating its clearer understanding.
Often an illustration is chosen based on the emotional resonance it can evoke. This is what Aristotle does, for example, who prefers a periodical style to a coherent style that does not have a clearly visible end: “...because everyone wants to see the end; for this reason, those who compete in running suffocate and weaken on turns, while before they did not feel tired, seeing the limit of running in front of them.
A comparison used in argumentation that is not a comparative assessment (preference) is usually an illustration of one case by another, with both cases being considered as concretizations of the same general principle. A typical example of comparison: “People are shown by circumstances. So, when some circumstance falls to you, remember that it was God, like a gymnastics teacher, who pushed you to a rough end ”(Epictetus).
Samples and ratings
A pattern is the behavior of a person or group of people to be followed. The sample is fundamentally different from the example: the example tells what is in reality and is used to support descriptive statements, the sample says what should be and is used to reinforce general evaluative statements. By virtue of its special social prestige, the model not only supports the assessment, but also serves as a guarantee for the type of behavior chosen: following the generally accepted model guarantees a high assessment of behavior in the eyes of society.
Models play an exceptional role in social life, in the formation and strengthening of social values. A person, a society, an epoch are largely characterized by the patterns they follow and by the
how these patterns are understood by them. There are models intended for general imitation, but there are also designed only for a narrow circle of people. Don Quixote is a kind of model: he is imitated precisely because he was able to selflessly follow the model chosen by himself. An example can be a real person, taken in all the variety of his inherent properties, but a person’s behavior in a certain, rather narrow area can also act as a model: there are examples of love for one’s neighbor, love of life, self-sacrifice, etc. An example may be the behavior of a fictitious person: a literary hero, a mythical hero, etc. Sometimes such a hero does not act as a whole person, but demonstrates only individual virtues by his behavior. You can, for example, imitate Ivan the Terrible or Pierre Bezukhov, but you can also strive to follow in your behavior the altruism of Dr. P.F. Haaz, the loving nature of Don Juan, etc. Indifference to a model can itself look like a model: the one who knows how to avoid the temptation of imitation is sometimes set as an example. If the model is an integral person, who usually has not only advantages, but also known shortcomings, it often happens that his shortcomings have a greater impact on people's behavior than his undeniable advantages. As B. Pascal noted, “an example of the purity of morals of Alexander the Great is much less likely to incline people to abstinence than the example of his drunkenness to licentiousness. It is not at all shameful to be less virtuous than he is, and it is pardonable to be just as vicious."
Along with samples, there are also antisamples. The task of the latter is to give repulsive examples of behavior and thereby turn away such behavior. The exposure to the anti-pattern is, in the case of some people, even more effective than the exposure to the specimen. As determinants of behavior, pattern and anti-pattern are not entirely equal. Not everything that can be said about a pattern applies equally to the anti-pattern, which is generally less definite and can only be correctly interpreted by comparing it with a definite pattern: what does it mean not to behave like Sancho Panza, understandable only to those who know the behavior of Don Quixote.
An argument that appeals to a model is similar in structure to an argument that appeals to an example:
“If there must be the first, then there must be the second;
the second should be;
so it must be the first.
This reasoning goes from the statement of the consequence of the conditional statement to the statement of its foundation and is not a correct deductive conclusion.
Argumentation to a pattern is common in fiction. Here it is, as a rule, indirect in nature: the reader himself will have to choose the sample according to the indirect instructions of the author.
Along with patterns of human actions, there are also patterns of other things: objects, events, situations, and so on. The first examples are called ideals the second - standards. For all objects that a person regularly encounters, be it hammers, watches, medicines, etc., there are standards that say what objects of this kind should be. Reference to these standards is a common argument in support of estimates. The standard for items of a certain type usually takes into account their typical function; in addition to functional properties, it may also include some morphological features. For example, no hammer can be called good if it cannot be used to hammer nails; it will also not be good if, while allowing nails to be driven in, it still has a bad handle.
Analogy
There is an interesting way of reasoning that requires not only the mind, but also a rich imagination, full of poetic flight, but not giving solid knowledge, and often simply misleading. This very popular method is inference by analogy.
The child sees a little monkey in the zoo and asks his parents to buy him this “little man in a fur coat” so that he can play and talk with him at home. The child is convinced that the monkey is a man, but only in a fur coat, that he can, like a man, play and talk. Where does this conviction come from? By appearance, facial expressions, gestures, the monkey resembles a person. It seems to the child that with her, as with a person, you can play and talk.
When we get to know the journalist, we learn that this intelligent, well-educated man is fluent in English, German and French. Having then met another journalist, intelligent, educated, fluent in English and German, we may not be tempted to ask if he speaks French as well.
) the term "deduction" is used as a synonym for the more precise, but more cumbersome, term "deductive reasoning" and is understood in a narrower sense: as inference, in which the general conclusion is built on the basis of private premises. It is believed that if the premises of deduction are true, then [subject to the correct form of reasoning] its consequences (conclusions) are also true. In deductive reasoning, the relation between premises and conclusion is logical consequence(see), in which the logical content of the conclusion (its information without taking into account the meanings of non-logical terms) is part of the total logical content of the premises. In this sense, the term "deduction" is used to refer to specific conclusions of consequences from premises, that is, as a synonym for the term "inference" in one of its meanings. All this leads to a close connection (and sometimes even identification) of the concept of deduction with the concepts of inference and consequence, which is also reflected in logical terminology; Thus, the “deduction theorem” is usually called one of the important relationships between the logical link of implication (formalizing the verbal phrase “If ..., then ...”) and the relation of logical consequence (deducibility): if from the premise A a consequence is deduced B, then the implication A ≡ B("If a A…, then B…”) is provable (that is, derivable already without any premises, from axioms alone). (The deduction theorem, which is valid for some sufficiently general conditions for all “full-fledged” logical systems, in some cases it is simply postulated for them as an initial rule.) Other logical terms associated with the concept of deduction have a similar character; thus, sentences deduced from each other are said to be deductively equivalent; the deductive completeness of a system (with respect to some property) consists in the fact that all expressions of the given system that have this property (for example, true under some interpretation) are provable in it.
Along with this, the term "deduction" denotes a generic name for the general theory of constructing correct conclusions. In accordance with this last word usage, the sciences, the sentences of which are obtained (at least predominantly) as consequences of some general “basic laws” (principles, postulates, axioms, and so on), are usually called deductive (mathematics, theoretical mechanics, some branches of physics, and others). ), a axiomatic method, by means of which the conclusions of these particular propositions are made, is often called axiomatic-deductive. The opposite of deduction is induction(see), in which the general conclusion is also built on the basis of private premises, but at the same time, the premises can confirm or imply the truth, but do not guarantee its receipt. Accordingly, natural sciences are examples of inductive sciences. At the same time, the division of sciences into deductive and inductive, which was widespread at the beginning of the 20th century, has now largely lost its significance, since it is focused on science considered statically, that is, as a system of reliably and finally established truths.
The deduction method is widely used in all fields scientific knowledge, playing an important role in the construction of empirical knowledge and the transition from empirical to theoretical knowledge (see). In deduction, based on general knowledge, a private conclusion is made, therefore one of the premises of deduction is necessarily a general judgment. If it is obtained as a result of inductive reasoning, then deduction complements induction, expanding the amount of knowledge gained. The greatest 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, a new scientific idea. In this case, deduction plays not just an auxiliary role, complementing induction, but is the starting point for the emergence of a new theoretical system. Created in this way theoretical knowledge(see ) predetermines the further course of empirical research and purposefully guides the construction of new inductive generalizations. In general, at an early stage scientific research induction prevails, while deduction begins to play an important role in the development and substantiation of scientific knowledge. Thus, these two operations of scientific knowledge are inextricably linked and complement each other.
The general organization scheme of scientific and theoretical deductive systems includes:
- the original basis, that is, the totality of the original terms and statements;
- used logical means (inference rules and definitions);
- a set of statements (sentences) obtained from (1) by applying (2).
In the study of such theories, the relationships between their individual components, abstracted from the genesis and development of knowledge, are analyzed. Therefore, it is advisable to consider them as a kind of formalized languages that can be analyzed either in syntactic (when the relationship between the signs and expressions included in the language is studied without taking into account their extralinguistic meaning), or in the semantic (when the relationship between the signs and expressions of the system is considered from the point of view of their meaning) aspects. Deductive systems are divided into axiomatic (axiomatic method) and constructive (constructive method). The deductive method, when used in knowledge based on experience and experiment, acts as hypothetical-deductive method(cm. ). The analysis of the deductive method of constructing scientific knowledge began already in ancient philosophy(Plato, Aristotle, Euclid, the Stoics), occupied a significant place in the philosophy of the New Age (R. Descartes, B. Pascal, B. Spinoza, G. V. Leibniz and others), but the principles of the deductive organization of knowledge were formulated most fully and clearly only at the end of the 19th - beginning of the 20th century with the involvement of the apparatus of mathematical logic. Until the end of the 19th century, the deductive method was used mainly in the field of mathematics and logic. In the 20th century, attempts at the deductive (in particular, axiomatic) construction of many non-mathematical disciplines - separate sections of physics, biology, linguistics, sociology, and others - became widespread.
The study of deduction is the main task of logic; sometimes logic - anyway formal logic(see) - even defined as "deduction theory". Outside the limits of deductive logic are the so-called plausible reasoning(media inductive methods which are studied in inductive logic(cm. ). In deductive logic, methods of reasoning with standard, typical statements are explored; these methods take the form logical systems, or calculations.
Although the term "deduction" itself was first used, apparently, by Boethius ("Introduction to the categorical syllogism", 1492), the first systematic analysis of one of the varieties of deductive reasoning is syllogistic reasoning(see) - was carried out by Aristotle in the "First Analytics" ("First Analytics", II 25, 69a 20-36) and significantly developed by his ancient and medieval followers. Deductive reasoning based on the properties of propositional logical connectives, were studied in the school of the Stoics and especially in detail in medieval logic. Such important types of inferences as conditional-categorical (modus ponens, modus tollens), separative-categorical (modus tollendo ponens, modus ponendo tollens), conditional-separative (lemmatic) and others were singled out. In the philosophy and logic of modern times, there were significant differences in views on the role of deduction in a number of other methods of cognition. Thus, R. Descartes contrasted deduction with intuition, through which, in his opinion, the human mind "directly sees" the truth, while deduction provides the mind with only "mediated" (obtained by reasoning) knowledge. (The primacy of intuition over deduction proclaimed by Descartes was revived much later and in significantly modified and developed forms in the concepts intuitionism- see) F. Bacon, and later other English "inductivist logics" (W. Wavell, J. St. Mill, A. Bain and others), emphasizing that the conclusion obtained by deduction does not contain (if expressed in modern language) no "information" that would not be contained (albeit implicitly) in the premises, on this basis they considered deduction a "secondary" method, while, in their opinion, only induction gives true knowledge. In this sense, deductively correct reasoning was considered from the information-theoretic point of view as reasoning, the premises of which contain all the information contained in their conclusion. Proceeding from this, not a single deductively correct reasoning leads to the receipt of new information - it only makes the implicit content of its premises explicit. In turn, representatives of the direction, coming primarily from German philosophy (Chr. Wolf, G. W. Leibniz), also proceeding from the fact that deduction does not provide new information, it was on this basis that they came to the opposite conclusion: the obtained through deduction, knowledge is “true in all possible worlds” (or, as I. Kant later said, “analytically true”), which determines their “enduring” value, in contrast to the “actual” observational data and experience obtained by inductive generalization ( or "synthetic") truths, true "only by virtue of a combination of circumstances." From a modern point of view, the question of such advantages of deduction or induction has largely lost its meaning. Along with this, a certain philosophical interest is the question of the source of confidence in the truth of a deductively correct conclusion based on the truth of its premises. At present, it is generally accepted that this source is the meaning of the logical terms included in the argument; thus deductively correct reasoning turns out to be "analytically correct".
Within the framework of traditional logic, only a small part of deductive reasoning was described and there were no exact criteria for the logical correctness of reasoning. In modern symbolic logic(see), thanks to the use of formalization methods, the construction of logical calculus and formal semantics, the axiomatic method, the study of deductive reasoning was raised to a qualitatively different, theoretical level. By means of modern logical theory, it is possible to specify the entire set of forms of correct deductive reasoning within the framework of a certain formalized language. So, if the theory is built semantically, then the transition from formulas A 1 A 2 , … A n to formula B is declared a form of correct deductive reasoning in the presence of a logical consequence B from A 1 A 2 , … A n this relation is usually defined as follows: for any interpretation of non-logical symbols acceptable in this theory, for which A 1 A 2 , … A n take the distinguished value (truth value), the formula B also takes on the allocated value. In syntactically constructed logical systems (calculi), the criterion for the logical correctness of the transition from A 1 A 2 , … A n to B the existence of a formal derivation of the formula B from formulas A 1 A 2 , … A n carried out in accordance with the rules of this system.
The choice of a logical theory adequate for testing deductive reasoning is conditioned by the type of propositions included in it and by the expressive possibilities of the language of the theory. Thus, inferences containing complex statements can be analyzed by means of propositional logic(see), while the internal structure of simple statements as part of complex ones is ignored. syllogistic(see ) explores inferences from simple attributive statements based on volumetric relations in the field of general terms. means predicate logic(see) correct deductive inferences are distinguished based on taking into account the internal structure of simple statements in various ways different types. Inferences containing modal statements are considered within the framework of systems modal logic(see), those that contain timed statements - within the framework temporal logic(see) and so on.
It is necessary to distinguish between the method of induction and deduction used in economics. There are also differences between objective logic, the history of development, and methods of cognition.
Types of knowledge
Objective-logical thinking assumes a common line, an example is the transition of society from one formation to another.
The objective historical method is a concrete manifestation of a certain regularity in the infinite variety of its individual manifestations and features. In society, as an example, one can use the connection of individual destinies with real story countries.
Methods
These types of knowledge are analyzed by two methods: logical and historical. Any phenomenon can be understood, explained, only in its historical development. In order to know an object, it is necessary to reflect the history of its appearance. Without an understanding of the development path, it is difficult to understand the end result. History goes in zigzags and jumps, so that the sequence is not interrupted during its analysis, a variant of logical research is needed. To study history, you need:
- analysis;
- synthesis;
- induction;
- deduction;
- analogy.
Logical thinking presupposes a generalized reflection of historical development and explains its importance. This method often means a certain state of the object under study at a specific time interval. It depends on many factors, but the objectives of the study, as well as the nature of the object, are of decisive importance. So, for the discovery of his law, I. Kempler did not study the history of the planets.
Research methodology
Induction and deduction stand out as separate research methods. Let's analyze the features of each of them, try to identify character traits. How are induction and deduction different? Induction is a process of selection on the basis of general provisions of particular (single) facts. There is a division of it into two parts: incomplete and complete. The second is characterized by conclusions or judgments about objects based on information about the entire set. In practice, both induction and deduction are used, the choice depends on the specific situation. A frequent occurrence is the use of incomplete induction. In this case, conclusions about the object under study are made on the basis of partial information about the subject. Reliable information can be obtained by experimental studies conducted repeatedly.
Application in modern times
Induction and deduction are widely used today. Deduction involves reasoning from the general to the individual (private). All the conclusions that are obtained in the course of such reasoning are reliable only if the correct methods have been chosen for the analysis. In human thinking, induction and deduction are closely interrelated. Examples of such unity allow a person to analyze ongoing events, to look for the right ways to resolve a problem situation. Induction directs human thought to the derivation of empirically verifiable consequences from general hypotheses, their experimental confirmation or refutation. An experiment is characterized by a scientifically established experiment carried out to study the phenomenon caused by it. The researcher works under certain conditions, monitors the results obtained, using a variety of instruments and materials, directs him in the right direction.
Examples
How are induction and deduction different? Examples of the use of these methods can be found in any field of activity. modern man. When considering the deductive method of thinking as an example, the image of the legendary detective Sherlock Holmes immediately arises. This technique is associated with logic, analysis of many details, decision-making based on the information received.
Research in Economics
Induction and deduction in economics is a common phenomenon. Thanks to these methods, all analytical and statistical studies concrete decisions are made. For example, by deduction, economists study consumer demand for mortgage lending. The results obtained in the course of the research are analyzed, a general result is derived, and on its basis a decision is made to modernize the proposal for this type of lending to the population. Economic research is carried out according to a certain algorithm. First, an object of study is selected, which will become the basis for the work of extras. Next, a hypothesis is put forward, the final result of the study largely depends on the correctness of its formulation. In order to obtain reliable information, methods are selected, an algorithm of actions is created. The results are considered reliable only if the experiments were carried out not 1-2 times, but in several series of 2-3 studies.
Conclusion
We have analyzed such important terms as induction and deduction. Examples from different areas human activities confirm the feasibility of using two methods at once. For example, modern pedagogy is based on deductive methods. Before offering certain banking products to borrowers, they are carefully analyzed by specialists, all possible consequences of their appearance on the market are assumed. What exactly to choose: deduction or induction, professionals decide taking into account the specific situation. Deduction allows you to draw conclusions in which errors are practically excluded. It is this technique that psychologists recommend that people study in order to protect themselves from constant stress, to seek strength to deal with complex problems.
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.
Full 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 will be a good scientific method if you follow a few simple rules. 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.
In 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, but 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.
13JunWhat is Deduction and Induction
Deduction or deductive reasoning - This one of the two main forms of logical reasoning based on the idea that if something is true for a whole class of things, then it is true for all members of this class.
What is DEDUCT - in simple words. DEDUCTION METHOD
In simple terms, deduction is a variant of thinking in which a person draws certain logical conclusions based on knowledge about a class of things as a whole, and transfers certain features to a particular thing. In other words, we can say that deduction is a variant of logical reasoning directed from the general to the particular.
Despite the ornateness of the definition, the very concept of deduction is very simple, especially if you understand the principle of the deductive method. So, the Deductive method works as follows: If we know that all representatives of a certain class have some property, then when considering one of the representatives of this class, it is fair to assume that he also has this property. So for example: If we know that all people are mortal, and the hypothetical Seryozha is a man, then, therefore, he is also mortal.
DEDUCT example
- All birds have feathers. A parrot is a bird, therefore a parrot has feathers;
- Red meat contains iron. Beef is red meat, so beef has iron in it;
- Reptiles are cold-blooded, and snakes are reptiles. Therefore, snakes are cold-blooded;
- If A = B and B = C, then A = C;
What is INDUCTION - in simple words.
Induction or Inductive reasoning is a method of constructing a logical conclusion based on the principle: from the particular to the general. So for example, if we see that the hypothetical Seryozha died, and he is a man, then we can assume that all people are mortal .
Summing up, we can say that:
Inductive and deductive reasoning are two opposite, but not mutually exclusive, approaches that can be used to evaluate conclusions. Deductive reasoning presupposes the existence of a general statement, from which a conclusion about a particular case is further built. On the other hand, inductive reasoning takes as a basis a series of special cases from which a general theory is formed. Approaches differ, but it is important to understand that both inductive and deductive reasoning can be false, especially if the underlying premise of the argument is wrong. The best option when drawing logical conclusions is to use a combination of these methods.
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