11.1. Inductive reasoning Deduction and induction Deductive reasoning

Deduction is a special case of inference.

In a broad sense, inference is a logical operation, as a result of which a new statement is obtained from one or several accepted statements (assumptions) - a conclusion (conclusion, effect).

Depending on whether there is a connection between logical premise and conclusion of logical following, two kinds of conclusions can be distinguished.

In deductive reasoning, this connection is based on a logical law, by virtue of which the conclusion with logical necessity follows from the accepted assumptions. A distinctive feature of such a conclusion is that it always leads to a true conclusion from true premises.

In inductive reasoning, the connection between premises and conclusions is not based on the law of logic, but on some factual or psychological grounds that are not of a purely formal nature.

In ordinary reasoning, deduction appears only rarely in full and expanded form. Most often, we indicate not all used parcels, but only some. General statements about which it can be assumed that they are well known, as a rule, are omitted. Conclusions arising from the received assumptions are not always explicitly formulated. The very logical connection that exists between the original and deducible statements is only occasionally marked by words like the words "therefore" and "means."

Often deduction is so abbreviated that one can only guess about it. It can be difficult to restore it in full form, indicating all the necessary elements and their connections.

“Due to an old habit,” Sherlock Holmes once remarked, “I have a chain of conclusions so quickly that I came to the conclusion without even noticing the intermediate premises. However, they were these packages. ”

It is quite burdensome to carry out deductive reasoning, without omitting anything or shortening it. A person pointing out all the prerequisites of his conclusions creates the impression of a petty pedant. II, however, whenever there is doubt about the validity of the conclusion, one should return to the very beginning of the argument and reproduce it in the fullest possible form. Without this, it is difficult or even impossible to detect the mistake made.

Many literary critics believe that Sherlock Holmes was “written off” by A. Conan Doyle from Joseph Bell, a professor of medicine at the University of Edinburgh. The latter was known as a talented scientist who possessed a rare observation and well mastered the method of deduction. Among his students was the future creator of the image of the famous detective story.

One day, Copan Doyle tells in his autobiography, a patient came to the clinic, and Bell asked him:

- Did you serve in the army?

- Yes sir! - standing at attention, the patient answered.

- In the mountain rifle regiment?

- Yes, Mr. Doctor!

- Recently resigned?

- Yes sir!

- Were you a sergeant?

- Yes sir! - famously answered the patient.

- Stood pa Barbados?

- Yes, Mr. Doctor!

The students present at this dialogue looked at the professor in astonishment. Bell explained how simple and logical his conclusions are.

This person, having shown politeness and courtesy at the entrance to the office, still did not take off his hat. Affected army habit. If the patient had been retired for a long time, he would have long since learned civilian manners. In his posture is imperiousness, he is clearly Scottish by nationality, and this speaks for the fact that he was a commander. With regard to stay in Barbados, the one who came ill elephantism (elephantishness) - such a disease is common among the inhabitants of those places.

Here deductive reasoning is extremely abbreviated. In particular, all general statements, without which deduction would be impossible, are omitted.

Sherlock Holmes has become a very popular character. There were even jokes about him and his creator.

For example, in Rome, Conan Doyle takes a cab driver, and he says: "Oh, Mr. Doyle, I greet you after your trip to Constantinople and Milan!" “How could you know where I came from?” Copan Doyle was surprised at the Sherlockholm's 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 a 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 argumentation process. Deductive reasoning also serves to verify (indirectly confirm) statements: its empirical implications are deductively derived from a test position; confirmation of these effects is evaluated as an inductive argument in favor of the starting position. Deductive reasoning is also used to falsify assertions by showing that the consequences arising from them are false. Unsuccessful falsification is a weakened version of verification: failure to refute the empirical consequences of the tested hypothesis is an argument, although very weak, in support of this hypothesis. Finally, deduction is used to systematize a theory or system of knowledge, to trace the logical connections of its statements, to build explanations and understandings based on 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 common premises is an important contribution to the substantiation of its statements.

Deductive reasoning is universal, applicable in all areas of knowledge and in any audience. “And if bliss is nothing else than eternal life,” wrote the medieval philosopher John Scot Eriugen, “and eternal life is the knowledge of truth, then bliss is nothing else than the knowledge of truth.” This theological reasoning is a deductive reasoning, namely a syllogism.

The share of deductive reasoning in different areas of knowledge is significantly different. It is very widely used in mathematics and mathematical physics, and only sporadically in history or aesthetics. Referring to the scope of the application of deduction, Aristotle wrote: "You should not demand scientific evidence from a speaker, just as you should not demand emotional conviction from a mathematician." Deductive reasoning is a very powerful tool and, like any such tool, should be used narrowly. Attempting to build the argument in the form of deduction in those areas or in the audience that are not suitable for this, leads to superficial reasoning, able to create only the illusion of credibility.

Depending on how widely used deductive argumentation, all the sciences are usually divided into deductive and inductive. In the first, a predominantly or even solely deductive argument is used. Secondly, such an argument plays only a deliberately supporting role, and in the first place is an empirical argument, having an inductive, probabilistic character. Mathematics is considered a typical deductive science, natural sciences are a model of inductive sciences. However, the division of sciences into deductive and inductive, widespread at the beginning of the 20th century, has now largely lost its significance. It is focused on science, considered in statics as a system of reliably and finally established truths.

The concept of deduction is a general methodical concept. In logic, it corresponds to the notion of proof.