Deduction This is a way of reasoning from general provisions to particular conclusions.
Deductive reasoning only concretizes our knowledge. A deductive conclusion contains only the information that is in the accepted premises. Deduction allows you to obtain new truths from existing knowledge using pure reasoning.
Deduction gives a one hundred percent guarantee of the correct conclusion (with reliable premises). Deduction from truth produces truth.
Example 1.
All metals are ductile(b O least valid premise or main argument).
Bismuth is a metal(reliable premise).
Therefore, bismuth is plastic(correct conclusion).
Deductive reasoning that produces a true conclusion is called a syllogism.
Example 2.
All politicians who allow contradictions are a joke(b O the largest reliable premise).
E Ltsin B.N. admitted contradictions(reliable premise).
Therefore, E.B.N. is a joke(correct conclusion) .
Deduction from a lie comes a lie.
Example.
Help from the International Monetary Fund always leads to prosperity for everyone(false premise).
The IMF has been helping Russia for a long time(reliable premise).
Therefore, Russia is prospering(false conclusion).
Induction – a way of reasoning from particular provisions to general conclusions.
An inductive conclusion may contain information that is not contained in the accepted premises. The validity of the premises does not mean the validity of the inductive conclusion. Premises make the conclusion more or less likely.
Induction does not provide reliable, but probabilistic knowledge that needs to be verified.
Example 1.
G.M.S. - pea jester, E.B.N. - pea jester, Ch.A.B. - pea jester(reliable premises).
G.M.S., E.B.N., Ch.A.B. – politicians(reliable premises).
Therefore, all politicians are clowns(probabilistic conclusion).
The generalization is plausible. However, there are politicians who can think.
Example 2.
In recent years, military exercises have been held in area 1, area 2 and area 3, increasing the combat effectiveness of units(reliable premises).
In area 1, in area 2 and in area 3, units of the Russian Army took part in the exercises(reliable premises).
Consequently, in recent years, the combat effectiveness of all units of the Russian Army has increased(inductive invalid inference).
A general conclusion does not logically follow from particular provisions. Showy events do not prove that there is prosperity everywhere:
In fact, the overall combat capability of the Russian Army is catastrophically declining.
A variant of induction is inference by analogy (based on the similarity of two objects in one parameter, a conclusion is drawn about their similarity in other parameters as well).
Example. The planets Mars and Earth are similar in many ways. There is life on Earth. Since Mars is similar to Earth, Mars also has life.
This conclusion is, of course, only probabilistic.
Any inductive conclusion needs to be verified.Dmitry Mezentsev (coordinator of the project "Russian Society of Good Action") 2011
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 more accepted statements (premises) - 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.
IN deductive reasoning this connection is based on a logical law, due to which the conclusion follows with logical necessity from the accepted premises. The distinctive feature of such an inference is that it always leads to a true conclusion from true premises.
IN inductive reasoning the connection between premises and conclusion is based not on the law of logic, but on some factual or psychological grounds that are not of a purely formal nature. In such a mind-
conclusion the conclusion does not follow logically from sprinkles and may contain information not contained therein. The reliability of the premises does not therefore mean the reliability of the statement inductively derived from them. Induction gives only probable or believable, conclusions that need further verification.
Deductive inferences include, for example, the following:
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.”
Examples of induction include reasoning:
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 are Western European countries.
All Western European countries are republics.
Induction does not provide a complete guarantee of obtaining a new truth from existing ones. The maximum we can talk about is a certain degree of probability of the statement being inferred. Thus, the premises of both the first and second inductive inferences are true, but the conclusion of the first of them is true, and the second is true.
false. Indeed, all Latin American states are republics; but among Western European countries there are not only republics, but also monarchies, for example England, Belgium and Spain.
Particularly characteristic deductions are logical transitions from general knowledge to particular types:
All people are mortal.
All Greeks are people.
Therefore, all Greeks are mortal.
In all cases when it is necessary to consider some phenomena on the basis of an already known general rule and to draw the necessary conclusion regarding these phenomena, we conclude in the form of deduction. Reasoning leading from knowledge about some objects (private knowledge) to knowledge about all objects of a certain class (general knowledge) is typical induction. There is always the possibility that the generalization will turn out to be hasty and unfounded (“Napoleon is a commander; Suvorov is a commander; this means that 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 the argument, “Shakespeare wrote sonnets; therefore, it is not true that Shakespeare did not write sonnets.” There is a deduction, but there is no transition from the general to the specific. The reasoning “If aluminum is plastic or clay is plastic, then aluminum is plastic” is, as is commonly thought, 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 inferences include both transitions from the particular to the general, as well as analogy, methods for establishing causal relationships, confirmation of consequences, purposeful justification, etc.
The special interest shown in deductive reasoning is understandable. They allow you 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 one hundred percent 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 are sure to obtain reliable knowledge in all cases.
While emphasizing the importance of deduction in the process of unfolding and substantiating knowledge, one should not, however, separate it from induction and underestimate the latter. Almost all general provisions, including scientific laws, are the results of inductive generalization. In this sense, induction is the basis of our knowledge. In itself, it does not guarantee its truth and validity, but it gives rise to assumptions, connects them with experience and thereby gives them a certain credibility, 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 discussed reasoning patterns were examples of deductive reasoning. Propositional logic, modal logic, the logical theory of categorical syllogism are all sections of deductive logic.
Ordinary deductions
So, deduction is the derivation of conclusions that are as reliable 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 can be assumed to be well known are generally omitted. The conclusions that follow from the accepted premises are not always clearly formulated. The very logical connection that exists between the initial and deduced statements is only sometimes marked by words like “therefore” and “means”
Often the deduction is so abbreviated that one can only guess about it. It can be difficult to restore it in full form, indicating all the necessary elements and their connections.
“Thanks to a long-standing 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 there, these parcels,”
Carrying out deductive reasoning without omitting or shortening anything is quite cumbersome. A person who points out all the premises for his conclusions creates the impression of a petty pedant. And together with
Therefore, whenever doubt arises about the validity of the conclusion made, one should return to the very beginning of the reasoning and reproduce it in the most complete form possible. Without this, it is difficult or even impossible to detect a mistake.
Many literary critics believe that Sherlock Holmes was “copied” by A. Conan Doyle from Joseph Bell, a professor of medicine at the University of Edinburgh. The latter was known as a talented scientist with rare powers of observation and excellent command of the method of deduction. Among his students was the future creator of the image of the famous detective.
One day, Conan Doyle says in his autobiography, a patient 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 rifle regiment?
That's right, Mister Doctor!
Recently retired?
Yes sir!
Were you a sergeant?
Yes sir! - the patient answered dashingly.
Have you been to Barbados?
That's right, Mister Doctor!
The students present at this dialogue looked at the professor in amazement. Bell explained how simple and logical his conclusions were.
This man, having shown politeness and courtesy upon entering the office, still did not take off his hat. The army habit took its toll. If the patient had been retired for a long time, he would have long ago learned civil manners. His posture is imperious, his nationality is clearly Scottish, and this indicates that he was a commander. As for staying in Barbados, the visitor suffers from elephantiasis (elephantiasis) - such a disease is common among the inhabitants of those places.
Here deductive reasoning is extremely abbreviated. In particular, all general statements are omitted, without which deduction would be impossible.
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 driver, and he says: “Ah, Mr. Doyle, I greet you after your journey to Constantinople and Milan!” “How could you know where I came from?” - Conan Doyle was surprised at Sherlock Holmes’s insight. “According to the stickers on your suitcase,” the coachman smiled slyly.
This is another deduction, very short and simple.
Deductive argumentation
Deductive argumentation is the derivation of a substantiated position from other, previously accepted provisions. If the put forward position can be logically (deductively) deduced from already established provisions, this means that it is acceptable to the same extent as these provisions. Justifying some statements by reference to the truth or acceptability of other statements is not the only function performed by deduction in argumentation processes. Deductive reasoning also serves to verification(indirect confirmation) of statements: from the position being verified, its empirical consequences are deductively derived; confirmation of these consequences is assessed as an inductive argument in favor of the original position. Deductive reasoning is also used to falsification statements by showing that their consequences are false. Unsuccessful falsification is a weakened version of verification: failure to refute 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 logical connections, statements included in it, constructing explanations and understandings based on the general principles proposed by the theory. Clarifying the logical structure of a theory, strengthening its empirical basis, and identifying its general premises are important contributions to the substantiation of its claims.
Deductive argumentation is universal, applicable to all areas of knowledge and to any audience. “And if bliss is nothing other than eternal life,” writes the medieval philosopher I.S. Eriugena, “and eternal life is the knowledge of truth, then
bliss - it is nothing other than the knowledge of the truth.” This theological reasoning is a deductive reasoning, namely a syllogism.
The proportion of deductive argumentation in different fields of knowledge is significantly different. It is used very widely in mathematics and mathematical physics and only occasionally in history or aesthetics. Referring to the scope of deduction, Aristotle wrote: “Scientific proof should not be demanded of an orator, just as emotional persuasion should not be demanded of a mathematician.” Deductive argumentation is a very powerful tool and, like any such tool, must be used narrowly. Trying 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 argumentation is used, all sciences are usually divided into deductive And inductive. In the first, deductive argumentation is used primarily or even exclusively. Secondly, such argumentation plays only a obviously auxiliary role, and in the first place is empirical argumentation, which has an inductive, probabilistic nature. Mathematics is considered a typical deductive science; natural sciences are an example of inductive sciences. However, the division of sciences into deductive and inductive, widespread at the beginning of this century, has now largely lost its meaning. It is focused on science, considered statically, as a system of reliably and finally established truths.
The concept of deduction is a general methodological concept. In logic it corresponds to the concept proof.
Concept of proof
A proof is a reasoning that establishes the truth of a statement by citing other statements whose truth is no longer in doubt.
The proof differs thesis - the statement to be proven, and base, or arguments,- those statements with the help of which the thesis is proven. For example, the statement “Platinum conducts electricity” can be proven 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 all scientific theories.
Logic does not pretend to fully disclose the intuitive, or "naive", concept of proof. The evidence forms a rather vague body of evidence that cannot be captured 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 specific system or theory. At the same time, the existence of different concepts of proof related to different systems is allowed. For example, a proof in intuitionistic logic and the mathematics based on it differs significantly from the proof in classical logic and the mathematics based on it. In a 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.
Based on the method used, evidence is divided into two types. At direct evidence the task is to find such convincing arguments from which the thesis logically follows. Indirect 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 derived? Note that the diagonal divides the quadrilateral into two triangles. This means that the sum of its angles is equal to the sum of the angles of two triangles. It is known 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 space mechanics. It is known that these laws are universal: all bodies at any point in outer space obey them. It is also obvious that a spaceship is a cosmic body. Having noted this, we build the corresponding deductive conclusion. It is direct evidence of the statement in question.
In indirect proof, the reasoning goes in a roundabout way. Instead of directly finding
to nod arguments to deduce from them the position being proven, an antithesis, a negation of this position, is formulated. Further, in one way or another, the inconsistency of the antithesis is shown. According to the law of excluded middle, if one of the contradictory statements is false, the second must be true. The antithesis is false, which means the thesis is true.
Since indirect evidence uses the negation of the proposition being proven, it is, as they say, proof by contradiction.
Let’s say you need to construct 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. For this purpose, we derive consequences from it. If at least one of them turns out to be false, this will mean that the statement itself from which the corollary is derived is also false. In particular, the following corollary is false: a square has no corners. Since the antithesis is false, the original thesis must be true.
Another example. A doctor, convincing a patient that he does not have the flu, argues like this. If there really was a flu, there would be symptoms characteristic of it: headache, fever, etc. But there is nothing like it. This means there is no flu.
This is again indirect evidence. Instead of directly substantiating the thesis, an antithesis is put forward that the patient actually has the flu. Consequences are drawn from the antithesis, but they are refuted by objective data. This suggests that the influenza assumption is incorrect. It follows that the thesis “There is no flu” is true.
Evidence by contradiction is common in our reasoning, especially in argument. 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 consequence. Both of these concepts are not clear, and, therefore, the concept of proof defined through them also cannot be classified as clear.
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 what direction they need to be transformed. The description is required to be appropriate
there was reality. Successful advice (order, etc.) is characterized as effective or expedient, but not as true. The statement, "Water boils" is true if water actually boils; the command “Boil the water!” may be expedient, but has no relation to the truth. It is obvious that, 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 evidence, defined in terms of truth. It should cover not only descriptions, but also assessments, norms, etc. The problem of redefining proof has not yet been solved either by the logic of evaluations or by deontic (normative) logic. This makes the concept of evidence not entirely clear in its meaning.
There is, further, 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 implication available in modern logic are free from criticism and from what is commonly called “paradoxes of logical implication.”
The model of proof that all sciences strive to follow to one degree or another is mathematical proof. For a long time it was believed that it represented a clear and indisputable process. In our century, the attitude towards mathematical proof has changed. The mathematicians themselves split into hostile factions, each with its own interpretation of the proof. The reason for this was primarily a change in ideas about the logical principles underlying the proof. The confidence in their uniqueness and infallibility has disappeared. Logicism was convinced that logic was sufficient to justify all mathematics; according to formalists (D. Hilbert and others), logic alone is not enough for this and logical axioms must be supplemented with mathematical ones; representatives of the set-theoretic movement 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 has shown that there are no criteria for proof that do not depend on either
time, neither on what is required to be proven, nor on those who use the criteria. Mathematical proof is the paradigm of proof in general, but even in mathematics the proof is not absolute and final.
Types of induction
In inductive inference, 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 produce a false conclusion from true premises; its conclusion may contain information not contained in the premises. The concept of induction (inductive reasoning) is not entirely clear. Induction is defined essentially as "non-deduction" and is an even less clear concept than deduction. It is possible, however, to identify 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 inference, the result of which is a general conclusion about the entire class of objects based on knowledge of only some objects of this class, is usually called incomplete, or popular, induction.
For example, from the fact that the noble gases helium, neon and argon have a valence of zero, we can draw a general conclusion that all noble gases have the same valency. This is an incomplete induction, since knowledge of the three noble 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; iron, copper, zinc, silver, platinum, gold, nickel, barium, potassium, lead - 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 and hasty generalizations encountered in the history of science are given 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, let's imagine the shape of an ideally regular ball, put this ball on a plane; theoretically, he cannot hold still and will be in motion all the time. This was considered 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 the expression will be that such a material ball of any size will be supported on an ideal mirror plane by one atom, that is, it will be more capable of movement and less stable. An ideally round shape, it was believed then, by its essence is capable of supporting once communicated movement. This way explained the extremely rapid rotation of the celestial spheres and epicycles. These movements were once communicated to them by the deity and then continued for centuries as a property of the ideal spherical shape.” “How far these scientific views are from modern ones, and yet, in essence, these are strictly inductive constructions based on scientific observation. And even today among academic researchers we see attempts to revive essentially similar views,”
Hasty generalization those. generalizing without sufficient evidence is a common mistake in inductive reasoning.
Inductive generalizations require a certain amount of caution and caution. Much here depends on the number of cases studied. The broader the basis of induction, the more plausible the inductive conclusion. The diversity and heterogeneity of these cases is also important.
But the most essential is the analysis of the nature of the connections of objects and their characteristics, proof of the non-randomness of the observed regularity, its rootedness in the essence of the objects under study. Identifying the reasons 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 inductively, are not yet full-fledged truths. They have a long way to go
a difficult path until they turn from probabilistic assumptions into constituent elements of scientific knowledge.
Induction finds application not only in the field of descriptive statements, but also in the field of assessments, 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 reference to what is given in direct experience. At the same time, there are methods for justifying assessments that are in a certain respect similar to methods for justifying descriptions and which can therefore be called quasi-empirical. These include various inductive reasoning, among the premises of which there are estimates and the conclusion of which is also an estimate or a similar statement. Among such methods are incomplete induction, analogy, reference to a sample, purposeful justification (confirmation), etc.
Values are not given to a person in experience. They speak not 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 to inductively substantiate estimates is incomplete (popular) induction. Its general scheme:
S 1 must be R.
S 2 should be R.
S n must be R.
All S 1, S 2,...,S n are P.
All S's must be P's.
Here the first n premises are evaluations, the last premise is a descriptive statement; conclusion - evaluation. For example:
Suvorov must be persistent and courageous.
Napoleon must be persistent and courageous.
Eisenhower must be steadfast and courageous.
Suvorov, Napoleon, Eisenhower were commanders.
Every commander must be steadfast and courageous.
Along with incomplete induction, it is customary to distinguish as a special type of inductive reasoning floor-
new induction. In its 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 a given set have this property.
For example, a teacher, reading a list of students in a class, makes sure that everyone he named is present. Based on this, the teacher concludes that all students are present.
In complete induction, the conclusion is necessary and does not follow with some probability from the premises. This induction is thus a type of deductive inference.
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 popular induction, based on a simple listing of confirming examples. He wrote: “Induction, which is accomplished by simple enumeration, is a childish thing, it gives shaky conclusions and is exposed to the danger of contradictory particulars, making a decision for the most part 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 path of discovery of 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”. By entering into this kind of computer all the propositions relating to observations, we would receive at the output an exact system of laws explaining these observations.
Bacon's program was, of course, a pure utopia. No “inductive machine” that processes facts into new laws and theories is possible. Induction, leading from particular statements to general ones, gives only probable, not certain knowledge.
All this once again confirms a fundamentally simple idea: knowledge of the real world is always creativity. Standard rules, principles and techniques for
no matter how perfect they are, they do not guarantee the reliability of new knowledge. The strictest adherence to them does not protect against mistakes and misconceptions.
Every discovery requires talent and creativity. And even the very use of various techniques, which to some extent facilitate the path to discovery, is a creative process.
"Inverted Laws of Logic"
It has been suggested that all "reversed laws of logic" can be attributed to patterns of inductive reasoning. By “inverted laws” we mean formulas obtained from the laws of logic that have the form of implication (conditional statement) by reversing the places of reason and consequence. For example, if the expression:
“If A and B, then A” is a law of logic, then the expression:
"If A, then A and B"
there is a scheme of inductive inference. Likewise for:
“If A, then A or B” and diagrams:
“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 laws of logic, then the expressions:
“If A is possible, then A” and “If A, then A is necessary” are patterns of inductive reasoning. There are infinitely many laws of logic. This means that there are an infinite number of inductive reasoning schemes.
The assumption that “inverted laws of logic” are patterns of inductive reasoning, however, encounters serious objections: some “inverted laws” remain laws of deductive logic; a number of “inverted laws”, when interpreted as induction schemes, sound very paradoxical. The “inverted laws of logic” do not, of course, exhaust all possible induction schemes.
Indirect confirmation
In science, and not only in it, direct observation of what is said in the statement being verified is rare.
The most important and at the same time universal method of confirmation is derivation of logical consequences from a justified position
developments and their subsequent verification. Confirmation of the consequences is assessed 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 convey one's knowledge to someone else, perhaps far from the subject under discussion. If a person has this skill and his speech is clear and convincing, this can be taken as evidence that his thinking is also clear.
It is known that a very cool object in a warm room becomes covered with dew drops. If we see that a person’s glasses immediately fog up when they enter the house, we can conclude with reasonable certainty that it is frosty outside.
In each of these examples, the reasoning follows the scheme: “from the first the second follows; the second is true; this means that the first is also, in all likelihood, true” (“If it’s frosty outside, a person’s glasses fog up when they enter the house; the glasses actually fog up; that means it’s frosty outside”). This is not deductive reasoning; the truth of the premises does not guarantee the truth of the conclusion. 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 specifically cool them, say, in the refrigerator so that then make us believe that it is bitterly cold outside).
The derivation of consequences and their confirmation, taken in itself, is never able to establish the validity of the position being justified. Confirming the consequences only increases its likelihood.
The greater the number of consequences that have been confirmed, the higher the probability of the statement being verified. Hence the recommendation to derive as many logical consequences as possible from the provisions put forward and requiring a reliable foundation in order to verify them.
It is not only the number of consequences that matters, but also their nature. The more unexpected consequences of a proposition are confirmed, the stronger the argument they provide in its support. And vice versa, the more expected in the light of those who have already received support
confirmation of the consequences is a new consequence, the less its contribution to the substantiation of the position being verified.
A. Einstein's general theory of relativity predicted a peculiar and unexpected effect: not only do the planets revolve around the Sun, but also the ellipses that they describe should 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 detected. The ellipse of Mercury, the planet closest to the Sun, completes its rotation every 3 million years, which can be detected. And the rotation of this ellipse was indeed discovered by astronomers, long before Einstein. There was no explanation for this rotation. The theory of relativity did not rely in its formulation on data on the orbit of Mercury. Therefore, when the correct conclusion 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.
Confirming unexpected predictions made on the basis of a proposition greatly increases its credibility. 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 statement cannot, in principle, be proven based on just confirmation of the consequences that follow from it.
This is the central point of all discussions of empirical confirmation. Direct observation of what is said in a statement gives confidence in the truth of the statement. 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 credibility of a statement, but does not make it reliable.
The importance of empirically substantiating claims cannot be overstated. It is due primarily to the fact that the only source of our knowledge is experience. Knowledge begins with living, sensory contemplation, with what is given directly.
nom observation. Sensory experience connects a person with the world, theoretical knowledge is only a superstructure over the empirical basis.
At the same time, the theoretical cannot be completely reduced to the empirical. Experience is not an absolute and indisputable guarantor of the irrefutable knowledge. It can also be criticized, tested and revised. “In the empirical basis of objective science,” writes K. Popper, “there is nothing “absolute.” 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 the 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 and capable, at least for a while, of supporting 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 turn out to be incomprehensible how it is still possible to move from hypotheses to theories, from assumptions to true knowledge.
Purpose justification
Target inductive justification is a justification for a positive assessment of some object by reference to the fact that with its help another object that has a positive value can be obtained.
For example, you should do exercises in the morning, as this promotes health; one must respond with good for good, as this leads to justice in relations between people, etc. Purposeful justification is sometimes called motivational; if the goals mentioned in it are not human goals, it is usually called teleological.
As already mentioned, the central and most important way of empirically substantiating descriptive statements is the derivation of logical consequences from the position being justified and their subsequent experimental verification. Confirmation of the consequences is evidence in favor of the truth of the position itself. Schemes of indirect empirical confirmation:
/1/ From A logically follows B; B is confirmed by experience;
it means that A is probably true;
/2/ A is the cause of B; consequence B takes place;
This means that cause A probably also occurs.
An analogue of 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; So, apparently, it’s good that we’ll go to the cinema tomorrow and go to the theater.” This is an inductive reasoning that justifies one evaluation (“It’s good that we will go to the cinema tomorrow and go to the theater”) by reference to another evaluation (“It’s good that we will 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 justification (confirmation) of assessments:
/2*/ A is the cause of B; consequence B is positively valuable;
so it is likely that reason A is also positively valuable.
For example: “If it rains at the beginning of summer, the harvest will be large; It’s good that there will be a big harvest; So, apparently, it’s good that it rains at the beginning of summer.” This is again inductive reasoning, justifying one evaluation (“It’s good that it’s raining at the beginning of summer”) by reference to another evaluation (“It’s good that there will be a big harvest”) and a certain causal connection.
In the case of schemes /1*/ and /2*/ we are talking about quasi-empirical justification, since the confirmed consequences are estimates, and not empirical (descriptive) statements.
In the /2*/ scheme, 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 “cause-effect” connection turns into a “means-end” connection. . Scheme /2*/ can be reformulated as follows:
A is a means to achieve B; B is positively valuable; therefore, A is probably also positively valuable.
Reasoning following this scheme justifies the means by reference to the positive value of the achieved
with their help goals. It is, one might say, an expanded formulation of the well-known and always controversial principle “The end justifies the means.” The disputes are explained by the inductive nature of the principle of goal justification: the goal probably, but not always and not necessarily, justifies the means.
Another scheme of quasi-empirical target justification is the scheme:
/2**/ not-A is the reason not-B; but B is positively valuable;
therefore, A is probably also positively valuable.
For example: “If you don’t hurry up, we won’t arrive at the start of the performance; It would be nice to be there for the start of the performance; So, apparently, you should hurry up.”
It is sometimes argued that purposive justification for evaluations is deductive reasoning. However, it is not. Purposeful justification, and in particular, the so-called practical syllogism, represents inductive reasoning.
Purposeful justification for evaluations is widely used in a variety of areas of evaluative reasoning, from everyday, moral, and political discussions to methodological, philosophical and scientific disputes. Here is a typical example taken from B. Russell’s book “The History of Western Philosophy”: “Most of the opponents of the Lockean school,” writes Russell, “admired war as a heroic phenomenon and implying contempt for comfort and peace. Those who embraced utilitarian ethics, on the other hand, tended to consider most wars to be madness. This again, at least in the 19th century, led them to an alliance with the capitalists, who did not like wars, since wars interfered with trade. The motives of the capitalists, of course, were purely selfish, but they led to views more in tune with general interests than the views of the militarists and their ideologists.” This passage mentions three different target arguments to justify or condemn war:
War is a manifestation of heroism and fosters contempt for comfort and peace; heroism and contempt for comfort and peace are positively valuable; This means that war is also positively valuable.
War not only does not contribute to general happiness, but, on the contrary, seriously impedes it; general happiness is something to which we should strive in every possible way; This means that war must be categorically avoided.
War interferes with trade; trade is positively valuable; This means war is harmful.
The persuasiveness of the goal justification depends significantly on three circumstances: first, how effective is the connection between the goal and the means that are proposed to achieve it; secondly, whether the remedy itself is sufficiently acceptable; third, how acceptable and important is the assessment that captures the goal. The same target rationale may have different persuasiveness in different audiences. This means that the purpose rationale relates to contextual(situational) methods of argumentation that are not effective in all audiences.
Facts as examples
Empirical data, facts, can be used to directly confirm what is stated in the proposition put forward, or to confirm the logical consequences of this proposition. Confirmation of the consequences is an indirect confirmation of the position itself.
Facts or special cases can also be used as examples, illustrations And samples. In all these three cases we are talking about inductive confirmation of some general position by empirical data. By serving as an example, a particular case makes a generalization possible; by way of illustration it reinforces a general proposition already established; and finally, as a model, it encourages imitation.
The use of particular cases as exemplars has no bearing on argumentation in support of descriptive statements. It directly relates to the problem of justifying assessments and arguing in support of them.
Example- it is a fact or special case used as a starting point for a subsequent generalization and to reinforce the generalization made.“Next I say,” writes the 18th century philosopher. J. Berkeley - that sin or moral depravity does not consist in external physical action or movement,
but in the internal deviation of the will from the laws of reason and religion. After all, 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 (killing in war and in execution of a death sentence) intended to confirm the general point about sin or moral depravity. The use of facts or particular cases as examples must be distinguished from the use of them as illustrations. Acting as an example, a particular case makes a 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 following scheme:
“if the first, then the second; the second takes place;
this means that the first also takes place.”
This reasoning goes from asserting the consequence of a conditional statement to asserting its basis and is not correct deductive reasoning. The truth of the premises does not guarantee the truth of the conclusion drawn from them. Reasoning based on an example does not prove the position accompanied by the example, but only confirms it and makes it more plausible. The example, however, has a number of features that distinguish it from among all those facts and special cases that are used to confirm general provisions and hypotheses. An example is more convincing or weightier than other 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 an example explains its widespread use in argumentation processes, and especially in humanitarian and practical argumentation, as well as in everyday reasoning.
An example may only be used to support descriptive statements. He is not able to support assessments and statements that, like norms, oaths, promises, etc., tend towards assessments. An example cannot serve as source material for evaluative and similar statements. What is sometimes presented as an example, intended to somehow confirm an assessment, 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, from
relating to a particular case and establishing a particular standard, ideal, etc.
The purpose of the example is to lead to the formulation of a general position and, to some extent, to be an argument in support of the latter. Example selection criteria are associated with this purpose. First of all, the fact or particular case chosen as an example must appear clear and indisputable. It must also clearly express the tendency to generalize. Related to the requirement of bias, or typicality, of facts taken as examples is the recommendation to list several examples of the same type, if taken individually they do not show with the necessary certainty the direction of the upcoming generalization or do not reinforce the generalization already made. If the intention to argue with an example is not openly announced, 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 mere additional information. The event used as an example should be perceived, if not as ordinary, then at least as logically and physically possible. If this is not so, then the example simply breaks the sequence of reasoning and leads to the opposite result or to a comic effect. Examples should be selected and formulated in such a way that they encourage a move from the individual or particular to the general, and not from the particular back to the particular.
Requires special attention contradictory example. It is usually believed that such an example can only be used to refute erroneous generalizations and their falsification. However, a contradictory example is often used in another way: it is introduced with the intention of preventing an unlawful generalization and, demonstrating its incompatibility with it, suggesting the only direction in which the generalization can go. The task of a 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 belief in the correctness of an already known general position. An example pushes thought to a new generalization and reinforces this generalization.
The presentation, illustration, clarifies a well-known general proposition, demonstrates its meaning through a range of possible applications, and enhances the effect of its presence in the minds of the audience. The difference in the tasks of the example and illustration is associated with the difference in the criteria for their selection. The example should look like a fairly solid, unambiguously interpretable fact; the illustration has the right to raise slight doubts, but it should have a particularly vivid impact on the audience’s imagination and attract their attention. An illustration, to a much lesser extent than an example, runs the risk of being misinterpreted, since it is based on an already known position. The distinction between example and illustration is not always clear-cut. Aristotle distinguished two uses of example depending on whether the speaker has any general principles or not: “It is necessary to give many examples to the one who puts them at the beginning, and to the one who puts them at the end, for him one [example] is enough,” for a witness who deserves faith is useful even when he is alone.” The role of particular cases, according to Aristotle, is different depending on whether they precede the general situation to which they relate or follow it. The point, however, is that the facts given before the generalization are usually examples, while the one or few facts given after it are illustrations. This is also evidenced by Aristotle’s warning that the listener’s demands for an example are higher than for an illustration. An unsuccessful example casts doubt on the general point it is intended to reinforce. A contradictory example can even refute this position. The situation is different with an unsuccessful illustration: the general position to which it is brought is not questioned, and an inadequate illustration is regarded rather as a negative characteristic of the one who uses it, indicating his lack of understanding of the general principle or his inability to choose a successful illustration. A bad illustration can have a comic effect. The ironic use of illustration is especially effective when describing a particular person: first a positive characteristic is given to that person, and then an illustration is given that is directly inconsistent with it. So, in Shakespeare's Julius Caesar, Antony, constantly reminding that Brutus is an honest man, gives one
after another evidence of his ingratitude and betrayal.
By specifying the general situation with the help of a particular case, the illustration enhances the effect of presence. On this basis, they sometimes see in it an image, a living picture of an abstract thought. The illustration does not, however, set itself the goal of replacing the abstract with the concrete and thereby transferring consideration to other objects. It does analogy, an illustration is nothing more than a special case that confirms an already known general position or facilitates a clearer understanding of it.
Often an illustration is chosen based on the emotional resonance it can evoke. This is what Aristotle does, for example, preferring a periodic style to a coherent style that does not have a clearly visible end: “... because everyone wants to see the end; For this reason, those competing in the race become out of breath and become weak on turns, whereas before they did not feel tired, seeing the limit of the run in front of them.”
A comparison used in argumentation, which is not a comparative evaluation (preference), is usually an illustration of one case by another, both cases being considered as instantiations of the same general principle. A typical example of comparison: “People are shown by circumstances. Therefore, when some circumstance befalls you, remember that it was God, like a gymnastics teacher, who pushed you to a rough end” (Epictetus).
Samples and ratings
A pattern is a behavior that a person or group of people should follow. A pattern is fundamentally different from an example: an example says what actually is and is used to support descriptive statements, a sample says what should be and is used to support general evaluative statements. Due to its special social prestige, the model not only supports the assessment, but also serves as a guarantee of the chosen type of behavior: 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 era are largely characterized by the patterns they follow and the
how these patterns are understood by them. There are models intended for universal imitation, but there are also ones designed only for a narrow circle of people. Don Quixote is a unique model: he is imitated precisely because he was able to selflessly follow the model he himself had chosen. A model can be a real person, taken in all the diversity 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. The model can be the behavior of a fictional person: a literary hero, a hero of myth, etc. Sometimes such a hero does not act as a complete person, but demonstrates only individual virtues through 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. Haas, the love of Don Juan, etc. Indifference to a model can itself look like a model: the example is sometimes set to someone who knows how to avoid the temptation of imitation. If the model is an integral person, who usually has not only merits, but also certain shortcomings, it often happens that his shortcomings have a greater impact on people’s behavior than his undeniable advantages. As B. Pascal noted, “the 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’s not at all shameful to be less virtuous than him, and it’s forgivable to be just as vicious.”
Along with samples, there are also anti-samples. The task of the latter is to provide repulsive examples of behavior and thereby discourage such behavior. The effect of the anti-example is, in the case of some people, even more effective than the effect of the exemplary. As factors determining behavior, the model and the anti-model are not entirely equal. Not everything that can be said about a model is equally applicable to an anti-model, which is, as a rule, less definite and can only be correctly interpreted by comparing it with a specific model: what does it mean not to resemble Sancho Panza in your behavior, understandable only to those who know the behavior of Don Quixote.
Reasoning appealing to a model is similar in structure to reasoning appealing to an example:
“If there must be the first, then there must be the second;
the second must be;
So it must be the first.”
This reasoning goes from asserting the consequence of a conditional statement to asserting its basis 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 must choose a sample based on indirect instructions from the author.
Along with patterns of human actions, there are also samples of other things: objects, events, situations, etc. The first samples are usually called ideals, second - standards. For all objects that a person regularly encounters, be it hammers, watches, medicines, etc., there are standards that indicate what objects of this kind should be. Reference to these standards is a common method of argumentation in support of assessments. A standard relating to items of a particular type usually takes into account their typical function; in addition to functional properties, it may also include some morphological characteristics. 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 you to drive nails, 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, filled with poetic flight, but does not provide solid knowledge, and is often simply misleading. This very popular method is inference by analogy.
A child sees a little monkey at 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 person, but only in a fur coat, that he can, like a person, play and talk. Where does this belief come from? In appearance, facial expressions, and gestures, the monkey resembles a human. It seems to the child that he can play and talk with her, just like with a person.
Having met the journalist, we learn that this intelligent, widely educated man speaks fluent English, German and French. Having then met another journalist, intelligent, educated, fluent in English and German, we may not resist the temptation to ask if he also speaks French.
Deduction This is a way of reasoning from general provisions to particular conclusions.
Deductive reasoning only concretizes our knowledge. A deductive conclusion contains only the information that is in the accepted premises. Deduction allows you to obtain new truths from existing knowledge using pure reasoning.
Deduction gives a one hundred percent guarantee of the correct conclusion (with reliable premises). Deduction from truth produces truth.
Example 1.
All metals are ductile(b O least valid premise or main argument).
Bismuth is a metal(reliable premise).
Therefore, bismuth is plastic(correct conclusion).
Deductive reasoning that produces a true conclusion is called a syllogism.
Example 2.
All politicians who allow contradictions are a joke(b O the largest reliable premise).
E Ltsin B.N. admitted contradictions(reliable premise).
Therefore, E.B.N. is a joke(correct conclusion) .
Deduction from a lie comes a lie.
Example.
Help from the International Monetary Fund always leads to prosperity for everyone(false premise).
The IMF has been helping Russia for a long time(reliable premise).
Therefore, Russia is prospering(false conclusion).
Induction – a way of reasoning from particular provisions to general conclusions.
An inductive conclusion may contain information that is not contained in the accepted premises. The validity of the premises does not mean the validity of the inductive conclusion. Premises make the conclusion more or less likely.
Induction does not provide reliable, but probabilistic knowledge that needs to be verified.
Example 1.
G.M.S. - pea jester, E.B.N. - pea jester, Ch.A.B. - pea jester(reliable premises).
G.M.S., E.B.N., Ch.A.B. – politicians(reliable premises).
Therefore, all politicians are clowns(probabilistic conclusion).
The generalization is plausible. However, there are politicians who can think.
Example 2.
In recent years, military exercises have been held in area 1, area 2 and area 3, increasing the combat effectiveness of units(reliable premises).
In area 1, in area 2 and in area 3, units of the Russian Army took part in the exercises(reliable premises).
Consequently, in recent years, the combat effectiveness of all units of the Russian Army has increased(inductive invalid inference).
A general conclusion does not logically follow from particular provisions. Showy events do not prove that there is prosperity everywhere:
In fact, the overall combat capability of the Russian Army is catastrophically declining.
A variant of induction is inference by analogy (based on the similarity of two objects in one parameter, a conclusion is drawn about their similarity in other parameters as well).
Example. The planets Mars and Earth are similar in many ways. There is life on Earth. Since Mars is similar to Earth, Mars also has life.
This conclusion is, of course, only probabilistic.
Any inductive conclusion needs to be verified.Dmitry Mezentsev (coordinator of the project "Russian Society of Good Action") 2011
Induction and deduction are interrelated, complementary methods of inference. A whole occurs in which a new statement is born from judgments based on several conclusions. The purpose of these methods is to derive new truth from pre-existing ones. Let's find out what it is and give examples of deduction and induction. The article will answer these questions in detail.
Deduction
Translated from Latin (deductio) it means “deduction”. Deduction is the logical conclusion of the particular from the general. This line of reasoning always leads to a true conclusion. The method is used in cases where it is necessary to derive the necessary conclusion about a phenomenon from a generally known truth. For example, metals are heat-conducting substances, gold is a metal, we conclude: gold is a heat-conducting element.
Descartes is considered the founder of this idea. He argued that the starting point of deduction begins with intellectual intuition. His method includes the following:
- Recognizing as true only what is known with maximum obviousness. There should not be any doubts in the mind, that is, one must judge only on irrefutable facts.
- Divide the phenomenon under study into as many simple parts as possible so that they can be easily overcome.
- Move from simple gradually to more complex.
- Compile the overall picture in detail, without any omissions.
Descartes believed that with the help of such an algorithm, the researcher would be able to find the true answer.
It is impossible to comprehend any knowledge except through intuition, reason and deduction. Descartes
Induction
Translated from Latin (inductio) it means “guidance”. Induction is the logical conclusion of the general from particular judgments. Unlike deduction, reasoning leads to a probable conclusion, all because several bases are generalized, and hasty conclusions are often drawn. For example, gold, like copper, silver, and lead, is a solid substance. This means that all metals are solids. The conclusion is not correct, since the conclusion was hasty, because there is a metal such as mercury, and it is a liquid. An example of deduction and induction: in the first case, the conclusion turned out to be true. And in the second - probable.
Economic sphere
Deduction and induction in economics are research methods on a par with such as observation, experiment, modeling, method of scientific abstractions, analysis and synthesis, systems approach, historical and geographical method. When using the inductive method, research begins with observation of economic phenomena, facts are accumulated, and then a generalization is made on their basis. When applying the deductive method, an economic theory is formulated, then hypotheses are tested based on it. That is, from theory to facts, research goes from general to specific.
Let us give examples of deduction and induction in economics. The increase in the cost of bread, meat, cereals and other goods forces us to conclude that prices are rising in our country. This is induction. The notification about the increase in the cost of living makes it seem that prices for gas, electricity, other utilities and consumer goods will increase. This is deduction.
Field of psychology
For the first time, the phenomena in psychology we are considering were mentioned in his works by an English thinker. His merit was the unification of rational and empirical knowledge. Hobbes insisted that there can only be one truth, achieved through experience and reason. In his opinion, knowledge begins with sensibility as the first step towards generalization. The general properties of phenomena are established using induction. Knowing the actions, you can find out the cause. After clarifying all the reasons, we need the opposite path, deduction, which makes it possible to understand new and different actions and phenomena. and deductions in psychology according to Hobbes show that these are interchangeable stages of one cognitive process, passing from each other.
Sphere of Logic
We are familiar with two types thanks to such a character as Sherlock Holmes. Arthur Conan Doyle introduced the deductive method to the whole world. Sherlock began the observation with the general picture of the crime and led to the specific, that is, he studied each suspect, every detail, motives and physical capabilities, and, using logical conclusions, figured out the criminal, arguing with iron-clad evidence.
Deduction and induction in logic are simple; without noticing, we use it every day in everyday life. We often react quickly, instantly jumping to the wrong conclusion. Deduction is longer thinking. To develop it, you need to constantly challenge your brain. To do this, you can solve problems from any field, mathematics, physics, geometry, even puzzles and crosswords will help develop thinking. Books, reference books, films, travel - everything that broadens one's horizons in various fields of activity will provide invaluable assistance. Observation will help you come to the correct logical conclusion. Every, even the most insignificant, detail can become part of one big picture.
Let's give an example of deduction and induction in logic. You see a woman about 40 years old, in her hand is a handbag with an unfastened zipper due to the large number of notebooks in it. She is dressed modestly, without frills or frilly details, on her hand is a thin watch and a white chalk mark. You will conclude that most likely she works as a teacher.
Sphere of pedagogy
The method of induction and deduction is often used in school education. Methodological literature for teachers is organized inductively. This type of thinking is widely applicable to studying technical devices and solving practical problems. And with the help of the deductive method it is easier to describe a large number of facts, explaining their general principles or properties. Examples of deduction and induction in pedagogy can be observed in any lesson. Often in physics or mathematics, the teacher gives a formula, and then during the lesson the students solve problems that fit this case.
In any field of activity, the methods of induction and deduction are always useful. And you don’t have to be a super detective or a genius in scientific fields to do this. Give your thinking a workout, develop your brain, train your memory, and in the future complex tasks will be solved on an instinctive level.
Inference is a logical operation, as a result of which, from one or more accepted statements (premises), a new statement is obtained - a conclusion (consequence).
Depending on whether there is a connection between the premises and the conclusion logical consequence, two types of inferences can be distinguished.
In deductive reasoning, this connection is based on a logical law, due to which the conclusion follows with logical necessity from the accepted premises. As already noted, the distinctive feature of such an inference is that it always leads from true premises to a true conclusion.
Deductive inferences include, for example, the following inferences:
If a given number is divisible by 6, then it is divisible by 3.
This number is divisible by 6.
This number is divisible by 3.
If helium is a metal, it is electrically conductive.
Helium is not electrically conductive.
Helium is not a metal.
The line separating the premises from the conclusion replaces the word “therefore.”
In inductive inference, the connection between premises and conclusion is based not on the law of logic, but on some factual or psychological grounds that are not of a purely formal nature. In such an inference, the conclusion does not follow logically from the premises and may contain information not contained in them. The reliability of the premises does not therefore mean the reliability of the statement inductively derived from them. Induction produces only probable, or plausible, conclusions that require further verification.
Examples of induction include reasoning:
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 are Western European countries.
All Western European countries are republics.
Induction does not provide a complete guarantee of obtaining a new truth from existing ones. The maximum we can talk about is a certain degree of probability inferred statement. Thus, the premises of both the first and second inductive inferences are true, but the conclusion of the first is true, and the second is false. Indeed, all Latin American states are republics; but among Western European countries there are not only republics, but also monarchies, for example, England, Belgium and Spain.
Particularly characteristic deductions are logical transitions from general knowledge to particular. In all cases when it is necessary to consider a phenomenon on the basis of an already known general principle and draw the necessary conclusion regarding this phenomenon, we conclude in the form of deduction (All poets are writers; Lermontov is a poet; therefore, Lermontov is a writer).
Reasoning leading from knowledge about some objects to general knowledge about all objects of a certain class are typical inductions, since there is always the possibility that the generalization will turn out to be hasty and unfounded (Plato is a philosopher; Aristotle is a philosopher; that means all people are philosophers) .
At the same time, one cannot identify deduction with the transition from the general to the particular, and induction with the transition from the particular to the general. Deduction is a logical transition from one truth to another, induction is a transition from reliable knowledge to probable. Inductive inferences include not only generalizations, but also likenings or analogies, conclusions about the causes of phenomena, etc.
Deduction plays a special role in justifying statements. If the provision in question logically follows from already established provisions, it is justified and acceptable to the same extent as the latter. This is a strictly logical way of justifying statements, using pure reasoning and not requiring recourse to observation, intuition, etc.
While emphasizing the importance of deduction in the process of justification, one should not, however, separate it from induction or underestimate the latter. Almost all general principles, including, of course, scientific laws, are the result of inductive generalization. In this sense, induction is the basis of our knowledge. In itself, it does not guarantee its truth and validity. But it gives rise to assumptions, connects them with experience and thereby gives them a certain verisimilitude, a more or less high degree of probability. Experience is the source and foundation of human knowledge. Induction, starting from what is comprehended in experience, is a necessary means of its generalization and systematization.
Deduction is the derivation of conclusions that are as valid as the premises accepted.
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 of them. General statements that can be assumed to be well known are generally omitted. The conclusions that follow from the accepted premises are not always clearly formulated. The very logical connection that exists between the initial and deduced statements is only sometimes marked by words like “therefore” and “means.”
Often the deduction is so abbreviated that one can only guess about it. It can be difficult to restore it in full form, indicating all the necessary elements and their connections.
Carrying out deductive reasoning without omitting or shortening anything is cumbersome. A person who points out all the premises for his conclusions gives the impression of some kind of pedant. And at the same time, whenever doubt arises about the validity of the conclusion made, one should return to the very beginning of the reasoning and reproduce it in the most complete form possible. Without this, it is difficult or even impossible to detect a mistake.
Many literary critics believe that Sherlock Holmes was “copied” by A. Conan-Doyle from Joseph Bell, a professor of medicine at the University of Edinburgh. The latter was known as a talented scientist with rare powers of observation and excellent command of the method of deduction. Among his students was the future creator of the image of the famous detective.
One day, Conan Doyle says in his autobiography, a patient 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 rifle regiment?
That's right, Mister Doctor!
Recently retired?
Yes sir!
Were you a sergeant?
Yes sir! - the patient answered dashingly.
Have you been to Barbados?
That's right, Mister Doctor!
The students present at this dialogue looked at the professor in amazement. Bell explained how simple and logical his conclusions were.
This man, having shown politeness and courtesy upon entering the office, still did not take off his hat. The army habit took its toll. If the patient had been retired for a long time, he would have long ago learned civil manners. His posture is imperious, his nationality is clearly Scottish, and this indicates that he was a commander. As for staying in Barbados, the visitor is sick with elephantiasis (elephantiasis) - such a disease is common among the inhabitants of those places.
Here deductive reasoning is extremely abbreviated. In particular, all general statements are omitted, without which deduction would be impossible.
The previously introduced concept of “correct reasoning (inference)” refers only to deductive reasoning. Only it can be right or wrong. In inductive reasoning, the conclusion is not logically related to the accepted premises. Since “correctness” is a characteristic of the logical connection between premises and conclusion, and this connection is not assumed by inductive inference, such a conclusion can be neither correct nor incorrect. Sometimes, on this basis, inductive reasoning is not included in the number of inferences at all.
