Statement is a more complex education than the name. With the decomposition of statements on simpler parts, we always receive certain names. Let's say, the saying "The Sun is a star" includes as its parts the name "Sun" and "Star".

Statement - grammatically correct proposal, taken together with the meaning expressed (content) and being true or false.

The concept of statement is one of the initial, key concepts of logic. As such, it does not allow accurate definition, equally applied in different sections.

The statement is considered true if the description given to them corresponds to a real situation, and false - if it does not correspond to it. "Truth" and "lies" are called "truth values \u200b\u200bof statements."

From individual statements different ways You can build new statements.

For example, from the statement "blows the wind" and "It's raining" you can form more complex statements "Blowing the wind, and it rains", "either the wind blows, or it rains", "if it rains, then the wind blows" and so on .

Statement is called simpleif it does not include other statements as its parts.

Statement is called i am complicatedif it is obtained using logical ligaments from other simpler statements.

Consider the best important methods Building complex statements.

Negative statement It consists of the initial statement and denial, and usually expressed by the words "not", "incorrectly, that." A negative statement is thus a complex statement: it includes a statement that is different from him. For example, the denial of statements "10 - even number" is the statement of "10 is not an even number" (or: "It is not true that 10 is an even number").

We denote the statements by letters A, B, C, ... The full meaning of the concept of denial of statement is given by the condition: if the statement is true, its denial is false, and if falsely, his denial is true. For example, since the statement "1 is a whole positive number" True, its denial "1 is not a whole positive number" falsely, and since "1 There is a simple number" falsely, its denial "1 is not a simple number" Truly.

The connection of two statements with the word "and" gives a complex statement called conjunction. The statements connected in this way are called "conjunction members".

For example, if the statements "today are hot" and "yesterday it was cold" to join in this way, the conjunction of "today is hot and yesterday was cold."

The conjunction is true only in the case when both statements included in it are true; If at least one of its members is false, then the whole conjunction is false.

In the usual language, two statements are connected by the Union "and" when they are interconnected by content, or meaning. The nature of this connection is not quite clear, but it is clear that we would not consider the conjunction "he was in a coat, and I went to the university" as an expression that makes sense and able to be true or false. Although the statements "2 - a simple number" and "Moscow - the Big City" are true, we are not inclined to consider the true also their conjunction "2 - a simple number, and Moscow is a big city," because the components of its statements are not related to each other. Simplifying the importance of conjunction and other logical ligaments and refusing to this from the unclear concept of "Communication of statements in meaning", the logic makes the meaning of these bundles at the same time and wider and clearer.

The connection of two statements with the word "or" gives disjunction These statements. The statements that form disjunction are called "members of disjunction" .

The word "or" in everyday language has two different meanings. Sometimes it means "one or different or both", and sometimes "one or another, but not both together." For example, the statement "This season I want to go to the" peak lady "or on Ayida" allows two-time visits to the opera. In the statement "He is studying in Moscow or Yaroslavl University" means that a mentioned person studies only in one of these universities.

The first meaning "or" is called non-exclusive. The disjunction of two statements taken in this sense means that at least one of these statements are truly, regardless of whether they are both true or not. Taught excluding, or strict, sense, the disjunction of two statements argues that one of the statements are true, and the second is false.

Incusable disjunction is true, when at least one of the statements included in it truly, and false only when both of her member is false.

Excending the disjunction is true when only one of its members is true, and it is false when both of its member are true or both false.

In logic and mathematics, the word "or" is almost always used in a non-exclusive value.

Conditional statement -a complex statement, formulated usually using a bundle "if ..., then ..." and establishing that one event, condition, etc. is in one way or another base or condition for the other.

For example: "If there is fire, that is, smoke", "if the number is divided into 9, it is divided into 3", etc.

The conditional statement is composed of two simpler statements. Then of them that the word "if" is prescribed is called base or anteceedent (previous), the statement coming after the word "that" is called consequence or conceiver (subsequent).

By approving the conditional statement, we first mean that it cannot be so that what is said about in his foundation, and what is said about what is said in the investigation was absent. In other words, it can not happen that the antecedent is true, and the consexient is false.

In terms of conditional statement, the concepts of sufficient and necessary conditions are usually determined: an antecedent (foundation) is a sufficient condition for the consexive (effect), and the consequent prerequisite For antecedent. For example, the truth of the conditional statement "If the choice is rational, then the best of the existing alternatives is selected," means that rationality is a sufficient basis for election of the best possible opportunities and that the choice of such an opportunity is the necessary condition for its rationality.

A typical function of conditional statement is the rationale for one statement by reference to another statement. For example, that silver electrically conductor can be justified by reference to the fact that it is metal: "If silver is metal, it is electrically conductive."

Expressed by the conditional statement the connection of the substantive and justified (ground and investigation) is difficult to describe in general, and only sometimes the nature of it is relatively clear. This relationship may be, permanently, the bond of a logical following, which takes place between the parcels and the conclusion of the right conclusion ("If all the living multicellular creatures are mortal, and the jellyfish is such a creature, then it is mortal"); voctern, the law of nature ("if the body is subjected to friction, it will begin to heat up"); Street, causing a connection ("If the moon in the new moon is in the node of his orbit, solar eclipse occurs"); Commonly, social law, rule, tradition ("if society changes, also a person is changing," if the Council is the intelligence, it must be performed "), etc.

With the connection expressed by the conditional statement, the conviction is usually connected that a consequence of a certain necessity "follows" from the ground and that there is some general law, it is possible to formulate that, we could logically derive a consequence of the foundation.

For example, the conditional statement "if bismuth is metal, it is plastic" as it is implies the general law "All Metals Plastic", which makes the consexient of this statement by a logical consequence of its antecedent.

And in the usual language, and in the language of science, the conditional statement besides the justification function can also be carried out by a number of other tasks: to formulate a condition that is not associated with Kakovylbo implied general law or rule ("if I want, I will cut your raincoat"); Fixed some sequence ("if the past summer was dry, then this year it is rainy"); express in a kind of unbelief form ("If you decide this task, I will prove the great theorem of the farm"); Countessing ("If the vegetable buzzin grows in the garden, the uncle lives in Kiev"), etc. The numerousness and heterogeneity of the functions of the conditional statement makes it difficult to analyze its analysis.

The use of conditional statement is associated with certain psychological factors. Usually we formulating such a statement only if we do not know with certainty, true or not its antecedent and consequent. IN otherwise Its use seems unnatural ("If the cotton is metal, it is electrically conductive").

Conditional statement finds very wide application In all spheres of reasoning. In logic, it seems usually by implicative statement, or implications. At the same time, logic clarifies, systematizes and simplifies the use of "if ..., then ...", frees it from the influence of psychological factors.

The logic is distracted, in particular, from the fact that the connection of the foundation and consequence characteristic of the conventional statement may be expressed using not only "if ..., then ...", but also other languages.

For example, "Since water is liquid, it transmits pressure in all sides evenly", "Although plasticine and not metal, it is plastic," "If the tree was metal, it would be electrically conductive", etc. These and the wrong statements They are submitted in the language of logic by implication, although the use of "if ..., then ..." It would not be quite natural.

By approving implication, we argue that it cannot happen that its foundation takes place, and the investigation was absent. In other words, the implication is false only when its basis is truly, and the result is false.

This definition assumes, as well as previous definitions of bundles, that any statement is either true or false and that the truth importance of a complex statement depends only on the truth values \u200b\u200bof the components of its statements and the method of their connection.

The implication of true when and its foundation, and its consequence is true or false; It is true if its foundation is false, and the consequence is true. Only in the fourth case, when the base is truly, and the result is false, the implication of false.

The implication does not assume that statements A and in some contents are connected. In the event of truth in the statement "If a, then in" True, regardless of whether it is true or false and is connected in meaning with or not.

For example, the true statements are considered: "If there is a life in the sun, then two are four", "if the Volga is a lake, then Tokyo is a big village", etc. The conditional statement is truly true also when it is false, and at the same time Actually, it is indifferent, truly in or not and is connected in content with or not. True belongs: "If the sun is a cube, the land is a triangle," if two two are five, then Tokyo - small city" etc.

In conventional reasoning, all these statements are unlikely to be considered as having meaning and even less as true.

Although implication is useful for many purposes, it is not entirely consistent with the usual understanding of the conditional communication. The implication covers many important features of the logical behavior of the conditional statement, but it is not at the same time sufficiently adequate description.

In the past half century, energetic attempts were made to reform the theory of implication. At the same time, it was not about the refusal of the described concept of implication, but about the introduction along with him another concept, which takes into account not only the trendy values \u200b\u200bof the statements, but also the connection of their content.

With implication closely connected equivalence, Sometimes called "double implication".

Equivalence - Complex statement "A, if only if in", formed from statements A and B and decomposing two implications: "If a, then in", and "if in, then a". For example: "The triangle is equilateral, if and only if it is equivalent." The term "equivalence" is denoted by the bunch of "..., if and only if ...", with which of the two statements, this complex statement is formed. Instead of "if and only if" for this purpose, "in that and only in the case when", "then and only when", etc., can be used.

If logical ligaments are determined in terms of truth and lies, the equivalence is true then and only when both components of its statements have the same truth value, that is, when they are both truth and both are false. Accordingly, the equivalence is false when one of the statements included in it is truly, and the other is false.

When considering the methods of education of complex statements from ordinary internal structure of simple statements, not taken into account. They were taken as indecomposable particles, possessing only one property: to be true or false. Simple statements

it is not accidentally called atomic: from them, like elementary bricks, with the help of logical ligaments "and", "or", etc., a variety of complex ("molecular") statements are built.

Now should dwell on the question about inner structure, or internal structure, simple statements themselves: from what specific parts they are composed and how these parts are interconnected.

Immediately it is necessary to emphasize that simple statements may decompose into the components of the ones. The result of decomposition depends on the target for which it is carried out, i.e., from that concept of logical output (logical follow), in which such statements are analyzed.

Of particular interest in categorical statement is due primarily to the fact that the development of logic as science began with the study of their logical connections. In addition, the statements of this type are widely used in our arguments. The theory of logical connections of categorical statements is usually referred to silchistic.

For example, in the statement "All dinosaurs extorted" dinosaurs attributed a sign "to be extinct". In the judgment, "some dinosaurs flew" the ability to fly is attributed to certain types of dinosaurs. In the judgment, "all comets is not asteroids" denies the presence of a sign "to be asteroid" in each comet. In the judgment, "some animals are not herbivores" deny the herbivities of some animals.

If you distract from the quantitative characteristic contained in the categorical statement and the words "all" and "some" and "some" words, then two options of such statements are: affirmative and negative. Their structure:

"S is r" and "s no р",

where the letter S represents the name of that subject in speaking in the statement, and the letter P is the name of a sign inherent or not inherent in this subject.

The name of the subject mentioned in a categorical statement is called subject, and his character name - predicat. Subject and predicate are referred to termines Categorical statements and interconnected by the bundles "there" or "not" ("is" or "is not" and so paragraph.). For example, in the statement of the "Sun there is a star" terms are the names of the "Sun" and "Star" (the first one is the subject of the statement, the second is its predicate), and the word "is" is a bunch.

Simple statements like "s is there (not) Р" is called attributes: they are at the attribution (attribution) of some kind of properties to the subject.

Attribute statements oppose the statements about relations in which relations are established between two or large number of subjects: "Three less than five", "Kiev is more Odessa", "spring is better than autumn", "Paris is located between Moscow and New York", etc. About relationships play a significant role in science, especially in mathematics. They are not reduced to categorically statements, since relations between several subjects (such as "equal", "loves", "warmer", "is between", etc.) do not reduce the properties of individual items. One of the essential drawbacks of traditional logic was that she considered judgments about relationships with the judgments about the properties.

In a categorical statement, the connection of the subject and the sign is not simply established, but also a certain quantitative characteristic of the subject of the statement is given. In the statements like "All S is (not) p" the word "all" means "each of the subjects of the corresponding class." In statements like "Some s is there (not) p" The word "some" is used in a non-exclusive sense and means "some, and maybe everything." In an exclusive sense, the word "some" means "only some", or "some, but not everything." The difference between the two meanings of this word can be demonstrated on the example of saying "Some stars have stars." In a non-exclusive sense, it means "some, and possibly all the stars are stars" and is obviously true. In the exclusive sense, this statement means "only some stars are stars" and is clearly false.

In categorical statements, it is approved or denying the belonging of any signs to the subjects under consideration and is indicated whether it is about all these subjects or some of them.

Thus are possible, thus four types of categorical statements:

All s is p - a secrect statement,

Some s there is p - a private complimentary statement,

All s is not p - a general negative statement,

Some s is not R - a particularly negative statement.

Categorical statements can be viewed as the results of the substitution of any names in the following expressions with spaces (dots): "Everything ... there is ...", "Some ... There is ...", "Everything ... is not ..." and "some ... not there ..." Each of these expressions is a logical constant (logical operation), which allows from two names to obtain a statement. For example, substituting instead of dull-lot the names of "flying" and "birds", we get, respectively, the following statements: "All flying birds", "some flying birds are",

Omlice

"All flying is not birds" and "some flying do not have birds." The first and third statements are false, and the second and fourth are true.

Omlice

"On one drop of water, a person who knows how to think logically, can conclude about the existence of the Atlantic Ocean or Niagara Falls, even if he did not see anything else and never heard about them ... on the nails of a person, in his hands, shoes, shoes, pants on the knees, on the thickening of the skin on the big and pointed fingers, according to the expression of the face and the shirts, it is not difficult to guess his profession on such trifles. And you can not doubt that all this, taken together, will tell the faithful conclusions to the knowledgeable observer. "

This is a quotation from a software article of the most famous in the world literature of the detective descent of Sherlock Holmes. Based the smallest detailsHe built a logically immaculate chain of reasoning and revealed intricate crimes, and often without leaving his apartment on Bakerustrite. Holmes used the deductive method created by him himself, which appeared, as his friend Dr. Watson believed, disclosure of crimes on the edge of precise science.

Of course, Holmes slightly exaggerated the meaning of deduction in criminalistics, but his arguments about the deductive method did their job. "Deduction" from a special and known only for a few term turned into a commonly used and even fashionable concept. Popularization of the art of the right argument, and above all deductive reasoning, is not a smaller merit of Holmes than all the crimes disclosed them. He managed to "give the logic to the charm of dreams, made through the crystal labyrinth of possible deductions to the only shiny conclusion" (V. Nabokov).

Deduction is private case Conclusion.

In a broad sense Review -a logical operation, as a result of which from one or more adopted statements (parcels), a new approval is obtained - conclusion (conclusion, consequence).

Depending on whether there is a connection between parcels and conclusion logic followation, You can select two types of conclusions.

Based on deductive conclusion Laying a logical law, which is why conclusion with a logical necessity flows from received parcels.

Distinctive feature Such a conclusion is that it always leads to true conclusion from true parcels.

IN inductive conclusion The connection between the parcels and the conclusion is based on the law of logic, but on some factual or psychological grounds that have no purely formal nature.

In such a conclusion, the conclusion should not be logically from the parcels and may contain information that is missing in them. The accuracy of the parcel does not mean that the accuracy of the inductive assertion derived from them. Induction gives only likely, or believable, conclusions that need further verification.

Deductive belongs, for example, such conclusions:

If it rains, the earth is wet. It's raining.

Land wet.

If helium is metal, it is electrically conducted. Helium is not electrically conductive.

Helium is not metal.

The trait separating the parcels from the conclusion replaces, as usual, the word "therefore".

Examples of induction can serve as reasoning:

Argentina is a republic; Brazil - Republic; Venezuela - Republic; Ecuador - Republic.

Argentina, Brazil, Venezuela, Ecuador - Latin American states.

All Latin American States are republics .

Italy - Republic, Portugal - Republic, Finland - Republic, France - Republic.

Italy, Portugal, Finland, France - Western European countries.

All Western European countries are republics.

Induction does not give a complete guarantee of obtaining new truth from existing. The maximum that can be said is a certain degree of probability of the approval deemed. So the parcels and the first and second inductive conclusions are true, but the conclusion of the first of them is true, and the second is false. Indeed, all Latin American states are represented; But among the Western European countries there are not only republics, but also monarchies, such as England, Belgium and Spain.

Omlice

Particularly characteristic deductions are logical transitions from the general knowledge to private, type:

All metals are plastic. Copper - metal.

Copper plastic.

In all cases, when it is required to consider the phenomena on the basis of a well-known common rule and bring the necessary conclusion regarding these phenomena, we conclusted in the form of deduction. The arguments leading from knowledge about the part of the objects (private knowledge) to know about all the subjects of a certain class (general knowledge) is typical induction. There is always the likelihood that the generalization will be hasty and unreasonable ("Napoleon is a commander; Suvorov is a commander; it means every person a commander").

However, at the same time, it is impossible to identify deduction with the transition from common to particular, and induction - with the transition from private to a common one.

In the reasoning "Shakespeare wrote sonnets; Consequently, it is not necessary that Shakespeare did not write sonnets "there is a deduction, but there is no transition from common to particular. The argument "If aluminum plastic or clay plastic, then aluminum plastic" is, as it is customary, inductive, but there is no transition from private to the common one.

Deduction is to derive the conclusions, as reliable as the received parcels, induction - the elimination of probable (plausible) conclusions. Inductive conclusions include both transitions from private to general and analogy, methods for establishing causal relations, confirmation of consequences, target justification, etc.

That particular interest that manifests itself to deductive conclusions is clear. They allow from the already existing knowledge to receive new truths, and moreover with the help of pure reasoning, without appeal to experience, intuition, common sense etc. Deduction gives one hundred percent guarantee of success, and not simply provides one or another - perhaps, and the high probability of true conclusion. Going away from true parcels and arguing deductive, we will definitely get reliable knowledge in all cases.

Stressing the importance of deduction in the process of deploying and justifying knowledge, it should not, however, tear 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. By itself, it does not guarantee its truth and validity, but it gives rise to assumptions, connects them with experience and thereby informs them some truthfulness, more or less high degree of probability. Experience - source and foundation of human knowledge. Induction, departing from what is being comprehended by experience, is a necessary means of generalization and systematization.

Logical laws

Chapter

The concept of a logical law

Logical laws make up the basis of human thinking. They determine when other statements are logically flowing out of some statements, and are the invisible iron frame, which holds a consistent reasoning and without which it turns into a chaotic, incoherent speech. Without a logical law, it is impossible to understand what is a logical following, and thus - what is evidence.

Correct, or, as they usually say, logical, thinking is thinking according to the laws of logic, on the abstract schemes that are fixed by them. Hence the entire importance of these laws is clear.

Uniform logical laws are combined into logical systems, which are also usually referred to as "logic". Each of them gives a description of the logical structure of a certain fragment, or type, of our reasoning.

For example, laws that describe logical connections of statements that do not depend on the internal structure of the latter, are combined into the system called "logic of statements". Logical laws that determine the relationships of categorical statements form a logical system called the "logic of categorical statements", or "syllogistic", and so on.

Logical laws are objective and independent of the will and consciousness of man. They are not the result of an agreement between people, some specially developed or spontaneously established convention. They are not both the generation of the "World Spirit", as Plato repel. The authorities of the laws of logic over the person, their mandatory for proper thinking is due to the fact that they represent a mapping in human thinking of the real world and the centuries-old experience of his knowledge and transformation by man.

Like all other scientific laws, logical laws are universal and necessary. They always act everywhere, extending equally to all people and any era. Representatives

The concept of a logical law

of different nations Both different cultures, men and women, the ancient Egyptians and modern Polynesians from the point of view of the logic of their reasoning do not differ from each other.

Inherent in logical laws, the need for a case is even more imperative and immutable than natural, or physical, necessity. It is impossible to even imagine that the logically necessary was different. If something contradicts the laws of nature and is physically impossible, then no engineer, with all its giftedness, will not be able to implement it. But if something contradicts the laws of logic and is logically impossible, then not only an engineer is even an almighty creature if it suddenly appeared, could not realize it into life.

As mentioned earlier, in the right argument, the conclusion follows from the parcels with a logical necessity, and general scheme Such reasoning is a logical law.

The number of proper reasoning schemes (logical laws) is infinite. Many of these schemes are known to us from the practice of reasoning. We apply them intuitively, without giving yourself a report that this or that logical law is used in each properly we spent.

Before entering general concept Logical law, we give a few examples of the argument schemes, which are logical laws. Instead of variables A, B, C, ... used usually used to designate statements, we use how it was done in antiquity, the words "first" and "second" replacing variables.

"If there is the first, that is, the second; there is the first; Consequently, there is a vehicle. " This scheme of reasoning allows from the approval of the conditional statement ("if there is the first, that is, the second") and the approval of its foundation ("there is the first") to proceed to the approval of the investigation ("there is a second"). According to this scheme proceeds, in particular, reasoning: "If the ice is heated, it melts; ice heat; Consequently, he melt. "

Another scheme of the right argument: "Or takes the first or second; there is the first; So, there is no second. " Through this scheme from two mutually exclusive alternatives and the establishment of which of them is, the transition to negation of the second alternative is carried out. For example: "Either Dostoevsky was born in Moscow, or he was born in St. Petersburg. Dostoevsky was born in Moscow. So, it is not true that he was born in Petersburg. " In the American western "good, bad and evil" one negative hero speaks to another: "Remember, the world is divided into two parts: on those who hold the revolver, and those who dig. Revolver is now me, so take a shovel. " This reasoning also relies on the specified scheme.

And the last preliminary example of a logical law, or the general scheme of the correct reasoning: "There is first or second. But there is no first. So, there is a second. " Substitute instead of expression "first" statement "Now day", and instead of the "second" - the statement "Now Night". From the abstract scheme we get reasoning: "Now day or now night. But incorrect that now day.

So now night. "

These are some simple schemes Proper reasoning illustrating the concept of a logical law. Hundreds and hundreds of similar schemes are sitting in our head, although we are not aware of this. Relying on them, we argue logical, or correctly.

Law of Logic (Logical Law) - An expression that includes only logical constant and variables instead of the substantive parts and is true in any area of \u200b\u200breasoning.

Take as an example of an expression consisting only of variables and logical constants, expression: "If a, then in; So, if nea, then nub. " Logical constant here are the propositional bonds "if, then" and "not". Variables A and B represent ackage of statements. Suppose, but this is the statement "there is a reason", and in the statement "there is a consequence." With this specific content we obtain reasoning: "If there is a reason, then there is a consequence; So, if there is no investigation, then there are no causes. " Suppose, then, instead of a statement, the saying "The number is divided into six", and instead of the statement "the number is divided into three." With this specific content on the basis of the scheme under consideration, we obtain reasoning: "If the number is divided by six, it is divided into three. Consequently, if the number is not divided into three, it is not divided into six. " Whatever other statements have put in place instead of variables A and B, if these statements are true, then the conclusion will be true.

In logic, a reservation is usually made that the area of \u200b\u200bobjects about which the reasoning is being conducted and the statements that are substituted into the logical law cannot be empty: there must be at least one subject in it. Otherwise, reasoning according to the scheme, which is a law of logic, can lead from true parcels to a false conclusion.

For example, from the true parcels "All Elephants - Animals" and "All Elephants have a trunk" under the law of logic follows the true conclusion of "Some animals have a trunk". But if the area of \u200b\u200bobjects in question is empty, following the law of logic does not guarantee a true conclusion in true parcels. We will argue according to the same scheme, but already about the golden mountains. We build a conclusion: "All Golden Mountains have mountains; All Golden Mountains - Golden; Consequently, some mountains are gold. " Both parcels of this conclusion are true. But his conclusion "Some Mountains - Golden" is clearly false: not a single golden mountain exists.

The concept of a logical law

Thus, for reasoning based on the law of logic, two features are characterized:

Such arguments are always leading from true parcels to true conclusion;

The investigation follows from the parcels with a logical necessity.

Logical law is accepted also called logical tautology.

Logic Tavtology - The expression remaining true, regardless of which objects are we talking about, or "always true" expression.

For example, all the results of substitutions to the logical law of double denial "If A, it is wrong that nea" are true statements: "If the soot is black, then it's wrong that it is not black," if a person trembles from fear, then it is wrong that it is not true that He does not tremble from fear ", etc.

As already mentioned, the concept of a logical law is directly related to the concept of logical following: the conclusion logically follows from the received parcels, if it is associated with a logical law. For example, from the parcels "if A, then in" and "if in, then with" logically, the conclusion "if a, then with", since the expression "if a, then in, and if in, then s, then if , then C "represents a logical law, namely transitivity law(transitional). Let's say, from the parcels "If a person's person, he is a parent" and "if a person is a parent, then he is a father or mother" in this law, the investigation implies "if a person is father, then he is a father or mother."

Logic followation - The ratio between the parcels and the conclusion of the conclusion, the general scheme of which is a logical law.

Since the connection of the logical rely on the logical law is characterized by two features:

Logical following leads from true parcels only to true conclusion;

The conclusion, the following from the parcels, follows from them with a logical necessity.

Not all logical laws directly determine the concept of logical follow. There are laws describing other logical connections: "And", "or", "it is not true that" and so on. And only indirectly related to the ratio of the logical retention. This, in particular, the following law of contradictions referred: "It is wrong that an arbitrarily taken statement and

Smart thoughts come only when nonsense has already been made.

Only those who are making absurd attempts will be able to achieve the impossible. Albert Einstein

Good friends, good books and sleeping conscience - here is an ideal life. Mark Twain

You can not return to the past and change your start, but you can start now and change your finish.

Upon closer examination, it becomes clear to me that those changes that seem to come with time, in fact, no change: only my mind changes. (Franz Kafka)

And even though the temptation is very large for two ways to go, it is impossible to play and with the devil and God ...

Appreciate those with whom you can be.
Without masks, shortcoming and ambitions.
And take care of them, they are sent to you fate.
After all, in your life they are only units

For an affirmative answer, only one word is enough - "yes." All other words are invented to say no. Don-Amanado

Ask a person: "What is happiness?" And you know what he is missing most.

If you want to understand life, then stop believing what they say and write, and watch and feel. Anton Chekhov

There is nothing destructive in the world, unbearable, like inaction and wait.

Implement your dreams to reality, work on ideas. Those who laugh at you earlier will be jealous.

Records exist in order to beat them.

You need to waste time, but to invest in it.

The history of mankind is the story of a rather small number of people who believed.

Brought yourself to the edge? Do not see sense to live more? So you are already close ... close to the decision to reach the bottom to push off from him and decide to be happy forever .. so do not be afraid of the bottom - use it ....

If you are honest and frank, then people will deceive you; Still honest and frank.

A man rarely succeeds in whatever if his occupation does not give him joy. Dale Carnegie

If at least one blooming branch remains in your soul, a singing bird will always sit on it. (Oriental wisdom)

One of the laws of life states that as soon as one door closes, another opens. But the whole trouble is that we look at the locked door and do not pay attention to the opening. Andre L.

Do not judge a person until you talk to him personally, because everything you hear - rumors. Michael Jackson.

First they ignore you, then you laugh at you, then fight you, then you win. Mahatma Gandhi

Human life decays into two halves: for the first half, they strive forward to the second, and within the second back to the first.

If you do nothing yourself, how can you help you? You can only manage a moving car

All will be. Only when you decide on it.

In this world, you can search for everything except love and death ... They themselves will find you when the time comes.

Internal satisfaction against the world of suffering is very valuable. Sridhar Maharaj

Starting now to live the life as you would like to see her at the end. Mark Arellium

It is necessary to live every day as in the last moment. We do not have a rehearsal - we have a life. We do not start it from Monday - we live today.

Every instant of life is another opportunity.

A year later, you will look at the world with other eyes and even this tree, which grows near your house, will seem otherwise.

Happiness do not need to look - they need to be. Osho

Almost every success story that I was known, began with the fact that the man lay a chance, defeated failures. Jim Ron.

Every long path begins with one, from the first step.

No one is better than you. No one is smarter than you. They just started earlier. Brian Tracy

Things one who runs. One who crawls does not fall. Pliny senior

It is enough just to understand that you live in the future, how immediately there will be.

I choose to live, and do not exist. James Alan Hetfield.

When you appreciate what you have, and not to live in the search for ideals, then you will truly become happy ..

Only those who are worse are thought about us, but those who are better than us, they simply not before us. Omar Khayam

Sometimes one call is separated from happiness ... one conversation ... one recognition ...

Recognizing its weakness, man becomes strong. Onre Balzac

The one who humbles his spirit is stronger than who conquers the city.

When the chance falls out - it is necessary to grab it. And when grabbed, succeeded - enjoy. Feel joy. And let them all suck the hose for the fact that there were goats when they were not allowed for you. And then - go away. Handsomely. And leave everyone in shock.

Never despair. And if you have already fell into despair, then continue to work in despair.

A decisive step forward is the result of a good kick back!

In Russia, it is necessary to be either famous or rich in order to treat you as in Europe relate to anyone. Konstantin Rikin

It all depends on your relationship. (Chuck Norris)

No reasoning is able to indicate a person the path he does not want to see Romain Rolland

What you believe in, becoming your world. Richard Matson

There's good where we are not. In the past, we are no longer there, and therefore it seems fine. Anton Chekhov

Rich are still rich because they learn to overcome financial difficulties. They see them the opportunity to learn, grow, develop and rich.

Everyone has his hell is not necessarily fire and resin! Our hell is wasted! Where dreams lead

It doesn't matter how much you work, the main result.

Only mom is the most affectionate hands, the most tender smile and the most loving heart ...

Winners in life always think in the spirit: I can, I want, I. Losers, on the contrary, focus their scattered thoughts on what they could have could do or that they cannot do. In other words, the winners are always charged with themselves, and the losers blame in their failures of circumstances or other people. Denis Watley.

Life - Mount Rise slowly, descend quickly. Gi de Maupassan

People are so afraid to take a step towards a new life that they are ready to close their eyes on everything that they are not satisfied. But it is still worse: wake up once and realize that there is not all right, not that ... Bernard Shaw

Friendship and trust are not bought and not sold.

Always, at every minute of your life, even when you are absolutely happy, have one installation in relation to the people around you: - I will do what I want, or without you.

In the world, it is only possible to choose between loneliness and vulgarity. Arthur Shopenhauer

It is only possible to look at things otherwise, and life will flow in a different direction.

Iron so said magnet: Most of all I hate you for attracting, without having enough strength to drag behind yourself! Friedrich Nietzsche

Thieme to live and then when life becomes unbearable. N. Ostrovsky

The picture you see in my mind will eventually become your life.

"The first half of life ask yourself what you are capable, but the second - and who needs it?"

It's never too late to put a new goal or find a new dream.

Manage your destiny, or someone else will do it.

beauty to see in the ugly
display in the streams of spills of rivers ...
who knows how to be happy to be happy
he really happy man! E. Asadov

The wiser asked:

How many types of friendship exist?

Four - he answered.
There are friends like food - every day you need them.
There are friends as a medicine, looking for them when you feel bad.
There are friends, like a disease, they themselves are looking for you.
But there are such friends like air - they are not visible, but they are always with you.

I will become a man who I want to become - if I believe that I will become them. Gandhi

Open your heart and listen to what it dreams about. Follow your dream, because only through who is not ashamed of themselves, the glory of the Lord will appear. Paulo Coelho

To be refuted - this is nothing to fear; It follows the other - to be incomprehensible. Immanuel Kant

Be realists - demand the impossible! Che Guevara

Do not postpone your plans if it rains on the street.
Do not give up a dream if people do not believe in you.
Go in nature, people. You are a person. You are strong.
And remember - there are no unattainable purposes - there is a high coefficient of laziness, lack of smelting and reserve of excuses.

Or you create the world, or the world creates you. Jack Nicholson

I love when people smile just like that. You go, for example, in the bus and you see how a person looks out the window or writes SMS and smiles. So good it becomes soul. And I myself want to smile.

Even under the most severe and coarse shell, the tender soul is hidden and a sensitive heart. Stephen Kovi.

Lessons denial

Among the statements of denial distinguish between statements with external and internal denial. Depending on the tasks of the study, the statement of denial can be viewed or as simple, or as a complex statement.

When considering the statement of denial as a simple statement of an important task is to determine the correct logical form of statement:

A simple statement containing internal denials is made to relate to negative statements (see "Types of attribute statements in quality"). For example: " Some residents of the Republic of Belarus do not use bank loans, "" No hare is a predator ";

The correct logical form of a simple statement with an external denial is contrary to this statement (see "Logical relationships between statements. Logical square"). For example: Saying "Not all people greedy" corresponds to the statement "Some people are not greedy».

Considering the statement of denial as a complex statement, it is necessary to determine its logical value.

Source statement: The sun is shining (R).

Decitation statement: The sun is not shining (┐R).

Double denial statement: It is wrong that the sun does not shine (┐┐R).

R	┐r	┐┐r.
AND	L.	AND
L.	AND	L.
Fig. sixteen

Statement denial is true only when the initial statement is false, and vice versa. The law of double denial is connected with the statement of denial: the double negation of an arbitrary statement is equivalent to this statement itself. The conditions for the truth of the removal statement is shown in Fig. sixteen.

Complex A statement consisting of several simple statements, connected with the help of logical unions "and", "or", "if ..., then ...", etc. The complex statements include connecting, dividing, conditional, equivalent statements, as well as statements denial.

Connecting statement (conjunction) - This is a complex statement consisting of simple connected with a logical ligament "and". The logical union "and" (conjunction) can be expressed in the natural language of the grammatical unions "and", "but", "however", "as well", etc. For example: "Close clouds, and went rain", "and big and small happy happy day". On the symbolic language of logic, these statements are recorded as follows: p∧Q.. The conjunction is true only when all its components of simple statements are true (Fig. 17).

Separation statement (disjunction).There are weak and strong disjunction. Weak disjunction Complies with the use of the union "or" in the connecting and dividing sense (or something, or other, or even more together). For example: "This student athlete or an excellent student" (p⋁Q.), "Hereditary factors, bad ecology and bad habits are the causes of most diseases"(p⋁Q⋁r.). Weak disjunction is true when truly at least one of the most part of simple statements (see Fig. 17).

Strong disjunction Complies with the use of the Union "either" in the excluding dividing sense (or something or the other, but not both together). For example: "In the evening I will be in class or go to the disco," "man is either alive or dead". Symbolic recording p⊻Q.. Strong disjunction is true when true only one of the most part of simple statements included in its composition (see Fig. 17).

Conditional statement (implication) - This is a complex statement consisting of two parts connected with the help of the logical union "if ... then ...". The statement that stands after a particle "if" is called the basis, and the statement that stands after "then" - the investigation. With a logical analysis of conditional statements, the foundation of the implication is always put at the beginning. In natural language, this rule is often not respected. An example of conditional statement: "If the swallows fly low, it will rain" (p → Q.). The implication is false only in one case, when its base is truly, and the consequence is false (see Fig. 17).

Equivalent statement - This is a statement consisting of simple connected with the help of a logical union "if and only if" ("if and only if ..., then ...). The equivalent statement implies the simultaneous presence or absence of two situations. In the natural language, the equivalence can be expressed by the grammatical unions "if ..., then ...", "only in the case when ...", etc. For example: "Our team will win only if it is good to prepare» ( p↔Q.). The equivalent statement will be true when the components of its statements are either both true or simultaneously false (see Fig. 17).

For the formalization of reasoning, it is necessary:

1) Find and identify by small consonants of the Latin alphabet. Simple statements that are part of a complex one. Variables are assigned arbitrarily, but if the same simple statement is found several times, then the corresponding variable is used as much time;

2) to find and designate logical constants Logic unions (∧, ⋁, ⊻, →. ↔, ┐);

3) if necessary, expand the technical signs [...], (...).

In fig. 18 shows an example of formalization of a complex statement .

I was already free (P) and (∧), if a me not Delay (┐Q.) or (⋁) not broke the car (┐r), then (→)i will come soon (s) .

p ∧ ((┐Q ⋁R) → s

Fig. eighteen

After the statement is written in a symbolic form, you can determine the type of formula. In logic, identity-true, identical and false and neutral formulas are distinguished. The identity-true formulas regardless of the values \u200b\u200bof the variables included in their composition always take the importance of "truth", and the identical-false is "false". Neutral formulas are taken as the value of "truth" and the value "false".

To determine the type of formula, a tabular method is used, a reduced method of checking the formula for the truth method by the method to absurdity and bring the formula to normal formula. The normal form of some formula is its expression that corresponds to the following conditions:

Does not contain amplification marks, equivalence, strict disjunction and double denial;

The signs of denial are only with variables.

Tabular method of determining the type of formula:

1. Build columns of input values \u200b\u200bfor each of the available variables. These columns are called free (independent), they take into account all possible combinations of variable values. If in the formula two variables, then build two free columns, if three variables, then three columns, etc.

2. For each subformula, that is, parts of the formula containing at least one union, build the column of its values. At the same time, the values \u200b\u200bof free columns and the characteristics of the logical union are taken into account (see Fig. 17).

3. Build a column of output values \u200b\u200bfor the entire formula as a whole. By the values \u200b\u200bobtained in the output column, the type of formula is determined. So, if there is only the value of "truth" in the output column, the formula will refer to identical and true, etc.

Tatt of truth for formula (P ^ Q) → R
P.	Q.	R.	P ^ Q.	(P ^ Q) → R
AND	AND	AND	AND	AND
L.	AND	L.	L.	AND
L.	L.	AND	L.	AND
AND	L.	L.	L.	AND
AND	AND	L.	AND	L.
AND	L.	AND	L.	AND
L.	AND	AND	L.	AND
L.	L.	L.	L.	AND
Fig. nineteen

The number of columns in the table is equal to the amount of variables included in the formula, and unions available in it. (For example: in the formula in Fig. 18 four variables and five unions, therefore, there will be nine columns in the table).

The number of rows in the table is calculated by the formula C \u003d 2 nwhere n. - Number of variables. (In the table according to the formula in Fig. 18 should be sixteen lines.)

In fig. 19 shows an example of a truth table.

An abbreviated way to verify the formula for the truth method by the method of accuracy:

((p⋁q) ⋁r) → (P⋁ (Q⋁R))

1. Suppose that this formula is not identical to true. Consequently, with some set of values, it takes the value "false".

2. This formula may take the value "falsely" only if the base of the implication (P⋁Q) ⋁r is "true", and the result of P⋁ (Q⋁R) is "false".

3. The investigation of the implication of P⋁ (Q⋁r) will be false in the case when P is "false" and Q⋁r - "falsely" (see the value of weak disjunction in Fig. 17).

4. If Q⋁R is "false", then Q and R - "falsely".

5. We found that P - "falsely", Q - "false" and R - "false". The base of the implication (P⋁Q) ⋁r is a weak disjunction of these variables. Since weak disjunction takes the value "falsely" when the false is all its components, the base of the implication (P⋁Q) ⋁R will also be "false".

6. In paragraph 2 found that the base of the implication (P⋁Q) ⋁r is "true", and in paragraph 5 that it is "false". The resulting contradiction indicates that the assumption made by us in paragraph 1 is wrong.

7. Since this formula, with any set of values \u200b\u200bof their variables, does not take the value "falsely", it is identically true.

3.8. Logic relationships between statements
(logical square)

Between statements that have similar meaning are established. Consider relations between simple and complex statements.

In logic, the entire totality of statements are divided into comparable and incomparable. Incomparable among simple statements are statements that have different subjects or predicates. For example: "All students are students" and "Some students are honors".

Comparison are statements with the same subjects and predicates and distinguished by a bundle and quantor. For example: "All citizens of the Republic of Belarus have the right to rest" and "no citizen of the Republic of Belarus has no right to rest."

Fig. twenty

Relations between comparable statements are expressed using a model called logical square (Fig. 20).

Among comparable statements distinguish compatible and incompatible.

Compatibility ratio

1. Equivalence (full compatibility) - statements that have the same logical characteristics: identical subjects and predicates, a similar affirmative or negative bond, the same logical characteristic. Equivalent statements vary by verbal expression of the same thought. With the help of a logical square, the relationship between these statements is not illustrated.

2. Partial compatibility (connectedness, subcontrotection). In this regard, there are private appropriate and particular negative statements (I and O). This means that two such statements can be true simultaneously, but cannot be simultaneously false. If one of them is false, then the second is necessarily true. If one of them is true, then the second is vague.

3. Submission (subordination). In this regard, there are a secrect and private approval of statements (A and i), as well as a general-negative and particular negative statement (E and O).

From the truth of the general statement always follows the truth of private. While the truth of a private statement testifies to the uncertainty of the overall statement.

From the falsity of the private statement always follows the fate of the general statement, but not the opposite.

The ratio of incompatibility.Incompatible are statements that cannot be simultaneously true:

1. Opportunity (controversy, contrast) - In this regard, there are a secrect and general negative statement (A and E). This ratio means that two such statements cannot be simultaneously true, but can be simultaneously false. If one of them is truly, then the second is sure - false. If one of them is false, then the second is uncertain.

2. Contradiction (counterfeitivity) - It is a general-affirmative and particular-negative statement (A and O), as well as a general-negative and private approval of statements (E and I). Two contradictory statements cannot be simultaneously false or simultaneously true. One must truly, and the other is false.

Comparison among complex statements are statements that have at least one identical component. Otherwise, complex statements are incomparable.

Comparable complex statements can be compatible or incompatible.

Compatibility ratio means that statements can be simultaneously true:

2. Partial compatibility This means that statements can be simultaneously true, but cannot be simultaneously false (Fig. 22).

P.	Q.	P → Q.	Q → P.
AND	AND	AND	AND
AND	L.	L.	AND
L.	AND	AND	L.
L.	L.	AND	AND
Fig. 22.

3. Relationship ratio (subordination) means that the trueness of one statement follows the truth of the other, but not the opposite (Fig. 23).	P. Q. R. (P → Q) ∧ (Q → R) P↔r. AND AND AND AND AND AND AND L. L. L. AND L. AND L. AND L. AND AND AND AND AND L. L. L. L. L. AND L. L. AND L. L. AND AND AND L. L. L. AND AND Fig. 23.
4. Clutch ratio means that the truth (felt) of one statement does not exclude the falsities (truth) of the other (Fig. 24).	P. Q. P → Q. ┐P → Q. AND AND AND AND AND L. L. AND L. AND AND AND L. L. AND L. Fig. 24.

The ratio of incompatibility means that statements can not be simultaneously true:

2. Contradiction - The relationship between statements that can neither simultaneously true or simultaneously false (Fig. 26).

P.	Q.	P → Q.	P∧┐Q.
AND	AND	AND	L.
AND	L.	L.	AND
L.	AND	AND	L.
L.	L.	AND	L.
Fig. 26.

Statement - A narrative offer, which can be said truly or false. In algebra, simple statements are set in accordance with logical variables (A, B, C, etc.)

Logical variable - This is a simple statement.
Logical variables are denoted by uppercase and lowercase latin letters (A-Z, A-Z) and can only receive two values \u200b\u200b- 1, if the statement is true, or 0, if the statement is false.

Example of statements:

Logical function - This is a complex statement, which is obtained as a result of logical operations over simple statements.

To form complex statements most commonly used basic logic operationsexpressed with the help of logical ligaments "and", "or", "not".
For example,

Many people do not like raw weather.

Let a \u003d "Many people love raw weather." We get a logical function F (A) \u003d not A.

Bundles "Not", "and", "or" Replaced with logical operations inversion , conjunction , disjunction . it basic logical operationsWith which you can write down any logical expression.

Logical formula (logical expression) - a formula containing only logical values \u200b\u200band signs of logical operations. The result of the calculation of the logical formula is the truth (1) or a lie (0).

The value of the logical function depends on the values \u200b\u200bof the logical variables included in it. Therefore, the value of a logical function can be determined using a special table ( tatasets of truth) In which all possible values \u200b\u200bof incoming logic variables and the corresponding function values \u200b\u200bare listed.

Basic (basic) logical operations:

1. Logical multiplication (conjunction), from lat. Konjunctio - I associate:
Combining two (or several) statements in one with the help of the Union and;
In programming languages \u200b\u200b- and.
Accepted notation: / \\, and, and.
In the algebra of sets of conjunction corresponds to the operation of the intersection of sets.

The conjunction is true then and only then, all the statements in it are true.

Example:
Consider the composite statement "2 2 \u003d 4 and 3 3 \u003d 10". We highlight simple statements:

B \u003d "3 3 \u003d 10" \u003d 0 (because this is a false statement)
Therefore, the logical function f (a, b) \u003d a / \\ b \u003d 1 / \\ 0 \u003d 0 (in accordance with the truth table), that is, this composite statement is false.

2. Logical addition (disjunction), from lat. Disjunctio - Difference:
Combining two (or several) statements in one with the help of the Union or;
In programming languages \u200b\u200b- OR.
Designation: \\ /, +, or, or.
In the algebra of sets of disjunction corresponds to the operation of combining sets.

The disjunction is false if and only then, all the statements in it are false.

Example:
Consider the composite statement "2 2 \u003d 4 or 2 2 \u003d 5". We highlight simple wrappers:
A \u003d "2 2 \u003d 4" \u003d 1 (because it is a true statement)
B \u003d "2 2 \u003d 5" \u003d 0 (because this is a false statement)
Therefore, the logical function f (a, b) \u003d a \\ / b \u003d 1 \\ / 0 \u003d 1 (in accordance with the truth table), that is, this composite statement is truly.

3. denial (inversion), from lat. Inversion - I turn over:

Corresponds to the particle not, the phrases are incorrectly, that or is not the truth that;
in programming languages \u200b\u200b- not;
Designation: Not A, ¬, not
In the algebra of sets, the operation of the supplement to the universal set corresponds to the logical denial.

Inversioni am a logical variable true if the variable itself is false, and, on the contrary, the inversion is false if the variable is true.

Example:

A \u003d (two multiply by two equals four) \u003d 1.

¬a \u003d ( Invalidly that Two multiply by two equals four) \u003d 0.

Consider the statement A: " The Moon is the Earth's satellite"; Then ¬ will be formulated like this: " The moon is not a satellite“.

Consider saying: "It is not true that 4 is divided into 3". Denote by a simple statement "4 is divided into 3". Then logic form denial of this statement has the form ¬

Priority of logical operations:

Operations in logical terms are performed from left to right, taking into account brackets in Next order:
1. Inversion;
2. conjunction;
3. disjunction;
To change the specified logical operation procedure, round brackets are used.

Composite logical expressions Algebras of statements are called formulas.
True or false value of the formula can be determined by the laws of logic algebra, without referring to the meaning:
F \u003d (0 \\ / 1) / \\ (¬0 \\ / ¬1) \u003d (0 \\ / 1) / \\ (1 \\ / 0) \u003d 1 / \\ 1 \u003d 1 - truth
F \u003d (¬0 / \\ ¬1) \\ / (¬1 \\ / ¬1) \u003d (1 / \\ 0) \\ / (0 \\ / 0) \u003d 0 \\ / 0 \u003d 0 - FALSE

Each person is individuality with various parameters that like a computer filling can perform various operations for different times. The person is certainly not a computer, it is much cooler, even if it is the most modern computer.

In each person laid a certain grain, this is called the grain of truth, if a person will care and cherish the grain within himself, will grow an excellent harvest that will delight him!

You understand that grain is our soul to feel the soul, you need to possess any ultra-suicual abilities.

Another example is a person daily produces the breed, leaving only gems. If, of course, he knows what the precious stones look like, and if she moves only the ore, passing diamonds and other gems, believing that these are just stones, then this person has problems in life.

Life is such a thing, she is like a person who shifts the ore to find diamonds! What is diamonds? This is a motivation that gives us to act in this world, but Motivation Motivation constantly melts, you need to refuel your motivation to continue to act effectively. What is the motivation born? The cornerstone is information, the correct information is like a compressed spring, if we take it correctly, the spring is squeezed and shoots exactly to the target and we very quickly we hope to goal. If we are taken incorrect to motivation, then why, then the spring fits into the forehead. Why is this happening? Because our inner intention is the basis, for what we act, what we want to get and will not bring harm to those around our motivated actions!

In this article, I collected the most motivational quotes and statuses, as they say all times and peoples. But of course, make the choice to you that you will hook. In the meantime, we are comfortable, we make a very clever face, turn off all the means of communication and just enjoy the wisdom of poets, artists and just plumbers are possible!

W.
mine I. wise quotes and statements about life

We have no knowledge enough, it is necessary to apply it. Desire - not enough, it is necessary to act.

And I stand on the right path. Standing. And I should go.

Work on yourself is the hardest job, so they are engaged in a few.

Life circumstances are formed not only by concrete actions, but also by the character of human thoughts. If you are hostile to the world, he will answer you the same. If you constantly express your discontent, there will be more reasons for this. If negativism prevails in your respect, then the world will turn to you with your worst party. And on the contrary, a positive attitude will be the most natural way to change your life for the better. Man gets what chooses. Such is the reality, you like it or not.

From the fact that you are offended, no longer follows that you are right. Ghervea

Year after year, month after month, day after day, an hour over an hour, minute a minute and even second in a second - time runs, without stopping for an instant. No strength is able to interrupt this run, it is not in our power. All we can - spend time with benefit, constructively, or spend it wasted, to harm. This choice is yours; Decision in our hands.

Under no circumstances should not lose hope. The feeling of despair is the true cause of failures. Remember you can overcome any difficulty.

The person is designed so that when something lights his soul - everything becomes possible. Jean de Lafondten

All that is happening with you now, you once created yourself. Vadim Zeland

Inside us there are many unnecessary habits and cases, on which we spend time, thoughts, energy and which do not give us to bloom. If we regularly discard all the more superfluous, then the released time and energy will help us in achieving true desires and goals. Removing all the old and useless in his life, we give the opportunity to bloom in our talents and feelings.

We are slaves of their habits. Change your habits, your life will change. Robert Kiyosaki

The person who is destined to become - is only the person who you yourself decide to become. Ralph Waldo Emerson

Magic is faith in yourself. And when you manage it, it is possible and everything else.

In a pair, everyone should develop the ability to feel the vibration of the other, they should have common associations and common values, the ability to hear what is important for another, and some mutual agreement on how to do, when they have some values do not match. Salvador Minukhin

Each person can be magnetically attractive and incredibly beautiful. True beauty is internally shining a man's soul.

I really appreciate two things - spiritual intimacy and the ability to deliver joy. Richard Bach

Fighting other only tricks to avoid the inner struggle. Osho

When a person begins to complain or invent an excuse for his failures, he begins to gradually degrade.

Good life motto - Help yourself.

Wise is not the one who knows a lot, but those whose knowledge is helpful. Eschyl

Some people are smiling because you smile. And some - so that you smile.

Who reigns inside itself and manages their passions, desires and fears, the more than the king. John Milton

Every man eventually chooses the woman who believes more than he himself.

You once pitch and listen, what does your soul want?

We are so often listening to the soul, in a habit somewhere rushing.

You are where you are, and the one who you are, because of how you perceive yourself. Change your opinion about yourself and you change your life. Brian Tracy

Life is three days yesterday, today and tomorrow. Yesterday has already passed and you will not change anything in it, tomorrow has not yet come. Therefore, try today to do it worthy to not regret.

A truly noble person is not born with a great soul, but it makes himself such great deals. Francesco Petraska

Always substitute your face sunlight And the shadows will be behind you Walt Wheatman

The only one who came wisely was my tailor. He filmed me a measure again every time I saw me. Bernard Show

People never fully use their own forces To achieve the good in life, because they hope for some external force for themselves - hope that it will do what they themselves are responsible.

Never go back to the past. It kills your precious time. Do not stay on the same place. People you need you will catch up.

It's time to shake bad thoughts from the head.

If you are looking for bad, you will definitely find it, and you will not notice anything good. Therefore, if all your life you will wait and prepare for the worst - it will definitely happen, and you will not be disappointed in your fears and fears, finding them all new and new confirmations. But if you hope and prepare for the better, you will not attract bad in your life, but just risk just sometimes to be disappointed - life is impossible without disappointment.

Waiting for the worst, you get it, I miss everything is all good that there is actually in it. And on the contrary, you can buy such a strength of the Spirit, thanks to which in any stress, critical situation in life, you will see her positive aspects.

As often, by stupidity or laziness, people miss their happiness.

Many are accustomed to exist, laying out life for tomorrow. They keep the future years in mind when they will create, create, do, know. They think they are full of time. This is the most ambitious error that can only be made. Time, in fact, we have extremely few.

Remember the feeling that you are experiencing, making the first step, no matter how it is, in any case it will be much better than that feeling you are experiencing, just sitting on the spot. So get up and do at least something. Make the first step - just a tiny step forward.

Circumstances have no meaning. Brilliant, abandoned in dirt no ceases to be a diamond. The heart filled with beauty and greatness can survive hunger, cold, betrayal and all sorts of losses, but to remain, to remain loving and seeking great ideals. Do not believe circumstances. Believe in your dream.

Buddha described three types of laziness the first - she laziness, about which we all know. When we do not have any desire to do something. This is too lazy to the wrong feeling of yourself - the laziness of thinking. "I never will do anything in life," "I can't do anything, you should not try." The time is permanent employment of non-essential affairs. We always have the opportunity to fill the vacuum of our time supporting your "employment." But, usually, it's just a way to avoid a meeting with yourself.

No matter how beautiful your words are, you will be evaluated by your actions.

Do not catch up on the past, you will not be there anymore.

Yes, your body will be in motion, your mind is alone, and the soul is transparent, like a mountain lake.

Who does not think positively - to live in life disgusting.

Happiness does not come to the house, where there is a day after day.

Sometimes, you just need to relax and remind yourself who you are and who you want to be.

The main thing in life is to learn all the turns of the fate to turn good luck into zigzags.

Do not let you go out of you that it can harm others. Do not impart into yourself what can harm you.

From any difficult situation now you will leave, if you just remember that you live not with a body, but soul, remember that you have something stronger in the world. Lev Tolstoy

Statuses about life. Wise statements.

Be honest even alone with him. Honesty makes a man one piece. When a person thinks, he says and makes the same thing, then his strength triple.

In life, the main thing is to find yourself, my own and your own.

There is no truth in the com, there is little good.

In the youth we are looking for a beautiful body, over the years - native soul. Vadim Zeland

It is important that a person does, and not what he wanted to do. William James.

Everything in this life is returned by boomerang, no doubt.

All obstacles and difficulties are the steps that we grow up.

Everyone can love, for they get this gift at birth.

All you pay attention - grows.

Everything that a person seems to him, speaks of others, - he actually talks about himself.

Entering twice in the same water, do not forget that forced you to come out from there for the first time.

You think this is just another day of your life. It's not just another day this is the only day that you can today.

Get out of the orbit time and enter the orbit of love. Hugo Winker.

Even imperfections can like if the soul manifested them.

Even a reasonable person will be fooling if he is not expensive.

Give us the strength to console, and not be comfortable; understand and not be understood; Love, not to be loved. For when we give, we get. And, forgive, find yourself forgiveness.

Moving along the way of life, you yourself create your universe.

The motto of my day is fine, and it will be even better! D. zhuliana Wilson

More expensive than your soul there is nothing in the world. Daniel Shelabarger

If inside - aggression, life will "attack" on you.

If you have a desire to fight, you will get rivals.

If within your resentment, life will give reasons to be offended even more.

If you have fear inside, life will scare you.

If you have a sense of guilt within you, life will find a way to "punish".

If I feel bad, then this is not the reason to deliver suffering to others.

If you ever want to find such a person who can overcome any, even the hardest trouble and make you happy, when no one can do it, you just look at the mirror and say hello.

If you don't like something - change it. If you lack time - stop staring at the TV.

If you are looking for the love of your life - stop. She will find you when you do only to what you love. Open your head, hands and heart for new. Do not be afraid to ask. And do not be afraid to respond. Do not be afraid to share a dream. Many opportunities appear only once. Life is people on your path and what you create with them. So start to create. Life is very fast. It's time to start.

If you are moving in the right direction, then you will feel it with a heart.

If you challenge the candle for someone, it will light up and your way too.

If you want to around you were good, good people, - try to treat them carefully, gently, politely - you will see that everyone will become better. Everything in life depends on you yourself, believe me.

If a person wants, the mountain will put on the mountain

Life is eternal movement, constant updating and development, from generation to generation, from infancy to wisdom, the movement of the mind and consciousness.

Life sees you as you from the inside.

Often the person who was defeated, learns about how to win more than one success comes at once.

Anger is the most useless of emotions. Destroys the brain and harms the heart.

Evil people I almost do not know at all. Once I met one, which I was afraid and thought that he was evil; But when I looked at it attentively, he was only unhappy.

And all this with one goal to show you what you are, what we carry in the shower.

Every time you want to respond to the usual old way, ask yourself if you want to be a prisoner of the past or pioneer of the future.

Everyone is a star and deserves the right to shine.

Whatever your problem is, its reason lies in your stereotype of thinking, and any stereotype can be changed.

When you do not know how to do - do it humanly.

Any difficulty gives wisdom.

Any kind of relationship - like the sand you hold in your hand. Keep free, in open hand - And the sand remains in it. At that moment, when you squeeze hard hand, the sand will start to be saturated through your fingers. So you can hold a little sand, but most will wake up. In relations - in the same way. Believe to another person and his freedom carefully and with respect, remaining close. But if they extell too much and with a claim to possess another person - the relationship rules and get squeezed.

Measure of dusty health is readiness to find a good one.

The world is full of tips, be careful to signs.

I don't understand only one thing as I, as we all manage to fill your life with such a quantity, doubts, regret, the past, which is no longer there, and the future that has not yet happened, fear, which, most likely, will never come true, If everything is so obvious simply.

There is a lot of talking and saying a lot.

We see everything is not the way it is - we see everything as we are.

Thoughts positively, if it does not work positively - not thought. Marilyn Monroe

Find a quiet world in your head and love in your heart. And no matter what happens around, do not let anything change these two things.

Not all of ours lead to positive changes in our lives, but will definitely be achieved by happiness without doing anything.

Do not let the noise of other opinions interrupt your inner voice. Keep bravery to follow the heart and intuition.

Do not turn your book of life in a complaint.

Do not rush to drive away the moments of loneliness. Perhaps this is the largest gift of the universe - to protect you for a while from all too much to allow you to become myself.

The invisible red thread is connected by those who are destined to meet, despite the time, place and circumstances. Thread can stretch or seed, but never breaks.

You can not give what you do not have. It is impossible to make other people happy if you yourself are unhappy.

It is impossible to defeat the one who does not give up.

No illusions - no disappointment. We need to be chewed to evaluate food, experience the cold to understand the benefit of warmth, and to visit the child to see the value of the parents.

You need to be able to forgive. Many believe that forgiveness is a sign of weakness. But the words "I forgive you" do not mean at all - "I am too soft, so I can't be offended and you can continue to spoil my life, I will not tell you a single word", they mean - "I will not allow the past to spoil your future And the present, so I forgive you and let go of all the insults. "

Resenting - like stones. Not a copy of them in yourself. Otherwise you will fall under their weight.

Once at the lesson social problems Our professor raised the black book and said this book red.

One of the main causes of apathy is the lack of a goal in life. When not to strive for, the decline of the forces comes, consciousness is immersed in a sleepy state. And on the contrary, when there is a desire to achieve something, the energy of intent is activated and the vital tone increases. To begin with, you can take yourself - to do yourself. What can bring you self-esteem and satisfaction? There are many ways of self-improvement. You can put yourself a goal to achieve improvement in any or more aspects. You better know what will bring satisfaction. Then the taste for life will appear, and everything else will work automatically.

He turned the book, and her rear cover was red. And then he said "Do not tell someone that he is wrong, until the moment, do not look at the situation from his point of view."

Pesssimist is a person who complains of noise when luck is knocking on the door. Peter Mamonov

Genuine spirituality is not imposed - she is fascinated.

Remember, sometimes silence is the best answer to questions.

Spoils people not poverty or wealth, but envy and greed.

The correctness of the path you choose is determined by how happy you are going through it.

Motivating quotes

Forgiveness does not change the past, but frees the future.

A human speech is the mirror of himself. All the fake and false, no matter how you try to hide it from others, all emptiness, worn or rudeness breaks through in speech with the same force and evidence, with what kind of sincerity and nobility, depth and subtlety of thoughts and feelings.

The most important thing is harmony in your soul, for it can create happiness from nothing.

The word "impossible" blocks your potential while the question "How can I do this?" Causes the brain to work on a complete coil.

The word should be true, the action should be decisive.

The meaning of life in the strength of the desire for the goal, and it is necessary that every moment of being had its high goal.

The bustle has no one and never led to success. The more rest in the shower, the easier and faster all the questions are solved.

There is enough light for those who want to see, and enough darkness for those who do not want.

There is one way to learn - real action. Celebrated conversations are meaningless.

Happiness is not clothes that can be bought in the store or sew in the studio.

Happiness is an internal harmony. It is impossible to achieve it from the outside. Only from the inside.

Dark clouds turn into heavenly flowers when light kisses them.

What you talk about others does not characterize them, but you.

What is in man is undoubtedly more importantlythat has a person.

The one who can be gentle has a large inner force.

You are free to do anything - just do not forget about the consequences.

He will succeed in him '- God said quietly.

He has no chance - the circumstances stated loudly. William Edward Hartpol Leki

Want to live in this world - live and rejoice, and do not go with a displeased face that the world is imperfect. The world create you - in your head.

A person can all. Only he usually interferes with laziness, fear and low self-esteem.

A person can change his life by changing only his point of view.

That the sage does at the beginning, then stupid makes at the end.

To become happy, you need to get rid of all too much. From extra things, too much fuss, and most importantly - from unnecessary thoughts.

I am not a body endowed with a soul, I am a soul, some of which is visible and called the body.