It is very important to learn to think logically - such skills help not only to calculate your actions in advance, but also to quickly find a way out of unforeseen situations. A person who has developed logical thinking will undoubtedly be able to achieve success even under not the most favorable circumstances. So, how to develop logical thinking?
Logic and logical thinking
Logic is
The concept of “logic” has its roots in the ancient Greek language, and is translated as thought (reasoning). In general, logic can be called the ability to think intelligently, and it can be considered as a science. We are talking about a branch of philosophy that studies intellectual activity. If you are capable of logical thinking, then based on the data you have, you will be able to come to the right conclusion. With the help of logic, you gain not only general knowledge about a particular subject, but also comprehend its nuances.
What is logical thinking and its types
It is worth noting that logical thinking is divided into several types, and by familiarizing yourself with their characteristics, you will be able to determine whether you possess any of them. In general, logical thinking is a thought process in which we arrive at a valid conclusion from existing premises.
Verbal and logical thinking
It uses logical constructs and concepts, acts based on linguistic means and represents the highest stage in the development of thinking. Using verbal and logical thinking, a person is able to come to general patterns and generalize various visual materials.
The formation of such thinking occurs gradually. During training, a person masters the methods of mental activity and analyzes the process of his own thoughts. When solving educational problems, it influences the formation of analysis, generalization, synthesis, classification, comparison. Let's look at these concepts in more detail.
Analysis is a mental operation in which a person is able to disassemble a complex object into elements.
Synthesis - usually acts in unity with analysis, carried out simultaneously. A person moves from parts to the whole.
Generalization is the combination of many elements according to a single characteristic. The comparison reveals something in common.
Classification - objects are grouped according to essential characteristics
Comparison is a comparison of phenomena and objects, as well as identifying their differences and common features.
Verbal-logical thinking
People who have this type of thinking tend to focus their attention on what they say rather than how they say it. Such logicians have a predisposition to accuracy and show interest in the semantic essence of any information. They try to compare newly acquired knowledge with those they already possessed.
It is worth noting that this type of thinking, alas, is not characterized by fast memory. A person needs a certain amount of time to carefully think and analyze everything. We also note that people with this type of thinking are prone to conservatism and weak expression of emotions.
The strengths of verbal-logical thinking include accuracy and consistency. The negative side is slow switching from one task to another.
Mathematical thinking
This type of thinking is characterized by flexibility, originality and depth. Let us consider these concepts in more detail, in the context of mathematical thinking.
Flexibility is the ability to vary options for solving a certain problem, easy transition from one way of solving a problem to another. We are also talking about the ability to leave the boundaries of familiar methods of action - a person is looking for new solutions, quickly adapting to changed conditions.
Originality is a factor that provides the highest level of unconventional thinking in this case.
Depth is the ability to comprehend the essence of all the facts being studied, their relationships, hidden features.
Associative-figurative thinking
It should also be noted that there are people who are characterized by associative-figurative thinking. Their memory is well developed, but differs from the memory of logicians. Trying to remember something, the lyricist immediately reproduces something else in his memory because he has a predisposition to associative perception of reality.
What are the main benefits of thinking like this? You can give examples of emotionality, rich imagination, and the ability to easily switch from one to another. A person perceives images holistically, connecting them with existing reality.
Disadvantages include inconsistent actions, increased idealization, excessive vulnerability, and increased sensuality. Such features do not always make it possible to look at the world objectively, although they make it very exciting.
Types of thinking
Thinking begins to form from birth, but for many this development stops for various reasons. It happens that having reached a certain level, it slows down or stops altogether. But if desired, this process can be accelerated or restarted.
There are the following types of thinking:
- logical;
- creative;
- figurative;
- visual;
- abstract (verbal-logical).
As a rule, each of us has several types of it, but only one is best. Today we’ll talk about the development of verbal and logical thinking.
Why does a person need to develop logic and memory?
Developed memory and logical thinking are simply necessary in everyday life - when performing professional tasks, as well as in everyday affairs.
By developing memory and logic, you will learn to concentrate your attention and control your thoughts. As a result, it will be easier for you to focus on current tasks and organize your own life.
By performing exercises to develop memory, after a certain period of time you will begin to notice that when solving problems, you use very non-standard and effective methods that would not have occurred to you before.
How to develop memory and thinking in adults
Tasks for the development of logical thinking
On the Internet you can easily find a variety of tasks with the help of which you will be able to develop logical thinking. Many sites will offer you different levels of tasks. Try to start with something not too difficult and gradually move on.
Learn to think logically through games, puzzles and strategies
Also, a variety of games, strategies and puzzles can greatly contribute to the development of logical thinking. To do this, it is not necessary to search for tasks on the Internet. Even by purchasing a box of puzzles, you can not only have an entertaining evening, but also significantly improve your level of logical thinking.
10 ways to develop your memory
1.) Read a lot of books
Of course, a person who is inclined to read has a better memory than one who does not show any interest in this activity. So how can this be used. Read a short story, then immediately retell it into the recorder. After a few hours, try repeating this retelling. Analyze what details you forgot, what you missed. Do these exercises regularly.
2.) Pronounce words backwards
This is also a very useful method to improve your memory. It is also impossible not to note the convenience of this method - you do not need a voice recorder or other auxiliary devices. Perform this task before going to bed, on the road, in line, and so on. If possible, you can do the exercise on a piece of paper, in a notepad - this way it will be more convenient for you to test yourself.
3.) Study poetry and new words
Memorizing poetry is a wonderful memory trainer. You can also learn new words that are unfamiliar to you. As soon as such a word catches your eye, at any opportunity, look up its meaning in the dictionary. After this, try “in your head” to compose several sentences in which the new word will be used.
4.) Remember everything in detail, analyze
Get into the habit of replaying in your memory every evening the events that happened to you over the past day. Start from the moment you wake up. Remember what you thought about when you woke up, what you ate for breakfast, who you talked to. Next, move on to memories of how your day went, what people you interacted with, what tasks you faced. Then move on to memories of the evening. Analyze what unpleasant events you could have avoided, what useful things you learned today, what action was senseless, and so on.
5.) Draw images in your head
Quite an interesting exercise that perfectly develops the imagination. For example, imagine yourself on vacation. Let's say, not just you sitting on the shore, but in more detail. Imagine that you are sitting on the warm sand, you have a glass of lemonade or beer in your hand, and there is a plate of shrimp or corn next to you - you can hear their smells. You also hear the sound of sea waves, and sometimes their splashes reach you. You can add any more details.
So, imagine whatever you want. For example, you find yourself in a summer garden: the shadow of the trees falls on you, you hear the smell of raspberries, and pear fruits periodically fall to the ground. The sun's rays break through the foliage.
6.) Get a good night's sleep
Undoubtedly, you have already heard that adequate sleep has an important effect on our memory. If you sleep at least seven hours a night, you can be sure that this has the best effect not only on memory, but also on concentration and even on the rejuvenation of body cells. Good sleep is essential for energy and overall health.
7.) Aivazovsky’s method develops photographic memory
This training technique got its name in honor of the famous artist. While writing his works and paintings, Ivan Konstantinovich mentally tried to stop the movement of the wave and transfer it to his painting so that it would not look frozen.
Aivazovsky devoted many hours to the process of observing water. At the same time, he closed his eyes from time to time, trying to reproduce what he saw in his memory.
How to use this technique?
- Study an object or landscape for 5 minutes.
- Covering your eyelids, try to reproduce the image of this picture in your memory. It is also important that it be colored.
- The effectiveness of training can be increased by fixing objects on a piece of paper.
- If you perform this exercise regularly, you will be able to achieve considerable progress in the development of visual memory.
8.) Schulte tables
Such tables are used to determine the degree of attention, which in turn is directly related to memory - you can find them in abundance on the Internet. To do this, just search for “Schulte tables online” and start training.
Note that we are talking about a field divided into squares, and in those, in turn, numbers from 1 to 25 are written in random order. Subsequently, you will need to find all the numbers in order using a stopwatch - the search speed should increase over time.
9.) Fortified healthy foods
Of course, for good memory it is important to eat food that is as rich in vitamins as possible. Which products should you pay the most attention to? Eat apples, salmon, blueberries, spinach, various seeds and nuts, and grapes.
10.) Develop your left hand if you are right-handed and vice versa
A very useful activity. Set yourself challenging goals. Train your left hand if you are left-handed, and your right hand if you are right-handed. Using your “unaccustomed” hand will be difficult at first, but over time you will master this skill.
Main rules of logic
The most important thing is to realize that there are two main types of reasoning: some of them are the most reliable, and others are not so much. The former are called deductive reasoning, the latter - plausible. Paradoxically, ordinary people for some reason prefer to use plausible rather than deductive reasoning.
There are a number of deductive arguments that simply need to be mastered.
Conditional categorical inferences
The conditionally categorical type of reasoning includes two correct ones: modus ponens and modus tollens.
Modus ponens.
This reasoning has the following structure:
"if A
, then
B
";«A
" means "
B
".
Logicians are interested in the very structure of these reasonings, but in reality they do not always appear to us in exactly this guise and can take on different linguistic and rhetorical forms. In human language it might look like this:
“if the Russian team wins against Spain, then I will get a tattoo”;
“The Russian team won against Spain” means “I’ll get a tattoo.”
Modus tollens.
This reasoning goes like this:
"if A
, then
B
";"not- B
" means "not-
A
".
Let's translate again:
“if the Russian team wins against Spain, then I will get a tattoo,”
“I didn’t get a tattoo” means “the Russian team didn’t win against Spain.”
It may look a little different: “if A
, then
B
” means “if not-
B
, then not-
A
.” In this form it is called “contraposition.”
For example, at the recent International Economic Forum in St. Petersburg, during a panel discussion, Alexey Kudrin used the mentioned modus tollens to demonstrate that anti-Russian sanctions are one of the significant factors influencing the rate of economic growth of the Russian economy, despite the fact that the government sets quite ambitious goals by its increase. Kudrin notes: “Now, after the latest wave of sanctions, their influence has increased to approximately 0.5% of GDP. Here, too, we must see that our tasks and plans are reduced by such foreign policy risks.” Within the framework of this remark, it is possible to reconstruct the notorious “contraposition”, thanks to which Kudrin came to this opinion: if economic sanctions are applied to Russia, then the growth of its economy decreases; Therefore, if economic policy is aimed at increasing economic growth, then economic sanctions should not be applied to Russia. And he did the right thing!
Very often, many of us make mistakes and use the following incorrect conditional categorical reasoning:
“if A, then B”; "B" therefore "A". And “if A, then B”; "not-A", therefore, "not-B".
An example is the erroneous reasoning of Alexey Venediktov during the release of his program “Minority Opinion”, in which he discussed with Ksenia Sobchak. In this fragment, Sobchak talks about what reforms of the judiciary she will carry out if she wins the presidential election. In response to this, Venediktov claims that after this speech, the electorate represented by “judges and members of their families” will not vote for Sobchak.
Venediktov’s reasoning can be reconstructed as follows: “if Ksenia Sobchak comes up with proposals that are attractive to voters, then these voters will vote for Sobchak”; “Sobchak does not come up with proposals that are attractive to voters,” therefore, “these voters will not vote for her.”
At first glance, it may seem that this reasoning does not contradict any logic, but this is not so.
The fact is that deductive reasoning has an essential characteristic, which makes it very reliable: in it, from true
premises necessarily follows
a true
conclusion.
In other words, for correct deductive reasoning there is no situation in which its premises will be true
and its conclusion will be
false
. For the type of reasoning that Venediktov uses in this case, such a situation with true premises and a false conclusion exists.
To make sure of this, we need to give a counterexample. For example, here are two premises: “if the Russian team wins against Croatia
, then
I will get a tattoo
”, “
the Russian team did not win against Croatia
” - from these two premises it does not at all follow that “
I did not get a tattoo
”, since I could have gotten this tattoo for completely different reasons: out of pride in Akinfeev’s leg, out of regret for his right hand, which almost saved one of the penalty kicks, etc. Indeed, both premises are true statements, but the conclusion in this case turns out to be false.
Many may have doubts whether the already mentioned correct types of reasoning: modus ponens and modus tollens will withstand such a test for lice. Well, try to find counterexamples to them (in logic there are more accurate and convenient methods for checking the correctness of reasoning, but, unfortunately, they cannot be considered within the scope of this article).
Reduction to absurdity and reasoning by contradiction
There are other methods of reasoning in logic: these are the so-called indirect inferences. There are two cool techniques among them, they are called “reduction to absurdity” and “proof by contradiction” (they are actually the same thing).
Reduction to the absurd.
We want to refute some statement "A". Armed with the technique of reductio ad absurdum, we must assume that proposition "A" is true - and then try to use some reasoning to demonstrate that this assumption leads to a contradiction. If we manage to arrive at a contradiction, then our initial assumption was incorrect. Thus, we refute statement "A".
Proof by contradiction.
It is constructed a little differently: the initial goal is not to refute “A”, but to substantiate “A”. To achieve this goal, it is first assumed that “A” is false, and then everything is the same: a contradiction is derived that allows us to justify the incorrectness of the original assumption.
People often use these two reasoning techniques. Consider, for example, the “by contradiction” method.
We will assume that you are interrogating a person suspected of murder. The crime was committed with a pistol that was found in the suspect’s apartment.
The latter, of course, denies his involvement and has no idea who the real killer was. In addition, he claims that he spent the entire ill-fated day at home. In order to strengthen your argument in favor of the suspect's guilt, you assume
that the gun really wasn't his. From this assumption we can conclude that the gun was planted on him. But in this case, the suspect must have known the killer or been absent from home at some point on the day of the murder. Both of these alternatives contradict the suspect's testimony, which means your assumption that the gun does not belong to him is incorrect. Therefore, the gun still belongs to the suspect.
How to develop logic and thinking in a teenager
Tasks, puzzles and charades
On the Internet you can find many puzzles that you and your teenager can try to solve. Try to look for tasks that contain the correct answer - if the goal is not achieved, you can see how it could have been achieved.
A special application with tasks for a smartphone
On Google Play you can easily find an application called “Logic, Problems, Puzzles” - it can be installed on your smartphone. The essence of the application is to develop analytical skills in adults and adolescents. There are also apps like Brain Training, Lumosity and many others.
How to develop ingenuity and intelligence
Many factors influence intelligence and ingenuity. If you are forced to subject your body to constant stress, then it is not surprising that your reactions will leave much to be desired. During peak periods, the human body produces cortisol, which has a detrimental effect on brain cells. If you have to take on a ton of things in the morning, then you should try to slow down your usual pace of life at least a little. Start by not jumping out of bed immediately after the alarm clock rings - allow yourself some time (15-25 minutes) to lie down and think about the coming day.
Ways to improve your intelligence
Music.
Periodically take a break from the daily hustle and bustle by listening to music. By the way, scientists believe that classical works are very useful for activating the brain. For example, people who listen to Mozart from time to time are characterized by increased speed of thinking.
Don't waste energy.
Don't take on many tasks at once. To do something well, it is important to focus on it. If you have to answer a letter, talk on the phone and listen to the news at the same time, then, of course, attention will begin to dissipate among several sources of information. The result will be a decrease in concentration and even the level of intelligence.
More positive.
Do not deny yourself positive emotions - your performance directly depends on them. Visit parks more often, go to the movies, meet friends.
Development.
Regularly search the Internet for exercises to develop memory and enrich your vocabulary. It is unlikely that you will be “illuminated” by unexpected solutions if you have a poor vocabulary that is almost unable to hold anything in your head. To develop memory, learn poetry, just read books.
Books that develop logical thinking
“Applied Logic” by N. Nepeyvod
This book can be considered a simple introduction to the world of modern mathematical logic. The textbook was recommended by the State Committee of the Russian Federation for Higher Education, and has become an excellent source of knowledge for many students of higher educational institutions.
“Textbook of Logic” G. Chelpanov
This is a book that clearly explains the basics of logic. The main emphasis is on syllogistics. The textbook contains tasks with the help of which the student is able to learn to apply certain rules in practice in a short period of time.
“Logic” A. Ivin
A textbook that talks about how to learn to think logically - who finds it difficult, and who easily overcomes barriers. Contains useful tasks.
Where is it used?
Children, with the help of abstract thinking, draw, design, sculpt, understand the meaning of riddles, can solve problems, and coherently express their thoughts when describing events. During school years, this type of mental activity helps schoolchildren master mathematics, which requires the ability to operate with a lot of data, divide them into groups, and look for relationships.
Abstract thinking is used in logic, physics, astronomy and other exact sciences, where one must be able to measure, count, calculate, and combine elements into one group. It is necessary for psychologists, philosophers, writers, engineers. Time management is unthinkable without it.
In everyday life, people also constantly use abstract-logical mental activity. Examples of abstract thinking reflect everyday human thought processes. Planning often intersects in the imagination with dreams and fantasies. Young people looking for a job can come up with so many things that, when faced with reality, they cannot stand the conditions offered to them. So girls, waiting for a prince on a white horse, mentally endow their future chosen one with unrealistic traits. This inevitably leads to disappointment in the future.
