The concept of “logic” originated in Ancient Greece and literally means “the art of reasoning.” It was then that people first began to get involved in logic games. At the same time, philosophers and entire schools began to appear, which began to become sophisticated in proving their own theories through chains of logical deductions.
Logical thinking is not given to a person at birth, but develops as an integral property of the individual. Man is a social being, and in the social order the influence of logic on significant processes in the interests of power elites is seriously reduced. If logic had more weight, then humanity would set more adequate goals for itself. And all wars would stop in the world, there would be fewer disadvantaged people. The paradox of logic lies in its versatility. Despite the existence of formalized laws, almost every person can find loopholes for himself and justify his behavior.
Law of Identity
Each thought should be equal to itself, should not have more than one meaning.
What's the point
Even before our era, Aristotle said: “...To have more than one meaning means not to have a single meaning; if words do not have (definite) meanings, then all possibility of reasoning with each other, and in reality with oneself, is lost, for it is impossible to think anything if you do not think one thing every time.”
Examples of violation
The most popular example of a violation of the law of identity is the phrase “the students listened to the lecture.” The word “listened” can be understood in two meanings: either the students listened carefully to the teacher, or they missed everything.
An example of a violation of the law of identity is this joke:
— I broke my arm in two places.
- Don't go to these places again.
Slightly more complex violations of the law of identity result in sophistry. Sophistry is the outwardly correct proof of a false thought through a deliberate violation of the laws of logic.
Which is better: eternal bliss or a sandwich? Of course, eternal bliss. And what could be better than eternal bliss? Of course, nothing! But a sandwich is better than nothing, so a sandwich is better than eternal bliss.
The catch here is that the word “nothing” was used first in the sense of “not a single object or phenomenon”, and then in the sense of “absence of something”
How to apply it in life
The first law of logic will help you recognize sophisms. The first thing to pay attention to is ambiguous words.
Why is logic needed?
The main goal of logic is to provide effective tools for finding solutions and proofs, applicable in any field of knowledge. Thanks to logic, we can operate with facts whose reliability has been established and proven. Logic is necessary when solving problems such as:
- Cognition. In any science, all accumulated knowledge is interconnected by logical connections. Some of this knowledge is obtained empirically, and some is obtained through theoretical analysis using logic.
- Resolution of disputes. In any area of life, controversial situations may arise in which opposing points of view collide. And logical analysis helps to find the truth. For example, legal proceedings are based on the use of formal logic to find the truth and determine the degree to which each side is right.
- Productive communication. When communicating with someone, we try to express our thoughts logically in order to be understood unambiguously. At the same time, we expect that our interlocutor is guided by the same rules of logical thinking as we are.
- Finding answers. In any field of knowledge, the rules of formal or mathematical logic are used when searching for answers, solutions and proofs.
Law of contradiction
A statement and its negation cannot be true at the same time.
What's the point
If one judgment affirms something, and another denies the same thing about the same object at the same time and in the same respect, then they cannot be true at the same time.
For example, two propositions - “the cat is black” and “the cat is white” - cannot be true at the same time if we are talking about the same cat, at the same time and in the same respect. That is, the color of the cat is compared with the same palette.
Examples of violation
“This ginger cat left black hairs all over the carpet.” And from childhood - “Shut your mouth and eat.”
How to apply it in life
The most difficult thing is to identify the contradiction. The phrase “I didn’t have a childhood as a child” does not violate the law of contradiction, but “made an oral report in writing” does. So, the main thing is to understand whether there is a contradiction or a play on words.
What is logic?
Logic is the science of forms, techniques and operations of thinking that make it possible to establish or refute the truth of certain statements based on known facts. It is difficult to say exactly when it arose. Certain elements of logic are present in the works of ancient Greek, ancient Chinese and ancient Indian thinkers of the 6th-5th centuries BC. e., but Aristotle was the first to formulate its basic principles in the 4th century BC. e.
Initially, it arose as a direction in philosophy, but over time it developed into a complex system of knowledge and became an independent scientific discipline - formal logic. It differs from other sciences that study thinking in that it abstracts from the content of thoughts and statements, and studies their structure and internal patterns.
The term “logic” is derived from the Greek word λόγος (logos – thought, word, reason). Today it has two main meanings. It can denote both a scientific discipline that studies the patterns of thought processes and logical constructions, and a set of rules that must be followed when constructing consistent conclusions.
Law of the excluded middle
Two contradictory judgments about the same subject at the same time and in the same respect cannot be both true and cannot be false at the same time.
What's the point
Judgments can be opposite and contradictory.
Opposite judgments always presuppose some third, intermediate option. For example, for the judgments “the house is big” and “the house is small,” the intermediate will be “a medium-sized house.” There is no third option for conflicting judgments. For example, for the judgments “the house is big” and “the house is small”, there is no third correct option.
So, two contradictory judgments about the same subject, at the same time and in the same respect cannot be simultaneously true and cannot be false at the same time.
Example of a violation
The judgments “the cat is old” and “the cat is not old” about the same cat at the same time cannot be simultaneously true.
How to apply it in life
The examples are simple to the point of disgrace, but in life the law of contradiction is violated rather like this: between contradictory judgments there is still part of a monologue, and the judgments themselves may not be expressed very clearly. How to deal with this? Listen carefully to what the interlocutor says and follow the thought. If all other laws are not violated, take another look at the wording. Perhaps there are disguised contradictory judgments here.
Types of logic
When explaining what logic is, they usually talk first of all about formal logic. At the same time, there are two more sections that are actually independent disciplines: mathematical (symbolic) logic and dialectical logic. Let's look at each section in more detail.
Formal logic
Formal logic is a scientific discipline that studies the structure and truth of statements. Its creator is considered to be Aristotle (4th century BC), who considered it as an opportunity to operate with formal facts, abstracting from their nature and content. This makes it possible to ensure the logical correctness of judgments, since only the structure of the statement is analyzed, but not its content.
In essence, our thinking is subject to formal logic. Based on the available facts, we draw logical conclusions and make decisions. However, we cannot completely abstract from the nature and content of judgments, in addition, emotions can have a very strong influence on our conclusions and actions. Therefore, people tend to act illogically.
Mathematical logic
Initially, it was part of formal logic, but in the 19th century it became an independent section (at the same time, it still respects all the principles of formal logic). It has been replenished with new mathematical methods and specialized notations. Thanks to this, symbolic logic has become a powerful tool used by modern sciences in solving problems and proving theories.
This model makes the process of cognition more accurate, since in it words of natural languages with a vague meaning are replaced by formal definitions that eliminate ambiguity and vagueness of judgments. All judgments of mathematical logic are formulated in a precise language that does not allow ambiguous interpretations. For such languages, semantics (meanings of terms) and syntax (a set of formulas or rules for constructing language objects) are clearly defined.
Dialectical logic
This is a philosophical discipline that studies thinking in general. Its founder is considered to be the German philosopher Georg Hegel (1770-1831). It is based on formal logic, and yet it takes into account the content of phenomena, objects and processes. It uses the following principles:
- principle of objectivity;
- principle of comprehensiveness;
- the principle of historicism (identification of patterns in the history of the object under consideration);
- the principle of concreteness (taking into account the characteristics of a specific object and the conditions of its existence).
Law of Sufficient Reason
In order to be valid, any thought (thesis) must be proven by some arguments, and these arguments must be sufficient to support the original thought, that is, it must follow from them.
What's the point
Remember what the presumption of innocence is? It is based on the law of sufficient reason. The principle of presumption of innocence dictates that a person be considered innocent, even if he testifies against himself, until his guilt is reliably proven by any facts. In other words, a guilty plea does not guarantee that a person actually committed a crime, but evidence and evidence may well. That is, an admission of guilt is not a sufficient basis, but the facts and evidence pointing to the criminal are sufficient.
Example of a violation
“Don’t give me a bad mark. I have read the entire textbook and may have some answer.” The conclusion does not follow from the basis: the student could read the entire textbook, but it does not follow from this that he will be able to answer anything.
Bottom line
Let's summarize. You need to find the truth, you need to learn to follow the laws of logic. Just because something sounds convincing doesn't mean it's true. Listen carefully to what they tell you, do not allow concepts to be substituted in a conversation, do not allow contradictions and check the facts. In principle, everything is simple - only 4 laws of logic.
Here is a final logical paradox for you, at one time it puzzled me: “I always lie . Graceful, isn't it?
That's all I have for today. If it seemed to you that I was lost, then I was not lost (oops, violation of the laws of logic). I’m currently working on a series of articles about motivation. Everything is interconnected; I wrote it in one place and have to redo it in another. In short, I came up with a headache, so I decided to take a break on this topic.
Subscribe to blog updates, see you! Yours Alexander Gorokhov
Judgment
A judgment (or statement) is a form of thinking in which something is affirmed or denied. For example:
- If a person reads, it means he knows the letters.
- Every child needs a mother.
- All dogs are not cats.
- Many flowers smell nice.
Let's look at the basic properties of a judgment to understand how it differs from a concept.
- Any judgment consists of interconnected concepts. For example, let’s take two concepts – man and woman. Several conclusions can be drawn from them:
- men and women are people;
- men are not women;
- some women are stronger than men.
- Any judgment is expressed in the form of a sentence (while a concept is expressed in a word). However, not every sentence must be a judgment.
- Any proposition is either true or false. If it corresponds to reality, it is true, and if it does not correspond, it is false.
- Judgments can be simple or complex. Complex propositions consist of simple ones connected by some kind of conjunction.
From all of the above it follows that a judgment is a much more complex form of logical thinking than a concept. That is why there are four parts in a judgment: subject, predicate, connective and quantifier.
Don't be afraid of these words, they are not at all as complicated as they seem at first glance. Let's look at them briefly.
The subject (S) is what the judgment is about. In the proposition “All plants are not animals” we are talking about plants, so in this case the subject is plants.
A predicate (P) is what is said about the subject. In the same judgment “All plants are not animals” it is said about the subject “plants” that they are “not animals”, therefore the predicate of this judgment is the concept “animals”.
A connective is what connects the subject and the predicate. The role of a connective can be played by a variety of words: there is, is, is, this, etc.
A quantifier is a pointer to the volume of a subject. The quantifier can be the words all, some, every fifth, half, none, etc.
To reinforce this, let’s analyze the simple proposition “Many schoolchildren love physical education.”
- Subject – “schoolchildren”
- Predicate – “physical education”
- Connection - “love”
- Quantifier – “many”
We hope this is clear. It is also worth noting that in some judgments the quantifier may be absent. However, it is necessarily implied. In the proposition “Butterflies are insects,” the quantifier is visibly absent, but it is implied—the word “all.”
Questions in logic
Now let's understand what a question is and why its correctness is so important for logic.
The fact is that the question itself is very close to a judgment. In essence, a question is a logical form aimed at obtaining an answer in the form of a judgment.
Any question consists of two parts:
- Main (basic), expressed by a certain judgment (premise of the question);
- The desired one, indicating the need to supplement this judgment with some kind of answer.
From a logical point of view, one of the main requirements for posing a question is the truth of the judgment of the basic part. Otherwise, the question is considered logically incorrect.
For example, the question: “In what year did Dostoevsky write War and Peace?” should be recognized as logically incorrect, since its basic part is expressed by the false proposition “Dostoevsky wrote “War and Peace”.”
Logical thinking
Why do you need to study the laws of logic, and is it so important for the development of logical thinking? By and large, a reasonable person can express himself extremely clearly and logically correctly even without knowledge of the science of logic.
But if you want to learn how to identify logical errors (your own and others), then you will still have to master some basics of logic.
The eminent philosopher John Stuart Mill wrote:
“...Logic dispels the fog that hides our ignorance from us and makes us think that we understand a subject when we do not. I am convinced that in modern education nothing is more useful for developing accurate thinkers than logic.”
Forms of thinking
For a mandatory understanding of logic, you should know that there are three main forms of thinking: concept, judgment and inference. Let's look briefly at each of them.
A concept is a form of thinking that designates an object or its attribute. For example: chair, beauty, smile, air, man, conscience, space, rationality, gift.
Judgment is a form of thinking that consists of interconnected concepts. A judgment necessarily affirms or denies something. For example: all stars are celestial bodies, many athletes have injuries, any pen is not a pencil.
Inference is a form of thinking in which a new judgment (conclusion) follows from two or more initial judgments (premises).
It is worth making an important digression here. The fact is that logic studies not only the forms of thinking, but also deals with its laws.
A little history
Sophistry
More than 2500 years ago, schools of sophistry actively spread in Ancient Greece. There they gave lessons to aspiring politicians: how to achieve their goals with the help of oratory. The sophists differed from the philosophers who also flourished in the ancient cities mainly in that they did not consider any universal tasks and theoretical reflections important, but recognized the achievement of a practical goal as the main thing.
It is interesting that sophistry appeared before logic as a formalized science, and, most likely, it was the sophists who pushed philosophers to create it (as a tool to counter demagogues who misled the people for their own purposes).
«He
(Protagoras, who lived approximately in the period 485 - 410 BC, a hundred years before Aristotle - author's note) was the
first to say that every subject can be said in two ways and in the opposite way... he did not care about thought, argued about words, and the ubiquitous current tribe of debaters originates from him
,” Diogenes Laertius wrote about the most prominent representative of the Sophists in his book “On the Life, Teachings and Sayings of Famous Philosophers.”
Aristotle conquers everyone
Plato scolded the sophists, and his student Aristotle decided to put an end to fooling the people (at least he tried - we still fall for the same tricks that were known 2500 years ago). He created the scientific basis of formal logic (which he himself called “Analytics”) and classified the logical errors used by the sophists.
In principle, a logical error and a logical trick are the same thing, it’s just that the error is made unconsciously, and the trick is deliberately introduced into speech.
Aristotle in his work “On Sophistic Refutations” clearly showed that if you decompose any sophism, you will see a specially introduced error into it, thanks to which the sophist’s conclusions seem logical.
After Aristotle, the Romans Cicero and Quintilian, and then the medieval scholastics, contributed a lot to the development of formal logic - we will further use their typology of logical errors, so do not be surprised by the Latin terms.
Logical paradoxes
Before we talk about the basic laws of logic, we will present interesting logical paradoxes that are classic.
Concept
A concept is a form of thinking that designates an object or its property. Here are a few random concepts:
- tree
- smile
- telephone
- Sun
- molecule
- sandwich
- beauty
At the same time, you might think that the concept and the word are one and the same. After all, we express the concept of a child with the word child. However, a concept and a word are different things.
A concept is a mental designation of an object (a thought about it), and a word is only a linguistic expression of this thought. In other words, a concept is a form of thinking, and a word is a form of language.
The concept of a newborn is the same for all people in the world: it means a recently born person, and not a table, air or a pencil. But the verbal expression of this concept will be different in all languages.
