A logical square is a diagram that clearly shows how true and false judgments interact with each other when the wider one includes the narrower one. If a wider proposition is true, then the narrower proposition included in it is all the more true. For example: if all Greeks are slim, then the Greeks living in Athens are slim too. If a narrower judgment is false, then a wider judgment, which includes a narrower or more specific one, will be no less false. The assertion that all people who weigh no more than 70 kilograms live in Athens is false, which means that the broader that all slender people live in Greece is also not reliable.
Law of Exclusion of the Third
The rules of the logical square are easy to remember and are based on one important logical law - the law of exclusion of the third: if the judgment is true on the one hand, then it is false on the other and vice versa. A statement can be either true or false, and, accordingly, its denial will be true or false. There are no other, third options. The statement “All cars are red” is false. Therefore, the statement “Not all cars are red” is true. And here the magic word “some” appears, which will almost always turn a false statement into a true one: “Some cars are red.”
Square and Cross
To understand the rules of the logical square by ear, it should also be remembered that the logic of the machine from the above statement is called the subject, and red is called the predicate.
A predicate as an attribution of a subject can be a verb or quality. Or another quality that is attached to the subject using the verb-connective "essence". It looks like a logical square, like a square. This is not surprising. The corners of the square are marked with the letters A, E, I, O. But the opposite is E, I is partially compatible with O, I is subordinate to A, and E dominates O. The square is crossed by two lines of contradictions. Using the mechanics of a square, one can work with judgments. This tool is more important to lyricists than physicists, physicists are strict, and so on, and lyricians constantly need mechanisms to allow them to question and verify the truth of their judgments. Of course, in the world of lies and ambiguity, the beauty of truth and the desire to achieve it at any cost have somewhat lost, but in some cases (in court, in traffic, in charging a fee) objective truth has its own value.
Square in History
Logic as a science was founded by the ancient Greeks. They were very fond of arguing, and arguing is always annoying if the opponent is wrong. The laws of logic were created by the Greeks in order to clearly explain to the opponent that it was he who was mistaken.
The Greek square was invented and introduced by the Greek philosopher Michael Psell in the 11th century, much later than the time when Socrates invented scholasticism. Obviously, for some time the concept of absolute truth was not necessary for the Greeks, and only at the time of universal clarity was a logical square invented. The examples that are usually given in the description of his scheme, almost all are based on Aristotelian logic, but contain elegant Byzantine generalizations.