The 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 broader proposition is true, then the narrower proposition included in it is all the more true. For example: if all Greeks are slender, then the Greeks living in Athens are slender too. If a narrower proposition is false, then a broad proposition, which includes a narrower or more specific one, will be no less false. The statement that all people who weigh no more than 70 kilograms live in Athens is false, which means that the wider statement 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 a 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, true orits denial would be false. There are no other third options. The statement "All cars are red" is false. So the statement "Not all cars are red" is true. And here comes the magic word “some”, which will almost always turn a false statement into a true one: “Some cars are red.”
Square and cross
To learn by ear the rules of the logical square, you should also remember that the logic of the machine from the above statement is called the subject, and the redness is called the predicate.The predicate as an attribution of the subject can be a verb or a quality. Or some other quality that is attached to the subject using the linking verb "essence". A logical square looks like a square. This is not surprising. The corners of the square are marked A, E, I, O. A is opposite to 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 the square, you can work with judgments. This tool is more important to lyricists than to physicists, physicists are already strict, and lyricists constantly need mechanisms that allow them to question and verify the truth of their judgments. Of course, in a world of lies and ambiguity, the beauty of truth and the desire to achieve it at any cost are somewhat lost, but in some cases (in court, in traffic, in charging a patch), objective truth has its own value.
A square in history
Logic as a science was founded by the ancient Greeks.They were very fond of arguing, and arguing people are always annoyed if the opponent is wrong. The laws of logic were created by the Greeks in order to clearly explain to the opponent that he is wrong.
The logical square was invented and put into use by the Greek philosopher Michael Psellus in the 11th century, much later than the time when Socrates invented scholasticism. It is obvious that for some time the Greeks did not need the concept of absolute truth, and only at the time of universal clarity was the logical square invented. The examples that are usually given in the description of his scheme are almost all based on Aristotelian logic, but contain elegant Byzantine generalizations.