8.2 Logical necessity

Let us briefly discuss the logical and physical modalities, as well as the modalities associated with values.

Logical modal concepts are “(logically) necessary,” “(logically) possible”, “(logically) impossible” and “(logically) randomly.”

Logical necessity is a characteristic of a utterance, the negation of which is a logical contradiction.

In particular, the statement “It is not true that neon is an inert gas and yet not an inert gas” is logically necessary, since the negation of this statement (“Neon is an inert gas and neon is not an inert gas”) is internally contradictory (it is a negation law of contradiction). The statement “Grass is green or it is not green” is logically necessary, since its negation (“It is not true that the grass is green or it is not green”) is contradictory (the negation of the law of the excluded middle). The statement “All bachelors are not married” is also logically necessary, since its denial (“There are bachelors who are married”) is contradictory.

The truth of a logically necessary utterance can be established independently of experience, on the basis of a simple analysis of the meanings of words included in this utterance. For example, the statement “Snow is white” is actually true, empirical observation is required to confirm its truth. The statements “Snow is snow”, “White is white”, “Every single bachelor is not married”, etc. it is necessary to be true: to establish their truth, one does not need to turn to experience, it is enough to know the meaning of the words contained in them.

The concept of logical necessity is connected with the concept of logical law: the laws of logic and everything that follows from them are logically necessary.

The logical possibility is a characteristic of an internally consistent statement.

For example, the statement “The efficiency of a steam engine is 100%” is obviously false, but it is internally consistent and, therefore, logically possible. But the statement “The efficiency of such a machine is above 100%” is contradictory, and therefore it is logically impossible.

A logical possibility can be explained through the concept of a logical law: any statement that does not contradict the laws of logic is logically possible. Say, the statement “Viruses are living organisms” is compatible with the laws of logic and, therefore, is logically possible. The statement “It is not true that if a person is a lawyer, he is a lawyer” contradicts the logical law of identity and therefore is impossible.

Logical randomness is a “two-sided possibility,” or a logical possibility of both a statement and its denial.

Accidentally what may or may not be. From the point of view of logic, by chance, for example, that all multicellular creatures are mortal: neither the statement of this fact, nor its negation contain an internal (logical) contradiction.

The logical impossibility is the internal inconsistency of the statement. For example, statements are logically impossible: “Plants breathe and plants do not breathe”, “It is not true that if the Universe is infinite, then it is infinite”, “Some wives are not married”, etc.

Logical modalities can be defined through each other.

“Statement A is logically necessary” means “Denial of A is not logically possible.”

For example, “It is necessary that cold is cold” means “It is impossible that cold was not cold.”

“A is logically possible” means “Denial of A is not logically necessary.”

For example, "It is possible that cadmium is metal" means "It is not true that it is necessary that cadmium is not metal."