Explanation of the four properties of logic

It is usually expressed as A is not non-A, or A cannot be both B and not B. In traditional logic, the law of contradiction is firstly formulated as a law of things, which means that any thing cannot be both a property and not a property at the same time. As a law of thought, it means that no proposition can be true and untrue at the same time. The law of contradiction is also presented as a normative law of cognitive activity, meaning that no one should assert both a proposition (A) and its negation (not A). That is, one should not be ambivalent about a proposition and its negation in order not to contradict oneself. The law of contradiction is also seen as a law of logical semantics, i.e., the same word or statement should not express an idea and not express an idea at the same time in the same context. By violating the law of contradiction, a thought is in logical contradiction (A and not A) . And any thought that contains logical contradiction is always wrong, so the non-contradiction of thought is an indispensable condition for correct thinking and one of the important principles for constructing a theoretical system. In modern logic, (A∧A) ( read as A and non-A is false ), is the embodiment of the law of contradiction in propositional logic; ?x(F(x)∧F(x)) (read as there is not an individual x, and x has both the property F and not the property F), is the embodiment of the law of contradiction in predicate logic.

Second, the law of exclusion:

In modern logic, A∨┐A (read: A or non-A), is the embodiment of the law of exclusion in propositional logic; "x(F(x)∨┐F(x)) (read: for any individual x, x has property F or not) is the embodiment of the law of exclusion in predicate logic. Since constructive logic does not recognize the existence of real infinity in the real world, but only recognizes infinity as a process, the law of exclusion does not hold in that logic when infinite objects are involved; and proving an existence proposition by contrapositive is not a valid method of proof.

One of the fundamental laws of traditional logic. Often stated as A is B or is not B. Traditional logic begins by treating the law of exclusion as a law of things, meaning that any given thing has or does not have a certain property at the same time, and that there is no other possibility. It is also a law of thought, meaning that a proposition is true or not true, and there is no other possibility. It is also a normative law of cognitive activity, meaning that no one should deny both a proposition (A) and its negation (not A), i.e., no one can say two things about a proposition and its negation. The law of exclusion has also been taken as a law of logical semantics, meaning that any word or statement should either express a certain idea or not express that idea in the same context. As the latter two laws, it is also called the requirement of the law of exclusion. The law of excluded middle does not exclude that there are intermediate steps in the process of development of concrete things and there are many states and possibilities. In modern logic, A∨A (read: A or non-A), is a manifestation of the law of neutrality in propositional logic; "x (F(x)∨F(x)) (read: for any individual x, x has property F or not) is a manifestation of the law of neutrality in predicate logic. Since constructive logic does not recognize the existence of real infinity in the real world, but only recognizes infinity as a process, the law of neutrality does not hold in that logic when infinite objects are involved; and proving an existence proposition by contrapositive is not a valid method of proof.

Example sentence: It violates the principle of the law of exclusion to say both "this weed is sharp and invulnerable" and "this shield is strong and cannot be pierced".

Three, the same law:

One of the basic laws of formal logic is that in the same thinking process, must be used in the same sense of concepts and judgments, can not be confused with different concepts and judgments. The formula is: "A is A" or "A is equal to A" includes three aspects:

(1) The same object of thinking. In the same thinking process, the object of thinking must remain the same; in the discussion of the question, answer the question or refute others, all parties to the object of thinking must also remain the same.

(2) The same concept. In the same thinking process, the concepts used must remain the same; in discussing a question, answering a question or refuting someone else, the concepts used by all parties must also remain the same.

(3) The same judgment. The same subject (individual or collective) at the same time (the corresponding objective things in a relatively stable state), from the same side of the same thing to make the same judgment must remain the same. The same law requires the certainty of thinking, but it does not deny the development and change of thinking. It speaks exclusively to the process of thinking and does not require that objective things remain the same, absolutely unchanged.

The "law of sameness" aspect of logic should include "the same position" and "the same space-time" in it.

Fourth, the law of sufficient reason:

Logicians who claim that the law of sufficient reason is also one of the basic laws of traditional logic usually express this law as follows: any judgment must be justified. The Law of Sufficient Reason originated from the German philosopher Leibniz, G.W., in the late 17th and early 18th centuries. He said in The Monadology: "Our reasoning is founded on two great principles, namely: (1) the principle of contradiction, ...... (2) the principle of sufficient reason, by virtue of which we hold that if any thing is true, or real, and if any statement is true, there must be a reason why it is so and not so, and if it is true, there must be a reason why it is so and not so. There must be a sufficient reason why it is so and not so, though these reasons are often always unknown to us. However, Leibniz himself did not take the principle of sufficient reason as a law of logic. What exactly he meant by the principle of sufficient reason has also been a matter of debate. According to Kant, I., both the law of contradiction and the law of sufficient reason are logical or formal criteria of truth. In his view, the law of contradiction is a negative criterion, because a thought that obeys the law of contradiction is not necessarily true, and a thought that violates the law of contradiction cannot be true; while the law of sufficient reason is a positive criterion, because a thought that obeys the law of sufficient reason must be well-founded, and must be a thought that follows from some principle and does not lead to a false conclusion. However, traditional logicians have generally held that the law of sufficient reason is not so much a law about the form of thought and formal logic as it is a law about existence and facts. It is for this reason that this law is not stated in many traditional logical works, and is not discussed in modern logic.