The principle of non-contradiction states that a statement cannot be both true and false at the same time and in the same sense. This means that if a statement is true, then it cannot also be false, and vice versa.

Aristotle is often credited with formulating the principle of non-contradiction in his work Metaphysics.

The logical symbol for the principle of non-contradiction is ¬(A ∧ ¬A), which means "not (A and not A)".

The principle of non-contradiction is sometimes called the Law of Contradiction.

The opposite of the principle of non-contradiction is the principle of contradiction, which states that a statement can be both true and false at the same time and in the same sense.

The principle of non-contradiction is used to argue against a wide range of philosophical and religious beliefs, such as the belief that there is a god who is both all-powerful and all-loving, or the belief that there is a soul that survives the death of the body.

A square circle exists is an example of a statement that violates the principle of non-contradiction because it is a statement that is both true and false at the same time and in the same sense. A square is a shape with four straight sides and four right angles, while a circle is a shape with no sides and no angles. Therefore, a square circle cannot exist.

The principle of non-contradiction is based on the law of identity, which states that a thing is what it is. This means that a statement cannot be both true and false at the same time and in the same sense because a thing cannot be both itself and not itself at the same time and in the same sense.

The principle of non-contradiction is sometimes used to prove the existence of the external world. This is because if the external world did not exist, then it would be possible for a statement to be both true and false at the same time and in the same sense. For example, it would be possible for a statement to be true in the external world but false in the mind of a person who is dreaming.

The principle of non-contradiction is sometimes used to argue against the existence of God. This is because if God exists, then he must be both all-powerful and all-loving. However, these two attributes are contradictory because an all-powerful being could create a world without evil, while an all-loving being would not want to create a world with evil.

The principle of non-contradiction is sometimes used to explain the nature of truth. This is because truth is often defined as that which is true in all possible worlds. However, a statement cannot be true in all possible worlds if it is both true and false at the same time and in the same sense.

The principle of non-contradiction is sometimes used to justify moral beliefs. This is because moral beliefs are often based on the idea that certain actions are right and certain actions are wrong. However, if the principle of non-contradiction is true, then it is impossible for an action to be both right and wrong at the same time and in the same sense.

The principle of non-contradiction is sometimes used to criticize religious beliefs. This is because religious beliefs are often based on the idea that there is a supernatural being who is both all-powerful and all-loving. However, as we saw earlier, these two attributes are contradictory.

The principle of non-contradiction is sometimes used to defend scientific beliefs. This is because scientific beliefs are often based on the idea that the universe is governed by natural laws. These natural laws are often expressed in the form of mathematical equations. However, if the principle of non-contradiction is true, then it is impossible for a mathematical equation to be both true and false at the same time and in the same sense.