# Irrationality and why we have logical paradox

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1: Rational thinking and the self of rational thinking
If and only if we know the definition of self in human thinking, can we know the structure of human thinking. I will start by discussing the basis of rational thinking-formal logic and use logical paradox as testing.

There are three basic laws of formal logic.

1: The law of identity

3: The law of excluded middle
The law of identity states that
something is what it is. Expressed as symbols: A = A.
says that a statement cannot be both true or false at the same time and in the same way. Expressed as symbols: A ≠ -A.

The law of excluded middle says that a statement is either true or false. Expressed as symbols: = A or = -A.

When thinking rationally, there must be a "self" existing in the process of thinking. The three laws of formal logic only use opposing concepts A and -A. To define the self of rational thinking, in addition to A and -A, we must introduce a third presence. This is in conflict with formal logic. Formal logic proves that the self of rational thinking cannot exist outside of A and –A. As it is not A or -A, the self of rational thinking can be defined as below.

1: ≠ A and ≠ -A.

2: inseparable with both A and -A.

2: Irrational thinking and the self of irrational thinking

By putting all three laws of formal logic through reversion, I derive the laws of anti-logic.  The way to achieve reversion is to reverse the signs into their opposites: the “=” is now “≠”; the “≠” is now “=”; the “A” is now “-A” and the “or” is now “and”. Here I only do the odd-numbered transformation because the even-numbered transformation does not produce results of anti-logic.
The law of identity becomes two laws of difference. 1: A ≠ A; 2: A = -A.
The law of non-contradiction becomes two laws of contradiction. 1: A = -A; 2: A ≠ A.
The law of excluded middle is more complex, it can offer a variety of results. It produces two laws of middle. 1: ≠ A and ≠ -A; 2: = A and = -A.

The law of excluded middle can also derive: ≠ A or = -A, = A or ≠ -A, etc. These are not anti-logic, therefore not required.
It is easy to tell that the law of difference 1 and the law of contradiction 2 are the same; the law of difference 2, the law of contradiction 1 and the law of middle 2 are same. Removing duplicates, we get three laws of anti-logic. The law of difference: A ≠ A; The law of contradiction: A = -A; The law of middle: ≠ A and ≠ -A. The law of contradiction and the law of middle are in conflict. We separate these three anti-logic laws into two groups.

Group 1: The law of different: A ≠ A; the law of contradiction: A = -A.

Group 2: The law of different: A ≠ A; the law of middle: ≠ A and ≠ -A.

Each group represents one type of irrational thinking.

Group 1 is the feature of Chinese philosophy.

Group 2 is the feature of Indian philosophy.

Rationality, as everyone knows, is the feature of Greek philosophy.

The laws of anti-logic also only use opposing concepts A and -A, therefore the self of irrational thinking has same definition as the self of rational thinking. This guarantees that the self of thinking could freely switch between rational and irrational thinking. It’s easy to find that the self of thinking's definition include the law of middle.

Below I will discuss the relationship between the two types of irrational thinking. This is related with logical paradox.

3: Conversion between two type of irrational thinking and Logical paradox
Conversion 1: When the law of contradiction exists, applying the law of non-contradiction (cannot be both true), Any of A and -A is denied, it will result in the law of middle. Because A = -A. Denying A will also deny -A, denying -A will also deny A.
Conversion 2: When the law of middle exists, applying the law of excluded middle (cannot be both false), Any of A or -A is affirmed, it will result in the law of contradiction. Because the law of middle logically requires that "A is affirmed" will result in "-A is affirmed",

"-A is affirmed" will result in "A is affirmed".

If a self-referential proposition "I am A" is -A. The symbol is expressed as: "I = A" = -A, can infer A = -A. This proposition contains contradictory laws. If "I am A" is a self-denying judgment, then at least one of A and -A is denied. According to the conversion 1, this "I" logically satisfies the intermediate law, and this "I" is the same as the self of thinking. According to the conversion 2, the intermediate law leads to the law of contradiction. That’s the reason we have logical paradox. According to the above discussion, a proposition leading to paradox must satisfy two conditions, and 1) is a direct or indirect self-referential judgment. 2) This judgment is actually self-denying and introduces a set of contradictory propositions.

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Moderator Note

This is the third identical thread you have started.