Paradoxes of Lies, Anti-truth and the Limits of Truth

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Sha-logic: Paradoxes of Lies, Anti-truth and the Limits of Truth
Sha S.V. + ChatGPT

Introduction
This work is a combination of three logical-philosophical articles devoted to the study of the differences between the concepts of Lie, Anti-truth and Truth. Based on the construction of a formal system of lies and the analysis of the Liar's paradox, a new view of the foundations of logic and reasoning is proposed. The work reveals the structure of Sha-logic, in which a lie is not considered an equal logical element, but is defined through its parasitism on the truth.

1. Lies and anti-truth
The anti-truth of the statement "red" is "not red". The anti-anti-truth of "red" is "not not red", i.e. "red". In this sense, anti-truth works as a logical opposite, similar to negation in logic.
The lie of "red" can be, for example, "green". The lie of "green" can be "blue". Thus, a lie of a lie can generate an arbitrary meaning, not directly related to the original. This distinguishes a lie from an anti-truth. An anti-truth is logically definable, a lie is not. This explains the impossibility of productive reasoning based on a lie, and thus resolves the Liar's paradox: nothing follows from a lie.

2. Axioms of the formal system of lies
1. Anti-truth is the logical opposite of the statement (¬A).
2. A lie is not a logical function, but a random (undefined) value, not related to the original statement.
3. No logical conclusion follows from a lie.
4. The Liar paradox is resolved by the fact that a lie from a lie does not generate truth, but breaks the chain of inference.

3. The boundary between truth and anti-truth
At the boundary between the sets of "Truth" and "Anti-truth" there is a point where the relation Truth = Anti-truth works. It is this place that gives rise to the effect of the Liar paradox. This boundary belongs to both sets, which explains the persistence of the paradox.

4. Logic and multiplication
Traditionally in logic, Truth is assigned 1, and Falsehood is assigned (-1). Then:
1 * 1 = 1 (Truth from Truth - Truth)
1 * (-1) = -1 (Truth from Falsehood - Falsehood)
(-1) * 1 = -1 (Falsehood from Truth - Falsehood)
(-1) * (-1) = 1 (Falsehood from Falsehood - Truth)
However, if Falsehood is considered an unequal element, it is better to use 0:
1 * 1 = 1
1 * 0 = 0
0 * 1 = 0
0 * 0 = 0
This reflects the idea that Falsehood does not produce meaning and does not generate new significance.

Conclusion
Sha-logic is an attempt to construct an intuitively and philosophically consistent system of reasoning, where lies are not an instrument of inference. This approach opens up new horizons in understanding logic, language, philosophy and formal thinking.