Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics.

The first incompleteness theorem states that no consistent system of axioms is capable of proving all truths about the arithmetic of natural numbers.

The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency.

Are Gödel's theorems applicable to the laws governing the life of human society?
It is no secret that the legislation of many countries is ultimately based on the axioms postulated in Ten Commandments and is merely an extension and refinement of these axioms.

If Gödel's theorems apply to this set of axioms (Ten Commandments), then this system of axioms is incapable of proving all truths about and shows that the system cannot demonstrate its own consistency.
This means that legislation based on these principles is incomplete and contradictory and has little to do with social justice.