Living a life with incompleteness - and self-referencing problem.

Russells paradox, and Godels incompleteness theorem.

I do not wish to be a mathematician. At least after reading first chapter of the book of proof by Richerd Hammock. I came to the conclusion, by no means there is any complete mathematician ever lived on earth. So, I wouldn't. And the enlightenment came with the Russells paradox, introduced in the first chapter itself. Even in the book of mathematics, which are supposed to be provable, and "True" there are contradictions, that exist, which are inconsistent with knowledge and unprovable. I do not wish to explain, Russells paradox and Godel's incompleteness theorem in detail here. Yet I will summaries their conclusions, as it is important to understand the fundamentals of living with incompleteness.

AI summary.

Gödel’s incompleteness theorems state that in any consistent mathematical system capable of basic arithmetic, there will always be true statements that cannot be proven within that system; Gödel showed this by constructing a self-referential statement that essentially says “this statement is not provable,” which, if the system is consistent, must be true but unprovable—revealing that no such system can be both complete (able to prove all truths) and consistent at the same time.

Incomplete

Self-referencing problem.

Let's forget about mathematics and proofs for a moment. The problems arise when a system is used to reference itself. Mathematics is one such system. I cannot stop thinking about similarity of human mind with such systems. Human consciousness is essentially a similar system to mathematics, with ability to self-reference itself. It seems mathematics and fundamental philosophy are sharing this common feature of self-referencing and then fall into paradoxes. Let's compare some of the cleaver solutions mathematicians have come up with to overcome such problems of self-referencing and how these are applied to human understanding of self.

Solution 1 - Using hierarchy.

Introduced by Burtrand Russell by himself, the solution means, that there are only hierarchies, and we can only refer to things that are at a lower level. So, the problem of self-referencing does not occur. If you compare this to the version of "God". You can say, agreeing to the fact the self is made by the God, would build a hierarchy that we do not and cannot reference to ourselves as standalone "thing" creating a paradox of existence. This is clever solution in a way. Almost like avoiding the problem, by creating a different framework. But for some obviously this doesn't come as an agreeable solution as there is little evidence to such imaginary hierarchy exists.

Solution 2 - Putting restrictions.

We can put a rule to our language "Self-referencing is prohibited". So, there would be never problems of self-referencing. This is comparative to the life of a person who never ask questions about their existence. They have decided it is fundamentally wrong to ask such questions. But I see danger in this, as it looks like blissful ignorance to the facts, rather than intelligent choice. One should not choose to live with ignorance, when they can chose intelligence.

Acceptance

Solution 3 - Acceptance.

Godel has proved every system is incomplete. A rational thing to do here is accept this as an inherent error in any system. Any system we have built, and going to built is not devoid of error. By accepting this we can lower our expectation of everything will work out eventually well. It may not. There exist limits of life. There exists no solution to these limits. By accepting, we can achieve our freedom from expectations. Isn't it a smart thing to do?