How to solve "impossible" problems?

In mathematics and philosophy there are some unsolvable problems like Russell's paradox or the liar's paradox that are usually said to be undecidable... There are also other "impossibilities" such as finding positive integers to divide a prime number other than the number itself and 1.

However, could we use some kind of alternative logic to classical logic in order to solve these problems? Or perhaps if our brains evolved or developed more, could we find a solution to these situations?

• Russell's paradox is resolved by the axiom schema of specification. It dates back to Zermelo in the early 20th century. en.wikipedia.org/wiki/Axiom_schema_of_specification Nov 27, 2022 at 1:17
• If it's truly impossible to solve, then there will never ever be a solution. The only exception, is solving a mathematical impossibility without mathematics. If you accept, "I am certain I am aware, therefore I have awareness", as proof that you have awareness, it could also be true that your awareness is a mathematical impossibility. If it's simply not mathematical, therefore, no contradiction, despite seemingly contradictory statements. Nov 27, 2022 at 13:28
• Ill-formed question: you are wrongly assuming that something TRUE can be FALSE in classical logic (breaks the identity law) and using such assumption to address a secondary issue (making possible the actual problem solution impossibility). Wrong. You have it all messed up. You need to find such logic first, and only then, use it to address the secondary problem. It is impossible even to provide an example, because it is impossible to know which logic that accepts breaking the first law you are going to apply. Dec 4, 2022 at 3:00

I find keeping an open mind can result in solutions that are easy to understand and make sense, but sadly to me only. The problem is, this approach can only produce solutions that nobody is willing to consider.

Problem

Awareness and purpose make no mathematical sense, as our laws of physics seem to prevent them, and the Chinese Room argument is a strong argument that cannot be overcome.

Solution making it appear impossible

Expected assumption, possibly something similar to this, "consciousness is explained mathematically, but nobody has any mathematical explanation because it is so extremely complicated, that nobody understand.".

Simple solution nobody will consider

Awareness and purpose make no mathematical sense because they are not mathematical, they are the opposite of mathematical. The opposite in every way. Now we have physical laws that literally define consciousness and purpose.

I could write pages of logical arguments backing up my claim. No matter what though, I've never received a single comment logically supporting or contradicting my claims. I have had an argument that suggests I am correct being used against me before though, which doesn't even make sense. Refining a non-conventional theory, means you can be the only one contradicting it with relevant logical arguments.

Some problems don't exist.

What Is A Problem?

A problem in philosophy is shortcoming in understanding the world. The how of what happened.

If a situation never happen then there is no how in its happening because the happening itself dont exist.

Russell's paradox is a non-problem because it never happen. A barber is capable of cutting his own hairs.

You have to use one definition of sets, and stick with it. If you loose meaning of your terms half way through an analysis you have nothing left to analyze.

Container of objects is not similar to the objects. Different terms are needed.

One Who Is Not Sick Cannot Be Healed

Looking for a natural number between 1 and 2? That number do not exist. Trying harder to look for it don't make it exist.

A person who always lie cannot say "I always lie". This kind of thing, that a thing's existence deny its existence, never happen in world.

I just listened to a podcast on calculus (host Marcus du Sautoy, amazing bloke).

The problem was finding instantaneous velocity and existing math read the problem as 0 ÷ 0 i.e. it was, for all intents and purposes, unsolvable.

Leibniz and Newton came along, looked at the 0 ÷ 0 and in no time invented calculus - the mathematics of infinitesimals.

This is just one example of how great minds solve the unsolvable.