The fatal defects in the foundations of present science system inevitably lead to the existence of “self-refutation mechanism”. Our 2500 years unsuccessful “infinite relating paradoxes” fighting history (the most typical example is Zeno's “Achilles--Tortoise Paradox”) has proved clearly that in present science theory system, it is impossible to solve those self-refutation mechanism relating paradox family members produced by the fundamental defect of theory system itself (unsolvable). The underlying origin of self-refutation mechanism should be studied and the theory of “abstract concept and the carriers of abstract concept” should be studied and developed. This is the only way to eradicate thoroughly those paradox families produced by “self-refutation mechanism” in different fields of human science (including philosophy and mathematics).
I am afraid that science, as we know it today, will always lead to paradoxes and unprovable statements. It will always hit its impenetrable logical bottom.
We must remind a whole range of discoveries undermining the very foundations of perfect and consistent science.
- Bertrand Russell's paradoxes
- Kurt Gödels Incompleteness theorem
- Alan Turing's Halting problem (Russel's paradox used in the proof)
Explanation of Russell's paradox:
'The barber is the "one who shaves all those, and those only, who do not shave themselves." The question is, does the barber shave himself?'
Do not fry your brain while trying to solve this problem. To write down a table of logical outcomes is helpful.
It is a paradox that explains well all similar paradoxes. Untill science will be used on logic as we know it. We will always run into such paradoxes.
Those observations undermined attempts of mathematicians in the early 20th century led by David Hilbert to develop a unified and consistent mathematics going from the first principles. Instead we know that there will be patched of different disciplines that will cover just a part of mathematics and never one consistent theory of all mathematics.
This is my personal understanding: We will eventually find better explanations of quantum mechanics and that might lead to new mathematics that will be more suitable to describe the world from bottom-up.
Dear Mr. Jiří Kroc, thank you for your idea!
I fully agree with you that science is our human’s and we can do something to solve the defects disclosed by paradoxes.
It is true that people have been trying very hard to solve those infinite relating paradoxes closely relating to the “self-refutation mechanism”, but the mistaken working idea brought very little effect and the paradox families have been keeping thriving. Because people have not been studying seriously the consanguineous ties among the paradoxes in the syndrome since antiquity, have not been studying and solving seriously the fatal fundamental defects in present classical infinite theory system disclosed jointly by different infinite paradox families with the very same origin; but merely studied, made up and developed very hard all kinds of formal languages, formal operations and formal logics specially for solving surface problems.
Sincerely yours,
Geng
I am afraid that according to our current understanding of quantum mechanics and quantum fields, we are facing something that cannot be resolved. Inevitably we hit the limits where we can literally do nothing.
Maybe there exists some new, to us unknown, description of the Universe that will not generate paradoxes. So far, we have none of such possible theories.
Simply, we must accept the reality and work with what we do have in our hand now and here.
Dear Mr. Jiří Kroc, thank you for your idea!
Zeno's great creation of “Achilles--Tortoise paradox” is a very good start to begin in the work of developing something new-------not just accept the reality and work with what we do have in our hand.
1, something must be unscientific in the traditional infinite theory system basing on “potential infinite--actual infinite”.
2, something must be unscientific in the traditional mathematical analysis with classical limit theory.
Sincerely yours,
Geng