http://www.gaertner-servatius.de/highlights/sinnfrage/4-4.php

4.4. Excursion: Gödel's incompleteness sentences

Am 18. Oktober 2016

 

1. Incompleteness theorem: In any formal system, there is a formula that is not provable.
Put simply, there are statements that are not provable.
2. Incompleteness: The contradiction-free of a formal system can not be proved within the system.
Put simply, a system can not prove itself.
 
Kurt Gödel 1906-1978
www.wikipedia.org
These sentences refer to formal systems. A formal system is based on axioms. Axioms are basic principles that intuitively illuminate us without having to be proved. E.g. This axiom: for every natural number, there is exactly one successor, which is also a natural number. Only 3 can follow. This sounds trivial, but exactly so axioms must be. So trivial that we must assume they are true without having to prove them. A formal system in mathematics can deal with three to five axioms. Such axioms can be linked with defined signs to strictly demonstrable theorems. Intuition should be lacking in these evidence. Then we should demand hard evidence and not proceed intuitively or emotionally. But that is exactly what we have already done in the beginning! We have found the axioms intuitively! Our subjectivity is at the beginning, not objective provable principles. Even in mathematics there is no objectivity after this consideration.
Godel's "incompleteness sentences" are a unique homage to the creativity of the human mind! From a philosophical point of view there is no limit to human knowledge. We are not restricted to axioms, theorems, or logic. Godel was a man between genius and madness. He was often depressed and suffered from persecution. His wife always had to pay, because he was afraid to be poisoned. When she died, he starved, as he thought paradoxically to be poisoned by food.
(For further information, see: R. Goldstein, Kurt Gödel, Piper Verlag)
Consideration of paradoxes:
Paradoxes must not disturb us, they belong to life, they are natural on the spiritual and material level. What we perceive as truth is sometimes contradictory. Everyone is at the same time the most important in the world and a vanishing little dust in the universe. Everyone can love his life and still accept death without fear. The same applies to dichotomies. Paradoxies in natural sciences have been known since quantum physics. Here is the electron wave or particle, both true. Not an absolute, but a "both-as-also" and relativity.
Are Godel's sentences a proof of our impotence? No, impotence of logic! Not powerlessness of man!
I was most convinced by my own deliberation:
Logic is not a natural or at least a basic property of our mind.
Because: dreams are rarely logical! And they come directly and unfiltered out of our unconscious, our deepest source. On the other hand, let's look at a logically constructed machine, the computer, it can only work logically. Our mind does not work like a computer. Computers perform algorithms, but our intellect does not. Each PC works according to fixed rules of a formal system. If we ask the PC to tell us true sentences, it can only provide us with sentences that can be derived from logical rules of the input system. Therefore, there are propositions that escape these rules and are still true. For me this is soothing. In the past, I was afraid that computers will one day surpass our human brain. Now I know this will never work. The computer can only logically build on axioms that we have entered. A creativity that really creates new things can not arise. In addition, a PC will probably never develop feelings (except for Hell from Stanley Kubrick's movie "Odyssey in Space 2001"). Some scientists have recognized this and are trying to connect living nerve cells to computers, so to speak, to build a biological computer with brain function. I hope they never do it!
 
Roger Penrose
www.wikipedia.org
Roger Penrose:
The non-mechanistic nature of the mind, which follows from the first Gödel's theorem of incompleteness, should direct our thinking to non-mechanistic physical laws such as are set up in quantum mechanics. This also takes into account those aspects of the mind that are not computable.
 
 
 
Quintessence:
We humans know more than what can be derived logically.
There are more than sciences can describe.
The living knowledge goes further than logical "proofs".
Computers will never be able to achieve our creativity.
And we also know more than can be derived from science. 10: 3 = 3,333333333333333 ...... But 10 apples distributed to 3 people is no problem for us: each gets 3 and the last apple is divided by 3.
So listen to your inner voice, the deepest feelings in you. Trust in yourself, in your self. You have undefined inner powers in you. Reduced genetic potential through the Inquisition? Everyone has an unconscious that carries within himself the sum of human (and pre-human) evolution (collective unconscious, archetype according to C.G. Jung). Features such as creativity, spontaneity, emotionality, spirituality, intuition ... are no less valuable than "scientific" statements. They are different and limitless. They are much more important to us in the essential questions of life than objective truths and statistical statements. Science can excellently describe the objective world of matter. But this is not the essence of human existence. To us belongs also the subjective consciousness with his feelings, thoughts, hopes ... If we ignore this area and treat him as if he did not play a decisive role for our understanding of the world, we renounce the wealth of our existence, and Our understanding will not be perfect.
 
Pacific coast off 1/2008
This is the 6th sense.
Our culture says we have 5 senses: seeing, hearing, smelling, tasting and feeling. The mental experience, the consciousness of the first person (= I feel) is ignored. If we eat a strawberry, we see a color and shape, smell their scent, taste their flavor, but we also have a sensation that goes beyond it. An emotional total impression, a subjective sensation, perhaps the connection with an experience. It becomes even clearer when one experiences a close-knit man. For example, when I use e.g. Gabi, I can see it with all 5 senses, but it includes much more for me with all the memories of shared experiences, hope in a common future, etc. The 6th sense is therefore not a supernatural ability but our mental sense With subjective perceptions, our consciousness.
Do not restrict your field of view from allegedly knowing (scientists, teachers, gurus, Fachidioten ...). Be open to everything!
Neither from science, nor from philosophy do we really go further to the "ultimate, true foundation" of everything, and therefore not to the meaning of our lives.