Godel's incompleteness theorem and agnosticism

This article is machine-translated by Google.

From "on Feuerbach" about

"On Feuerbach" Only eleven short, it tells the Marxist philosophy was new but the core concept: Practice. It noted: the material determines consciousness, awareness of active substances in the reaction, the practice is an important process of transformation of the human world. Text around "practice" to expand, especially in the second, a direct negation of the theory of the human mind problem, I re-starting from a serious thought to my worldview. "On Feuerbach" article pointed out: "people thinking whether objective truth, this is not a theoretical question, but a practical question should prove the truth of their own thinking in practice. resistance, and the reality of their own thinking and strength. "

"On Feuerbach" in the human mind took a evasive attitude. I believe it is important to practice, but practice is limited after all, can not explain the problem can not practice. "On Feuerbach" to explain the truth to all the practice, can not help but planted Practice "there is reasonable" seeds. Many times this assertion lure people to reverse causality, to explain the reality of the result to the result in reasonable. This is a process of feedback, making what already exists more consolidated position, while stifling thing yet prevail, and thus prevent people from further practice. Practice really explain the truth of the human mind it? I express my deep suspicion.

My worldview Changes

Thinking about the human mind, directly determines my worldview. From small to large, in my mind produces many different philosophical worldview. I had a child spontaneously "presence that is considered" subjective Weixin worldview. With the open field of vision, but I received a materialism, a conflict began to feel, but slowly accepted into the other extreme. I was to agree on a tough decision but based on mechanical materialism, largely influenced by Newtonian physics, convinced that "Give me an initial value, I calculated the entire universe." Creed. As Laplace said: "We can now state of the universe considered as a result of their past and future results if you know an intelligent force some point all natural motion of all objects and natural components of the position, if he did. be able to analyze these data, it is the largest object in the universe to the smallest particle motion will be included in a simple formula. that nothing would be wise for these vague terms, as in the past and the future will appear in front of him like . "

In support of this view of the world, I gradually began to believe in fatalism, passive think free will does not exist, it is the fate of people who have manipulated puppets. So I started pessimistic, fall into hedonism, that since all life is predestined, totally immutable, life can only be accomplished by the instant gratification of its value.

"Godel's incompleteness theorem" and agnosticism

After slowly I was exposed to modern physics, learning the theory of relativity, quantum mechanics, Schrodinger equation, parallel universe theory, recognized the real world there are many irreversible process, the original creed into a Laplace "Laplace's Demon "simple determinism can not explain many phenomena, so I started thinking about the nature of the world again. Later, I studied mathematics in the process, I learned that in 1931, Hilbert proposed a formal axiom system all propositions can be proved or disprove the thesis, thereby trying to prove that the substance is a purely mathematical but formal system of axioms plus derivation rules by the expression of meaningless symbols constituted, and mathematical proof in this system is just playing word games. If this ground-breaking thesis is established, then thousands of years human mathematical research are all a piece of paper, in the future as long as we find a complete axiomatic system, all the proof can be omitted. Unfortunately, Godel's proof mercilessly shattered this dream. Godel proved that "any form compatible system can not be used to prove its own compliance" of "Godel incompleteness theorems." Godel's incompleteness theorem states that any system strong enough to prove the basic axioms of arithmetic, it is not complete, that is, we can never find a universal axiom system can tell the truth, but can not prove any falsehood, even if an axiomatic system can be used to prove the compatibility of its own, then it is incompatible. This theorem and axiomatic first-order logic coincides perfectly explains, "I said this sentence is false" is self-referential paradox.

Godel's incompleteness theorem give me the impact can be described as unprecedented, because the human mind can be abstracted as an axiomatic system, everything from philosophy to metaphysics, formal reasoning is the result of the axiom system. Frightening is that Gödel's incompleteness theorem states that this system of axioms can not prove its own completeness, some theorem of the existence of this system, it will not be out to prove this axiom system. Even assuming that the human mind is complete, or that is the truth, then you can deduce its internal irresolvable conflicts exist, so he is not the truth. If I have to prove the completeness of the human mind can not, have to rely on other than the "human mind" epitaxial bigger system, use it to prove the completeness of human thinking system. But this thing does not make sense, because even if it exists, is beyond human understanding, unless human evolution to "super-human", but by that time, "super-human" thinking completeness is still not self-certified. So, there must be something humans can never understand, even if it does not exist meaning. This is simply to give me a blow, because it hinders the human understanding of the world - some substances, the law is there and correct, but it is never human unknowable. Now, I'm beginning to believe that agnosticism, though it has a negative side, but it also encourages people to be seen in person to continue to explore the scope, because in spite of the presence of unknown people thinking things, but people can see what is infinite.

To my disappointment, "on Feuerbach," is based on the principle of it is intuitive and superficial. But it is no wonder, after all, any thought is the product of the times, Marxism can not be avoided at the time confined to the human perception of the world. However activism "on Feuerbach" advocated in today's opinion is extremely important. We must not remain in the brilliant achievements of their predecessors, especially not put anything as truth, because the truth can not be certified. By thinking of metaphysics, beyond our perception of the world is limited, as the axiom system is not self-certified its completeness, just given the significance of mathematical proofs. Is what we can see things is limited, just guide us only through practice in order to more fully understand the world.


The above system, "the basic principles of Marxism," My job sophomore course '' on Feuerbach "book report", posted the full text of the unused falsification.

In fact, on "Godel's incompleteness theorem" I understand in some places is not enough deep, and many of the conclusions I am not quite sure, dare stickers to let everyone criticism. "Godel's incompleteness theorem" There are two, the first: any formalized mathematical theory of a compatible, as long as it is strong enough to Peano arithmetic axioms of implication, which can be configured in the system can neither prove We can not permit proposition.

The second is the first corollary: Any form compatible system can not be used to prove the compatibility of its own.

It's about proof and detailed explanation, I strongly recommend an article, " Cantor, Godel, Turing - the eternal golden diagonal ." This theorem has a lot of misconceptions, such as: not all systems are incomplete, provided that Godel's incompleteness theorem is that it requires the definition of natural numbers and arithmetic system, like the first-order predicate axiom system, Euclidean geometry axiom systems are complete. Also non-formal system is not within the constraints of this theorem, such as experience, found.

In addition to the Godel incompleteness theorem, there is a similar logic theorem: "For an infinite order in the form of language, if it can prove that the meta-language proposition is no contradiction, it is impossible to construct a meta language in conventions are adequate in the sense of the definition of truth. "this is a truth of definable disproved, that" absolute truth "are not defined. Mathematical theorem called the greatest impact on a theorem of philosophy, it appears that the modern philosophy not to pursue "absolute truth", but rather to explore the truth of internal consistency. So Marxism bibles is ridiculous, many of the ideas have to say it is outdated.

As for the human mind is not axiomatic system, this is still controversial, I think that the operating mechanism of the human brain and the computer are actually the same, that is to say the human brain is a Turing-equivalent. The human mind can be abstracted into nerve impulses, inhibiting chemical signals, corresponding to the integrated digital electronic high and low level signals, the human brain is a computer, the Turing machine qualifying Godel incompleteness theorem (because Turing machine can be completely defined nature number and arithmetic axioms), so also in line with the human mind. As to why your computer can not simulate the human brain, a kind of view is that "the role of quantum mechanics, chaos and uncertainty of complex nonlinear systems common cause," but I think that is actually a computer chip precision and efficiency problems in the far the premise is less than the human brain, how can simulate the human brain? On this basis, from "Godel incompleteness theorem" is derived agnosticism very intuitive interpretation, "It's not the truth, just because in this mountain," had to be a profound truth.

Here I am reminded wrote science fiction "three-body" in the three-body who has created a "Tomoko" human sciences sealed the story appeared, "Godel's incompleteness theorems" strongly supports agnosticism, this will not block the possibility of human knowledge of the world out? I do not think so, at least for now will not, because the vast majority of the first field of human development is far from apparent arrival of the bottleneck caused by the second non-axiomatic system is not restricted, for example, experiments, we can rely on non-formal means to "blind cat encountered dead rat."

Related posts