[Document No.] 1-1340
[Original source] Study of Natural Dialectics
[Original topic name] Beijing
[Original publication No.] 199911
[Original publication page number] 29 ~ 34
[Classification Number] B2
[Classification name] Philosophy of Science and Technology
[Copy date number] 200002
[Question] geder's solution to the question of mind-brain-computer
[Title comment] This article is the achievement of the national planning for philosophy and social sciences (Approval No.: 98bzx029) stage.
[Author] Liu Xiaoli
[Author] Liu Xiaoli, female, born in 1954, is a professor at the Department of Philosophy, Inner Mongolia University. Zip code: Hohhot, Inner Mongolia 010021
[Abstract] "Can a computer replace a human brain?" Is it better than a computer "? This is the favorite puzzle of contemporary philosophers of mind. Another group of scientists and philosophers with a mathematical background are hard to resist the use of Godel (Kurt G @ ① del) the Incompleteness Theorem demonstrates the temptation to "win the hearts of the people over computers. However, Godel himself believes that, based solely on the Incompleteness Theorem, it is not enough to launch such a tough argument, and other philosophical assumptions need to be attached. This article explores his unique solution to the question of mind-brain-computer based on the important manuscripts and private conversation records published by coder in recent years. It is expected that this will serve as a reference for the contemporary philosophical debate of mind.
[Zheng Wen]
Today, computer culture has become more important in human culture. "Can computers replace the human brain?", "is human mind better than computers?", and "Can humans become slaves of machines "? This type of problem has become a hot topic of public attention as the super computer "Deep Blue" overcomes the extraordinary actions of World Chess Masters, the question of mind-brain-computer, which has been controversial for more than half a century, has once again become increasingly popular among spiritual philosophers, natural scientists, and AI experts at the end of the 20th century. The supporter of strong artificial intelligence seems to have obtained support evidence from the "Deep Blue" behavior. From their point of view, the mental activity process is the same as the machine execution program, but is engaged in a well-defined computing process called an algorithm. The main difference between a human brain and a simple computer is that human brain activities are more complex, or appear in a more advanced structure, but all human mental qualities, thinking, emotion, wisdom, and consciousness are just the "algorithm" Features of brain execution. These ideas were once highly criticized by many scientists. Since 1990s, they have been deeply criticized by some spiritual philosophers who oppose the same mind-brain theory.
According to one of the most famous representatives in the field of contemporary spiritual philosophy (J. r. searle) strictly differentiate, the weak AI viewpoint that the main value of computer lies in providing favorable tools for the research of the mind (MIND), for example, it allows us to normalize, program, and verify various hypotheses in a more rigorous and accurate manner. Strong artificial intelligence not only regards computers as research tools, but also thinks that appropriate procedural computers are in their own state of mind, computers that believe to be given the right program can indeed understand things and have other cognitive states. In this way, "computer programs can not only help us verify our psychological interpretations, but, on the contrary, programs themselves are explanations ." In 1997, Syl published his new book "The Mystery of consciousness", a brain-computer question, and launched a new round of philosophical offensive against the strong AI viewpoint.
By telling the story of the famous "hamburger" and using his so-called "Chinese house" concept, Sel refuted the viewpoint held by strong AI experts: In a precise sense, computers are capable of understanding stories and answering related questions. In his opinion, computer comprehension is no different from that of cars and calculators. Compared with human mind, computer comprehension is not only incomplete, but also completely blank. Of course, for Sel, it is important not to argue that "computer cannot think", but to answer "is correct input/output and correct computing enough to ensure the existence of thinking ?" "If we say a machine is a physical system with a certain function, or from a computing point of view, the brain is a computer." However, this is not the essence of our mind. Sel believes that computer programs are defined purely according to syntax rules, and the syntax itself is not sufficient to guarantee the intention and semantic presentation of the mind, the running of a program only has the ability to generate a formal next step during machine running, and does not guarantee the appearance of the state of mind. Only those who use a computer and give it a certain amount of input can explain the output at the same time have intention. Intention is the function of the human heart, and the essence of the heart cannot be programmed. That is to say, the essence of the heart is not algorithm. Therefore, we should first clarify the concept of "Algorithm" to discuss the question of "Mind-brain-computer.
1. Evolution of algorithm concepts
Algorithms were just an intuitive concept before the 1930s S. People intuitively understand algorithms that can follow clearly defined calculation rules within a limited period of time, the mechanical step for obtaining the exact calculation result within a finite step. The most familiar example is Euclidean's classical algorithm for finding the maximum common divisor of two numbers. German mathematician Hilbert (D. hilbert) raised the following judgment question at the Bologna International mathematician Conference: whether there is a general solution in principle to all (which belongs to a properly defined class) mechanical steps for mathematical problems? The "mechanical steps" here are actually the intuitive concept of "algorithms. 1936 English mathematician, extraordinary cryptographic expert Turing (. m. turing) introduces the concept of "Turing Machine". For the first time, it gives a strict mathematical expression of the concept of an algorithm, that is, "algorithm Computability function", that is, "Turing Machine Computability function ". Since then, people have discovered that, "λ-computeable functions", "General recursive functions", "regular algorithms", and "post-calculus" are mathematical definitions of "algorithms" that are equivalent to "Turing Machine computeable functions ".. With the accurate definition of algorithms, people quickly prove that there are no general algorithms to solve all mathematical problems, it also proves that there are no algorithms to solve some important judgment problems (for example, determination of the predicate calculus, determination of the downtime problem, determination of the equivalence of words on the semi-group, and determination of the comprehensibility of the lost graph equation ). ). Turing proves that there is no general algorithm that determines whether all mathematical problems can be solved by proving that there is no algorithm that determines the downtime of the Turing Machine. Qiu Qi (. the same conclusion is proved using this completely different method. More importantly, it is precisely the mathematical expression of the concept of algorithms that enables the generation of electronic computers in the modern sense. Today, with the development of computer applications and theories, it has become an important specialized field to study static and dynamic complexity computing complexity theories of algorithms.
In 1936, Turing published an important article on the topic of computing-computing in the London Institute of Mathematics Bulletin, which states, "We will assume that the number of States to be counted is poor. This is because, if we acknowledge that there are infinite states, some of them will be obfuscated because of any closeness ." This section of Turing was once seen as an argument that "human spiritual activities cannot surpass mechanical procedures. In 1950, Turing published an article entitled "computer and mind" in the mind magazine, opening with the following: "I am going to consider a question: Can I think about machines? ", The concept of the famous "Turing test" is proposed. The article implies the argument that "people are equivalent to a computer". This argument is undoubtedly a strong support for the emerging AI solution in the late 1940s S, it naturally caused a big debate. In this debate, some philosophers and logics in the opposition camp are more keen to oppose Turing's argument based on the Golder theorem.
It is hard for people to resist a strong temptation: proving that "the hearts of the people are better than computers" from the Incompleteness Theorem of Godel in 1931. Because in any form system containing elementary number theory, there must be a non-deterministic proposition, that is, it and its negation cannot be proved in the system. In other words, any theorem proves that machines and programs will omit true mathematical propositions. mathematical truth cannot be completely classified as an algorithm.
In 1961, the American philosopher John Lucas wrote an article titled "heart, machine, and Godel" with extremely fierce words in philosophy. he tried to prove the conclusion that "people are more than computers" by using the godele theorem: "In my opinion, the godele theorem proves that the mechanical theory is wrong. That is to say, the heart cannot be interpreted as a machine." Because, "no matter how complicated a machine is constructed, as long as it is a machine, it corresponds to a formal system, then we can find an unverifiable formula in the system, which is affected by the Godel program. The machine cannot deduce this formula as a theorem, but it can be seen as true. Therefore, this machine is not an appropriate model. We always want to create a mechanical model of the heart, that is, the model is essentially a "dead" model, while the heart is a "active" model, it can always do better than any form of rigid system ". Then another American philosopher, waitley (C. h. whitely) in the next 37-volume philosophical magazine, the author published a brief but powerful redissed article "heart, machine, Godel-responding to Rokas", as a result, many people have been involved in and have been arguing for decades. In 1979, the best-selling book "Godel, Esher, Bach-an eternal Golden Belt" won the Prce literature Award. It is a unique method for the profound painting of Esher, the popular music of Bach and the gordeli theorem. connect, he wrote a heart-brain-computer "metaphor fugequ" in a dramatic way, and elaborated on how to use the godeli theorem to determine whether the intelligent solution of witnesses works from multiple perspectives. In 1989, the British mathematician and physicist Roger Penrose) the emperor's new brain, computer, mental intelligence, and physical law, which is popular all over the world, is still using a lot of pen and ink to directly demonstrate that "the hearts of the people are more than the computers" from the gordeli theorem ", it is called "a surprising strong application to the godeli theorem." Therefore, in the 13th journal behavior and brain sciences, the opportunity to review the book has aroused a debate that many people are involved in, (including the summary of the content of the book written by the author, the book reviews by others, and the answers to the book reviews by the author, there are as many as 62 pages, pp.643-705 .). Peng Ross' strong argument is roughly as follows: we can draw from the goldele theorem that the process of determining mathematical truth is beyond any algorithm, because consciousness is the key to understanding mathematical truth, this kind of consciousness is the true reasoning of some mathematical propositions that cannot be proved in the mathematical form system by intuition insight, and consciousness cannot be formally formed, it must be non-algorithm. Therefore, computers cannot surpass the human mind. Computers are just a pair of "emperor's new brain" favored by strong AI experts. The "algorithm" here has evolved into everything that computers can simulate, including "Parallel Computing", "Neural Networks", "inspiration", "Learning", and the role of the environment.
2 does the godeli theorem imply the conclusion that "the hearts of the people are better than computers?
We have learned from some of the most important manuscripts recently discovered by Corder and the conversation records with Wang Hao in 1970s, first of all, godel himself does not oppose the use of his theorem as part of the evidence to prove the conclusion that "the hearts of the people exceed the computer", because in his opinion, the Incompleteness Theorem does not give the limit of human reason, it only reveals the inherent limitations of formalism in mathematics. However, the use of his Incompleteness Theorem alone is not enough to make such a tough argument, and new assumptions need to be added. But Godel also makes it clear that "the function of the brain is just like an automatic computer", and the essence of the mind is not so.
In fact, after a strict distinction between the functions of the mind, the brain, and the computer, the question of "is the heart better than the computer" can be converted into two subquestions: ① whether the brain and the heart function are equivalent to a computer, while a computer is equivalent to a formal system. ② Whether all mental activities are computable and there is a computer capable of completely capturing all human mental activities. The first question is whether the identical theory of body and mind is correct. The second question is whether mental computabilism is true. The same mind and brain theory is a popular mainstream mind and philosophy theory in the West since the end of 1950s. Its core is to equate animal and human psychological activities with brain movements, among them, there is the same theory of the subject and brain (which is divided into Entity equivalence, language equivalence and functional equivalence theory) and the same theory of the subject and the same theory of the non-physicist. At the same time, mental Computability advocates the following topics. The brain and the heart function are basically like a computer, and the brain fully explains mental phenomena. All mental phenomena are computable, when it comes to the godele theorem, our attention will be more focused on the more specific question of "Can machines fully capture people's mathematical abilities. In some of Gödel's manuscripts and conversations with Wang Hao in 1970s, we can see that Gödel severely refuted the same theory of mind and Computability, in his opinion, the same theory of mind and Computability are completely "prejudice of the times ".
We know that the godele theorem implies that some machines that prove any theorem can intuitively see its truth, but this machine cannot prove that it is a mathematical proposition of the theorem. Therefore, this seems to indicate that people are more competent than any computer in proving the theorem. However, when we try to justify this strictly, we find that it contains an imperceptible vulnerability.
In his speech in 1951, "several basic theorems in the foundation of mathematics are extremely philosophical and imitations" (the manuscript of the speech was published in 1995), Godel pointed out that, "one possible conclusion I can draw from my theorem is that the decision judgment contains two propositions: Or (a) mathematics cannot be complete in the following sense, that is to say, its self-evident principle cannot be included in the rules of poverty, so the hearts of the people exceed the number of poor machines; or (B) there is an absolutely uncertain picture loss problem. ...... Both options are opposed to the philosophy of mechanical materialism. A is opposite to the theory of the mind. (B) Does it prove that the object of mathematics is just our idea of creation ."
In a 1972 Comment entitled "A philosophical mistake in Turing's work" (1972a), Godel First pointed out that, turing's argument that "the mental process cannot go further than the mechanical process" is inadequate because it relies on the assumption that the mind can only present the poorer and more distinct states, obviously, Turing ignores the fact that the mind is not static in its application, but constantly developing. Although the number of possible states in the heart is poor at each stage of its development, there is no reason to say that this number does not converge to infinity during the development process. Godel once said in a discussion with Wang Hao that the Turing argument will survive with two more assumptions: ① There is no heart separated from matter. ② The function of the brain is basically like a digital computer. Godel thinks. ② Is general, but whatever it is, ① Is going to be proved by science, and it is a prejudice of our times. Then Godel analyzed the decision based on his position called "rational optimism": if we are like Hilbert, we firmly believe that "the question raised by the human reason will surely be answered by the human reason", then we can deny the second choice, because, recognizing that there is an absolutely undefinable number theory that is rooted in our belief. In this way, the first choice should be true, that is, the hearts of the people are better than computers. It can be seen that, in godder's view, the philosophical assumption that "the question raised by the human reason will surely be answered by the human reason" can be used to bring out the conclusion that "the human heart is better than the computer. Of course, Godel also realized that this kind of evidence of the same-minded and Computability is not necessarily convincing, because it is, after all, a inferential.
It is worth noting that, in a form of the godele theorem, any suitable theorem proves the machine, or the theorem proof program. If it is consistent, then it cannot prove that the proposition that expresses its own consistency is a theorem. In his speech, coder came to the following conclusion along this line of thinking:
(1) "the hearts of the people are incapable of formulating all their mathematical intuition formula (formulating) (or mechanized mechanical izing ). That is to say, if some of its mathematical intuition is formulated, it will generate new intuitive knowledge, for example, about the consistency of the formal system. This fact can be called the mathematical incompletability ). On the other hand, based on the results we have proved so far, it is still not ruled out that there may be (or even can be discovered through empirical methods) a theorem to prove the machine, in fact, it is indeed equivalent to the [People's] mathematical intuition, but we cannot prove that it can do this, or even prove that it is just to come up with correcte) ".
(2) "or the hearts of the people beat all machines (more strictly speaking, it can determine more number theory problems than any machine ), or there is a [Absolute] undefinable number theory problem (it is not ruled out that both are true )."
Godel admitted that it was not ruled out that there was a theorem proving that machine m was indeed equivalent to mathematical intuition, but it was important that, assuming that there was such a machine, the incomplete theorem immediately concluded the following two conclusions: ① it is impossible to prove that m can indeed do this; ② M cannot even prove that it just produces a correct theorem. If we can prove that M is just generating the correct theorem, our intuition can prove that M is consistent, that is, the conclusion that M is consistent is intuitively correct, m should be able to prove that M itself is consistent, which is obviously in conflict with the godeli theorem. So ② is true. Furthermore, assuming that we can prove that M is indeed a theorem proving machine equivalent to human mathematical intuition, that is, it fully captures the mathematical ability of the people (there is reason to assume that, the "ability" here refers to the correct mathematical ability rather than the wrong mathematical ability; the "proof" refers to the proof of Exponent), then, this means that we have a mathematical proof, it can prove that m just produces the correct theorem, which is obviously in conflict with ②, And we have proved that ② is true by using the godel' theorem. Therefore, the core of the problem is not whether there is a machine that can capture human intuition. It is precisely because, even if such a machine exists, it cannot prove that it has done this step. As del said:
"Without such a possibility, there are all the rules (or a computer) of self-evident justice that can generate it ). However, if such a rule exists, it will never be known exactly according to our human understanding; that is, we will never be able to know exactly the theorem it produces in mathematics; or, in other words, we can only perceive (percive) the truth of a proposition with a finite number. However, all of them are truly at most empirical. Such assertion is based on the investigation of the special case of the full large number, or other inductive reasoning is used ."
Therefore, "There are no poor rules that can fully capture our mathematical intuition-because, if so, we can also know its consistency, which is beyond the rules themselves ."
Geder also distinguishes between subjective mathematics and objective mathematics: subjective mathematics is a system of all deterministic mathematical propositions; objective mathematics is the system of all true mathematical propositions. With this distinction, Godel pointed out that "or subjective mathematics exceeds the computing power of all computers, objective mathematics exceeds all subjective mathematics, or both are true ." Then Godel gave several arguments:
"If the first option is true, it implies that the operations of the human mind cannot be attributed to the operations of the brain. All the operations of the brain seem to be composed of many components, that is, the neurons and their connections constitute a poor machine."
"The second choice does not seem to prove that mathematics is just our own idea of creation, because the creator must know all the characteristics of his creation, because they cannot have other characteristics except those granted by creators, it seems that mathematical objects and mathematical facts (at least some of them) exist objectively, it is independent of our spiritual activities and willingness. That is to say, some form of 'Plato 'or 'realism' about mathematical objects is true."
If we accept this kind of reasoning from Godel, we have a variant of the above argument: that the computation is false, or that the Plato in mathematics is true; it is not ruled out that both conclusions are true. In fact, one of the purposes of his speech is to demonstrate the rationality of the Plato standpoint in mathematics. In his speech with Wang Hao in his later years, Godel reiterated his point of view:
"Incomplete results do not exclude the possibility of proving a computer by theorem that is actually equivalent to mathematical intuition. However, the theorem implies that, in this case, we cannot know exactly the details of this computer, or we cannot know exactly whether it will work correctly (correctly ."
"My Incompleteness Theorem makes it possible that the mind is not a machine, or that machine cannot understand its own conclusions ."
"If we combine our results with those held by Hilbert and use the rational stance that I cannot refute with my results (the rational question can be answered, then [we can launch] the mind is not a clear conclusion of the machine. This is because if the mind is a machine, a number theory problem that the human mind cannot determine will be in conflict with this irrational stance ."
Godel once explained to Wang Hao:
"My mind refers to the mind of an individual with infinite life. This is different from the mental aggregation of species. Imagine a person who is committed to solving the entire problem set: This is related to the issue of authenticity, so people will constantly introduce new truths ."
3. The solution of the problem also depends on the elimination of the connotation paradox and scientific progress.
In addition to the necessary philosophical assumptions, the difficulty in answering the question of "is people better than computers" is that it is related to the connotation paradox.
In August 1972, at the conference commemorating von noriman, Godel asked: "Is there anything unreasonable in the concept of 'machine that knows its own process ?"
Obviously, whether humans can surpass themselves-or whether computer programs can jump out of themselves-is a very interesting topic. Number theory systems can talk about themselves, but cannot surpass themselves. A computer can modify its own program, but cannot violate its own commands-at best, it can only change some of its own parts by obeying its own commands. This is similar to the humorous paradox of "Can God create a stone that cannot be lifted by himself.
The godeli theorem concludes that a consistent form system or theorem proves that a machine cannot prove its own consistency. In order to prove testability, a clear idea is to find an argument that shows that the mind can prove its own consistency. Obviously, this argument has a self-directed nature. In his conversation with Wang Hao, Godel gave several arguments along this line of thinking:
"Because general concepts such as 'conceptual ', 'proposition', and 'evidentiary 'are involved in the existence of unsolvable connotation paradox in their most general sense, self-directed arguments that do not use these concepts can be regarded as deterministic at the current stage of logical development. However, when these paradox is successfully resolved, such arguments may become deterministic." "If a person can eliminate the paradox of meaning, he will be able to get a clear proof that his mind is not a machine. The general concept of 'proof 'is similar to the situation of the general concept of' Concept '(concept, this is because we cannot eliminate the contradictions surrounding these general concepts. Otherwise, once we understand the general concept of proof, we also rely on our mind to have a proof of its own consistency. In this case, we can truly derive contradictions from the general concept of proof, including proof of Self-application. Our understanding of the proof concept is incomplete ,...... Something is not in line with our logic, which is extremely obvious ."
A major idea of Godel is that if we can gradually better understand the general concept of proof, we can see it in a direct way (see) the entire scope of our ability to implement mathematical proofs is actually consistent. In this case, unlike computers, mathematical intuition can tell and prove its own consistency. If we can regard absolute proof as a concept, we can present and prove things about it in a systematic way. In particular, we will be able to apply our exceptional mathematical intuition to prove our own consistency. However, this relies on our ability to eliminate the connotation paradox and on our understanding of abstract concepts such as proof by seeking new and higher-level new truths. Godel wrote his "Comments on mathematics at the 1946 anniversary of Princeton" and the draft of his speech in 1965 (published in 200) on 1961 (published in 1995) this is an in-depth discussion of modern advances in mathematical basics from a philosophical perspective.
After thinking on various philosophical aspects, Godel acknowledges that the final solution to the question of mind-thing still depends on the further development of the entire science including brain physiology. "Many so-called philosophical problems are scientific problems, but they are often not scientifically handled. For example, the question of whether the heart is separated from the matter remains a constant debate in the philosophers before the scientists prepare to discuss it. Therefore, one of the functions of philosophy is to guide scientific research ." Godel asserted that "the brain is a computer connected to the Spirit ." "One day, the proposition 'no separated from theme 'will be evidenced by the fact that science develops ." In old age, Godel even guessed that to grasp the abstract impression (relative to the feeling), it was necessary to evolve enough physical organs, which must be closely linked with the Central Nervous System in charge of language. Moreover, as a prejudice of the times, the mechanical principles in biology will be rejected. According to Godel, "one way to prove this is to [establish] A mathematical theorem. The general idea is, starting from the random distribution of basic particles and fields, the low probability of forming a person within the span of the geological age is similar to the probability that the atmosphere is divided into various [chemical] components due to opportunities. "...... Although Godel made a lot of scientific bold guesses about the heart-brain-computer, the mechanical in biology, and the more general heart-thing, he admitted, these topics are as original as those in the De mokelit era.
Apart from Plato in mathematics, the most discussed with Wang Hao in his later years is the question of the heart-brain-computer, that is, the relationship between the heart and the thing. Godel is so keen on this because his mind is superior to his brain. On the one hand, he can provide explanations for his Plato's Mathematical View, and on the other hand, he is opposed to mechanical materialism, it is an important basis for adhering to the general philosophy of objective idealism of racism. Therefore, the unique solution to the understanding of Godel's mind-brain-computer problem should be linked with the understanding of his mathematical philosophy and general world view to gain a holistic grasp.
[Responsible editor] Ma huizhen
[References]
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