Copyright © James R Meyer 2012 - 2017 www.jamesrmeyer.com
“What I call the theological world-view is the idea that the world and everything in it has meaning and reason, and in particular a good and indubitable meaning. It follows immediately that our worldly existence, since it has in itself at most a very dubious meaning, can only be means to the end of another existence. The idea that everything in the world has a meaning [reason] is an exact analogue of the principle that everything has a cause, on which rests all of science.” (Footnote: From Reflections on Kurt Gödel by Hao Wang, MIT Press, 1987.)
“I like Islam: it is a consistent [or consequential] idea of religion and open-minded.” (Footnote: Section 4.4.3 from A Logical Journey by Hao Wang, MIT Press, 1996.)
“If the world is rationally constructed and has meaning, then there must be such a thing [as an afterlife]. For what sense would there be in creating a being (man), which has such a wide realm of possibilities for its own development and for relationships to others, and then not allowing it to realize even a thousandth of those?” (Footnote: Letter of 23.07.1961 from A Logical Journey by Hao Wang, MIT Press, 1996.)
“I believe that mechanism in biology is a prejudice of our time which will be disproved. In this case, one disproof, in my opinion, will consist in a mathematical theorem to the effect that the formation within geological times of a human body by the laws of physics (or any other laws of a similar nature), starting from a random distribution of the elementary particles and the field, is as unlikely as the separation by chance of the atmosphere into its components.” (Footnote: Section 6.2.11 from A Logical Journey by Hao Wang, MIT Press, 1996.)
Note: Here Gödel is just one of the first in a long line of creationists and intelligent design fanatics who think that it is possible to produce a meaningful probability value that suggests a designer, despite our having no means of calculating such a probability. For example, if there are many universes, then we have no way of knowing how many universes are like ours.
“I don’t think the brain came in the Darwinian manner. In fact, it is disprovable. Simple mechanism can’t yield the brain. I think the basic elements of the universe are simple. Life force is a primitive element of the universe and it obeys certain laws of action. These laws are not simple, and they are not mechanical.” (Footnote: Section 6.2.12 from A Logical Journey by Hao Wang, MIT Press, 1996.)
“Darwinism does not envisage holistic laws but proceeds in terms of simple machines with few particles. The complexity of living bodies has to be present either in the material or in the laws. The materials which form the organs, if they are governed by mechanical laws, have to be of the same order of complexity as the living body.” (Footnote: Section 6.2.13 from A Logical Journey by Hao Wang, MIT Press, 1996.)
Mind is separate from matter: it is a separate object. In the case of matter, for something to be whole, it has to have an additional object. (Footnote: Section 6.2.9 from A Logical Journey by Hao Wang, MIT Press, 1996.)
“In materialism all elements behave the same. It is mysterious to think of them as spread out and automatically united. For something to be a whole, it has to have an additional object, say, a soul or a mind. “Matter” refers to one way of perceiving things, and elementary particles are a lower form of mind. Mind is separate from matter.” (Footnote: Section 9.4.12 from A Logical Journey by Hao Wang, MIT Press, 1996.)
“Even if the finite brain cannot store an infinite amount of information, the spirit may be able to. The brain is a computing machine connected with a spirit. If the brain is taken to be physical and as [to be] a digital computer, from quantum mechanics [it follows that] there are then only a finite number of states. Only by connecting it [the brain] to a spirit might it work in some other way.” (Footnote: Section 6.2.14 from A Logical Journey by Hao Wang, MIT Press, 1996.)
“The mere possibility that there may not be enough nerve cells to perform the function of the mind introduces an empirical component into the problem of mind and matter. For example, according to some psychologists, the mind is capable of recalling all details it ever experienced. It seems plausible that there are not enough nerve cells to accomplish this if the empirical storage mechanism would, as seems likely, be far from using the full storage capacity. Of course other possibilities of an empirical disproof are conceivable, while the whole question is usually disregarded in philosophical discussions about mind and matter.” (Footnote: Section 6.2.5 from A Logical Journey by Hao Wang, MIT Press, 1996.)
Note: It has been proved that we cannot recall previous experiences in detail.
“It is a logical possibility that the existence of mind [separate from matter] is an empirically decidable question. This possibility is not a conjecture. They don’t even realize that there is an empirical question behind it. They begin with an assumption that no [separate] mind exists. It is a reasonable assumption that in some sense one can recall every experience in one’s life in every detail: if this assumption is true, the existence of mind may already be provable from it.” (Footnote: Section 6.2.3 from A Logical Journey by Hao Wang, MIT Press, 1996.)
Note: It has been proved that we cannot recall previous experiences in detail.
“Logic deals with more general concepts; monadology, which contains general laws of biology, is more specific. The limits of science: Is it possible that all mind activities - infinite, for example, always changing, and so on - are brain activities? There can be a factual answer to this question. Saying no to thinking as a property of a specific nature calls for saying no also to elementary particles. Matter and mind are two different things.” (Footnote: Section 6.2.4 from A Logical Journey by Hao Wang, MIT Press, 1996.)
“It is by no means obvious that a finite mind is capable of only a finite number of distinguishable states. This thesis presupposes: (1) spirit is matter; (2) either physics is finitary or the brain is a computing machine with neurons.” (Footnote: Section 6.3.2 from A Logical Journey by Hao Wang, MIT Press, 1996.)
“The thesis of finitely many states presupposes: (a) no mind separate from matter; (b) the brain functions according to quantum mechanics or like a computer with neurons. A weaker condition is: physics remains of the same kind as today, that is, of limited precision. The limited precision may be magnified, but it will not be different in kind.” (Footnote: Section 6.3.3 from A Logical Journey by Hao Wang, MIT Press, 1996.)
“Attempted proofs for the equivalence of minds and machines are fallacious. One example is Turing’s alleged proof that every mental procedure for producing an infinite series of integers is equivalent to a mechanical procedure.” (Footnote: Section 6.3.5 from A Logical Journey by Hao Wang, MIT Press, 1996.)
“Turing, in his 1937, p. 250 [Davis 1965:136] gives an argument which is supposed to show that mental procedures cannot carry farther than mechanical procedures. However, this argument is inconclusive, because it depends on the supposition that a finite mind is capable of only a finite number of distinguishable states.” (Footnote: Section 6.3.6 from A Logical Journey by Hao Wang, MIT Press, 1996.)
“Although at each stage of the mind’s development the number of its possible states is finite, there is no reason why this number should not converge to infinity in the course of its development.” (Footnote: Section 6.3.14 from A Logical Journey by Hao Wang, MIT Press, 1996.)
This is hilarious: Gödel ‘the great logician’ here argues that a finite number of changes to a finite number of states over a finite time ‘converges to infinity’.
“Analysis, clarity and precision all are of great value, especially in philosophy. Just because a misapplied clarity is current or the wrong sort of precision is stressed, that is no reason to give up clarity of precision. Without precision, one cannot do anything in philosophy.” (Footnote: Section 9.3.9 from A Logical Journey by Hao Wang, MIT Press, 1996.)
Note: Hao Wang in the books ‘A Logical Journey’, and ‘Reflections on Kurt Gödel’ frequently stresses Gödel’s professed interest and constant desire for precision and clarity. This is especially interesting in view of the fact that Gödel never actually gave a precise proof of his widely celebrated Incompleteness theorem, see A Proof of Incompleteness?
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There is now a new page on Lebesgue measure theory and how it is contradictory.
There is now a new page Halbach and Zhang’s Yablo without Gödel which demonstrates the illogical assumptions used by Halbach and Zhang.
It has come to my notice that, when asked about the demonstration of the flaw in his proof (see A Fundamental Flaw in an Incompleteness Proof by Peter Smith PDF), Smith refuses to engage in any logical discussion, and instead attempts to deflect attention away from any such discussion. If any other reader has tried to engage with Smith regarding my demonstration of the flaw, I would be interested to know what the outcome was.
I found that making, adding or deleting footnotes in the traditional manner proved to be a major pain. So I developed a different system for footnotes which makes inserting or changing footnotes a doddle. You can check it out at Easy Footnotes for Web Pages (Accessibility friendly).
I have now added a new section to my paper on Russell O’Connor’s claim of a computer verified incompleteness proof. This shows that the flaw in the proof arises from a reliance on definitions that include unacceptable assumptions - assumptions that are not actually checked by the computer code. See also the new page Representability.
There is now a new page on Chaitin’s Constant (Chaitin’s Omega), which demonstrates that Chaitin has failed to prove that it is actually algorithmically irreducible.
For convenience, there are now two pages on this site with links to various material relating to Gödel and the Incompleteness Theorem
– a page with general links:
– and a page relating specifically to the Gödel mind-machine debate:
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Copyright © James R Meyer 2012 - 2017