[Jaro]

Dear Lal,

I have read your post “Gödel’s Incompleteness Theorem” and would like to make some comments.

Your write:

Mathematician Kurt Gödel, in his Incompleteness Theorem, proved that it is impossible to find complete “truth” or “complete explanations” of a system from WITHIN a system.

However, this is not about just any systems, but specifically about formal mathematical systems.

Mathematics is a system of deductive reasoning. This means that we take a finite set of axioms to be true without proof, and all conclusions follow logically from these axioms. A feature of deductive reasoning systems is that they are truth-preserving. That is, if the axioms are true, then any valid conclusions drawn are also true. This feature of deductive reasoning systems allows us to construct proofs: We make a statement, and if we can connect that statement back to the axioms through valid arguments, we know that the statement is true (at least within the framework of the axioms assumed). This is why Gödel’s incompleteness theorem is important in mathematics: it tells us that there are statements that are true within this set of axioms, and yet we cannot construct a formal proof.

I was very pleased to hear that

I do not want anyone to get the wrong impression from this post. I love science and physics in particular. Before discovering the pure Dhamma, physics was my passion, and I still try to keep up with new findings.

Then I’m sure you know that Physics, on the other hand, is an inductive system of reasoning. That is, it is guided by empirical evidence. The truth value of a statement is not determined by an internal logic, but by the question of whether or not the reality out there agrees with you. It is therefore impossible to prove a statement in physics in a formal sense.

Therefore, Gödel’s incompleteness theorem, which is a statement about deductive reasoning systems and is based on the existence of formal proofs, does not apply to physics or a wider world view.

Otherwise, I found your post very interesting, even if your argumentation is occasionally on very thin ice. I don’t mean to denigrate you or Godel’s theorem, which is a remarkable piece of mathematics; my comment is only emphatic because of the wildly incorrect ways in which this theorem is interpreted outside of pure mathematical logic.

I respect you as a scientist and welcome constructive discussion :-)

[Lal]

Hello Jaro,

I am happy to see you are interested in the subject. I think no one had commented on it, even though it was one of my earliest posts around 2014/2015 (revised in 2021 to include the two videos.) 

• I saw that those two videos got deleted when we recently transferred the website to a new host. I just added the videos.

So, you may want to watch the two videos. Also, have you read the references at the end of the post? Many have discussed the implications of the theorem in fields other than mathematics.

• Could you let me know whether you are a physicist, mathematician, philosopher, etc.? It can help me in formulating my response. As you noted, I am a physicist.

[Jaro]

I watched the video and also took note of the references, thank you for adding it back! I am sceptical about the implications that other intellectuals derive from Gödel’s theorems. 

Gödel himself was quite cautious about drawing specific philosophical or scientific implications from his incompleteness theorems, and he was reluctant to make any grand claims about their significance beyond the field of mathematical logic. He was primarily interested in the technical aspects of mathematical logic and the precise statements and proofs of his theorems.

I studied applied mathematics and physics and currently work as a software developer.

[Lal]

Yes. I agree that Gödel himself did not pay any attention to the implications of his theory in other areas. 

But many, especially philosophers, have discussed the implications of Gödel’s two theorems in other areas, especially for the mind. 

• For example, the last reference in the post, “Gödel, Escher, Bach – An Eternal Golden Braid”, by Douglas R. Hofstadter (1979), has been the topic of discussion among philosophers for many years now.

 

[Author]

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