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You can't have perfect knowledge through science

atanu

atanu

Member
Premium Member
gnomon said:
So I could be wrong. I'll make an attempt here.

If finding a complete and consistent set of axioms for all of mathematics is impossible this implies to me that the hard sciences, physics, chemistry, etc. are also limited by Godel's theorem given their reliance upon that same system of mathematics.
Click to expand...



Hello Gnomon

Godel approximately says: In any sufficiently strong formal system there are true arithmetical statements that can’t be proved (in the system).

More rigorously: If S is a formal system such that (i) the language of S contains the language of arithmetic, (ii) S includes Peano Arithmetic, and (iii) S is consistent, then the consistency of S, is not provable in S.

Freeman Dyson wrote:
Gödel’s theorem implies that pure mathematics is inexhaustible. No matter how many problems we solve, there will always be other problems that cannot be solved within the existing rules. … because of Gödel's theorem, physics is inexhaustible too. The laws of physics are a finite set of rules, and include the rules for doing mathematics, so that Gödel's theorem applies to them. (NYRB, May 13, 2004).


According to Dyson’s argument, there can’t be a Theory of Everything (TOE). It is also said that after having supported the pursuit of a TOE, Hawking concluded in his Dirac lecture of 2002 that there can’t be such a thing on account of Gödel’s theorem.

(Some thinkers however say that physical laws encapsulated within the System S can be known in completeness, although there are propositions of higher mathematics that are undecidable in S.).


The second problem is Under-determination of Scientific Theory.

http://plato.stanford.edu/entries/scientific-underdetermination/

 
idav

idav

Being
Premium Member
PolyHedral said:
My understanding of Godel's theorem is that it is a statement, "There exists a theorem that it is not possible to prove true or false in any given logical system." However, it says nothing about the structure of that theorem, and that's how physics escapes: physics isn't a system of describing statements as true or false; it is a description of a single system of functions. It doesn't produce theorems derived from axioms, but instead it is simply a collection of theorems about the world.

The equivalent in the art would be Godel saying, "I can prove that it is possible to paint a picture that cannot be a real object." The physicists ask, "We have an object. How do we paint it?"
Click to expand...
Thats a pretty interesting way of putting it. The argument is like asking what language is best for describing something. Well I only know english so lets start there.
 
gnomon

gnomon

Well-Known Member
atanu said:
Hello Gnomon

Godel approximately says: In any sufficiently strong formal system there are true arithmetical statements that can’t be proved (in the system).

More rigorously: If S is a formal system such that (i) the language of S contains the language of arithmetic, (ii) S includes Peano Arithmetic, and (iii) S is consistent, then the consistency of S, is not provable in S.

Freeman Dyson wrote:
Gödel’s theorem implies that pure mathematics is inexhaustible. No matter how many problems we solve, there will always be other problems that cannot be solved within the existing rules. … because of Gödel's theorem, physics is inexhaustible too. The laws of physics are a finite set of rules, and include the rules for doing mathematics, so that Gödel's theorem applies to them. (NYRB, May 13, 2004).


According to Dyson’s argument, there can’t be a Theory of Everything (TOE). It is also said that after having supported the pursuit of a TOE, Hawking concluded in his Dirac lecture of 2002 that there can’t be such a thing on account of Gödel’s theorem.

(Some thinkers however say that physical laws encapsulated within the System S can be known in completeness, although there are propositions of higher mathematics that are undecidable in S.).


The second problem is Under-determination of Scientific Theory.

http://plato.stanford.edu/entries/scientific-underdetermination/
Click to expand...

That's interesting.

I would have to agree with Dyson.

Although I have another concept as to why science cannot be perfect based upon the concept of observation and the overall unreliability of probability I would think that it's safe to assume that Godel has shown us that our methodology will ever be flawed to some extent. Although I think our flawed system is the best that we have to eliminate conjecture.
 
gnomon

gnomon

Well-Known Member
PolyHedral said:
My understanding of Godel's theorem is that it is a statement, "There exists a theorem that it is not possible to prove true or false in any given logical system." However, it says nothing about the structure of that theorem, and that's how physics escapes: physics isn't a system of describing statements as true or false; it is a description of a single system of functions. It doesn't produce theorems derived from axioms, but instead it is simply a collection of theorems about the world.

The equivalent in the art would be Godel saying, "I can prove that it is possible to paint a picture that cannot be a real object." The physicists ask, "We have an object. How do we paint it?"
Click to expand...

This reminds me of an explanation of Godel I found involving computation but I cannot seem to find it at the moment. If I come across it I will provide a link.

Yet, I fail to see the logic behind the statement that physics doesn't produce theorems derived from axioms but rather is a collection of theorems without recognizing that those theorems which make up the set of physics are not themselves derived from axioms.
 
Viker

Viker

Your beloved eccentric Auntie Cristal
I-Ching said:
The scientific method is based on a flawed axiom that we can know the reality through our senses. Unfortunately all human beings are subject to four defects:
1) Our senses are limited and imperfect
2) We make mistakes
3) We are in illusion
4) We cheat.

Due these defects we can not know the Truth through this method. In order to have perfect knowledge you must hear from higher authority. Just like if you want to know your father you have to ask your mother. You can't go to every man and test them.
Click to expand...

According to those four, we can never know the full truth. Not even an alleged "higher authority" can help us. How can we ever know what that authority is and what they can impart upon us? Wouldn't there be some degree of self-deception and misunderstanding then, too?
 
PolyHedral

PolyHedral

Superabacus Mystic
certainty.png
 
Viker

Viker

Your beloved eccentric Auntie Cristal
I think many have not figured out yet that science and it's method are the basic old quest for knowledge ( somewhat refined ) and not a way to debunk/replace supernatural, mystical or spiritual concepts.
 
PolyHedral

PolyHedral

Superabacus Mystic
Viker said:
I think many have not figured out yet that science and it's method are the basic old quest for knowledge ( somewhat refined ) and not a way to debunk/replace supernatural, mystical or spiritual concepts.
Click to expand...
If the supernatural and the mystical get in the way, crushing them under the march of science is entirely justified.
 
gnostic

gnostic

The Lost One
Science is like ongoing project, that will you could gain new knowledge as new data or evidence manifested. It go through stages of testings, very much like "trial-and-error", where scientists attempt to correct error in their hypothesis or theory. And in science there is always room provided, to take in margin of error.

Science is not about perfect knowledge, because we can either learn something new or improve (or correct) what we already know.

If science was perfect, then Newton (as an example) would have known everything about gravity, including Relativity and Quantum Physics.

And beside all this, the word "perfect" is not often used in science circle.

In any case, I would prefer to learn something about the natural or artificial (like computers, car building, etc) worlds from science than from religion.
 
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