Doubting the effects of Gödel's incompleteness theorems on Physics

In summary: Just because a theory is not capable of explaining everything in a rigorous manner,doesn't mean it can't be a TOE.In summary, Gödel's incompleteness theorems don't seem to be as broadly applicable as it is being applied in such discussions. I also read a book on mathematical logic and although I can't claim that i understood it in detail,I know enough to tell that Gödel's incompleteness theorems are talking about certain axiomatic systems which are somehow related to arithmetic. I don't know how to explain it,but it just seems they're pushing it so far! and I don't understand such ideas!
  • #1
ShayanJ
Insights Author
Gold Member
2,810
604
It is sometimes said that Gödel's incompleteness theorems imply that the existence of a TOE is impossible.But I can't accept this.

Gödel's incompleteness theorems don't seem to be as broadly applicable as it is being applied in such discussions!
I also have read a book on mathematical logic and although I can't claim that i understood it in detail,I know enough to tell that Gödel's incompleteness theorems are talking about certain axiomatic systems which are somehow related to arithmetic.I don't know how to explain it,but it just seems they're pushing it so far!and I don't understand such ideas!

Just consider Gödel's second theorem as stated in http://en.wikipedia.org/wiki/Gödel's_incompleteness_theorem#Second_incompleteness_theorem :

For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, if T includes a statement of its own consistency then T is inconsistent.

It is said that the theory should include basic arithmetical truths!But why a TOE should contain such things?I see now reason!
And also,a TOE doesn't have to include a statement about its own consistency.There is no reason to include such a thing in a TOE!We will just have in mind,that its OK.

Even if I forget about the above arguments,I can tell that Gödel's incompleteness theorems are just restricting the idea of TOE,mathematically.I mean a physical theory is a bunch of thoughts which initiate some calculations.It doesn't have to be such rigorous and hard,it doesn't have to be that much formal.We can have our ideas in mind and do calculations and be happy for having a TOE,but still when we hand it to mathematicians,they just turn around saying "Mathematically,this formal system is not capable of explaining everything!"blah blah blah!...But who cares?!
 
Physics news on Phys.org
  • #2
Alfred tarski proved that from certain axioms you can know all the truths of Euclidean geometry.
So Godels theorem doesn't necessarily apply to physics.
 
  • #3
cragar said:
Alfred tarski proved that from certain axioms you can know all the truths of Euclidean geometry.
So Godels theorem doesn't necessarily apply to physics.

I didn't know about Tarski's works,thanks.
But that's exactly what I meant.
I can't understand why there are people out there who rule out TOE based on incompleteness.
 

1. How do Gödel's incompleteness theorems affect our understanding of the physical world?

The Gödel's incompleteness theorems have a significant impact on our understanding of the physical world. These theorems establish that in any formal system, there will always be true statements that cannot be proven within that system. This means that there will always be limits to what we can understand and explain using mathematical and logical systems, including the laws of physics.

2. Can Gödel's incompleteness theorems be applied to physics?

Yes, Gödel's incompleteness theorems can be applied to physics. In fact, many scientists and philosophers have explored the potential implications of these theorems on our understanding of the physical world. Some have even proposed that these theorems could provide a new way of thinking about the fundamental laws of physics, beyond the traditional mathematical and logical frameworks.

3. Do Gödel's incompleteness theorems suggest that there are limits to what we can know about the universe?

Yes, Gödel's incompleteness theorems do suggest that there are limits to what we can know about the universe. These theorems show that there will always be true statements that cannot be proven within a formal system, and this applies to any system that we use to understand and explain the physical world. Therefore, there will always be questions and mysteries about the universe that may never be fully answered.

4. Is there any evidence that Gödel's incompleteness theorems have had a direct impact on physics?

There is currently no direct evidence that Gödel's incompleteness theorems have had a significant impact on physics. However, as mentioned earlier, many scientists and philosophers have explored the potential implications of these theorems on our understanding of the physical world. Some have proposed new theories and approaches to physics based on these theorems, but further research and evidence are needed to fully evaluate their impact.

5. How do scientists reconcile Gödel's incompleteness theorems with the success of physics in explaining and predicting natural phenomena?

Scientists do not necessarily need to reconcile Gödel's incompleteness theorems with the success of physics. These theorems do not invalidate the laws of physics or the scientific method; rather, they suggest that there may be limits to what we can understand and explain using these tools. Many scientists continue to use mathematical and logical frameworks to make groundbreaking discoveries in physics, while also acknowledging the potential limitations of these tools.

Similar threads

A Can Gödel's Theorem Inform Our Understanding of Physical Reality?
    • Beyond the Standard Models
Replies
19
Views
2K
Is a GUT Impossible Due to Godel's Incompleteness Theorem?
    • Other Physics Topics
2
Replies
57
Views
12K
B Is everything in math either an axiom or a theorem?
    • General Math
3
Replies
72
Views
4K
I An easy proof of Gödel's first incompleteness theorem?
    • Set Theory, Logic, Probability, Statistics
Replies
16
Views
2K
I Does the incompleteness theorem apply to physics at all?
    • Other Physics Topics
Replies
2
Views
2K
I Gödel's 1st Incompleteness Thm: Min Arithmetic Req'd?
    • Set Theory, Logic, Probability, Statistics
Replies
5
Views
1K
I Exploring the Philosophical Implications of Godel's Incompleteness Theorems
    • Set Theory, Logic, Probability, Statistics
Replies
34
Views
3K
MHB Gödel Number Usefulness to Determine an Infinite Set's Completeness
    • Set Theory, Logic, Probability, Statistics
Replies
1
Views
1K
I Godel's ITs & the Physical World: Is a ToE impossible?
    • Beyond the Standard Models
2
Replies
66
Views
6K
I Godel's ITs & the Physical World: Is a ToE impossible?
    • Beyond the Standard Models
Replies
9
Views
2K

Hot Threads

Recent Insights

Back
Top