4 ms·

I do not think that it is possible. Any physical system that can be described by a set of mathematical laws is bound to have some axioms that simply cannot be

by axilmar 12y ago

I do not think that it is possible. Any physical system that can be described by a set of mathematical laws is bound to have some axioms that simply cannot be proven within its context. Godel's incompleteness theorems prove that. Hence, we will never get to the bottom of the reality of our universe.

macspoofing 12y ago
What if we live in a universe/reality where anything that can happen, does happen. And the reason for this state is because it just is.
- fjolthor 12y ago
  You mean...the multiverse theory.
coliveira 12y ago
This argument is always used to try to reduce the power of mathematics, but the whole fact that mathematics was used to prove this tells me otherwise. There is a huge amount of properties of the universe that can be understood with mathematics despite Goedel's result.
fjolthor 12y ago
I agree with this but for a different reason. No matter how much we discover, everything we find is still something in existence. No matter what force or object you are observing, you can't doubt that it exists at some level, in some way (whichever multiverse or reality it is). This means that at some point, existence must have been started by something non-existent. Because we only comprehend cause-and-effect, we can't possibly find the origin in a provable way while researching from within existence.
john_b 12y ago
Godel's incompleteness theorems only place restrictions on deductive systems. In mathematics, you can't perform "experiments" and measure what happens. As long as we can observe and measure physical quantities, even if those quantities are only indirect effects of what physicists are actually trying to measure, incompleteness is not a strong limitation of physics.
smokel 12y ago
Your statement that we will never get to the bottom may be true, but the reasoning is flawed. Gödel's incompleteness theorems are about mathematical theories, not about physical theories. It may well be that for physical understanding a very limited arithmetic is sufficient. Also, there may be statements that are unprovable, but these might turn out to be irrelevant to sufficiently understanding the universe. Also, an axiom, by definition, can not be proven. The things that are proven are theorems, statements, etc. An axiom is an assumption. Eventually, it all depends on what level of understanding you want. But Gödel's theorems have little to do with that.
- mkaziz 12y ago
  Do you not have to start off with a set of axioms though? Assumptions that will never be proven?
  - dfox 12y ago
    From the mathematical point of view, physics is about finding smallest set of axioms from which you can mathematically derive complete theory of universe's behavior. Validity of such axioms is in turn validated by experiments (by testing whether results match theory derived from given axioms)
    - dllthomas 12y ago
      It is true that they will never be "proven", but that doesn't mean we can't build a tremendous confidence in them through experimentation. (Which is to say "I agree", but I wanted to put a slightly different spin on it.)
  - sp332 12y ago
    The incompleteness theorem describes a tradeoff: A system of axioms cannot be both consistent and complete. But that seems irrelevant, since you could make a system that describes all of physics while not being either consistent or complete. https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems#Background https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_...
kazinator 12y ago
If reality is just math, then it boils down to everything being generated from axioms. Gödel does not tell us that we cannot discover those axioms (and that they are axioms). Where Gödel comes into the picture is that he gives us no right to believe that only those axioms are all there is. If the reality is mathematics, Gödel justifies the Multiverse hypothesis: just because we are objects within some theory doesn't mean there don't exist other theories (perhaps superset of this one). "Unable to prove" in the Gödel sense can be then equated with "unable to peer into another universe". Gödel's sentence becomes analogous to some phenomenon or artifact of another universe which cannot exist in ours because it cannot be derived from its axioms.
Tloewald 12y ago
Not axioms, tautologies (true statements). Godel's incompleteness theorem assumes you know the axioms.
Tloewald 12y ago
Not axioms, tautologies (true statements). Godel's incompleteness theorem assumes you know the axioms. Godel doesn't tell us whether we can discover the axioms, although perhaps it implies that as a corollary.

by axilmar 12y ago

macspoofing 12y ago

What if we live in a universe/reality where anything that can happen, does happen. And the reason for this state is because it just is.

fjolthor 12y ago
You mean...the multiverse theory.

coliveira 12y ago

This argument is always used to try to reduce the power of mathematics, but the whole fact that mathematics was used to prove this tells me otherwise. There is a huge amount of properties of the universe that can be understood with mathematics despite Goedel's result.

fjolthor 12y ago

I agree with this but for a different reason. No matter how much we discover, everything we find is still something in existence. No matter what force or object you are observing, you can't doubt that it exists at some level, in some way (whichever multiverse or reality it is). This means that at some point, existence must have been started by something non-existent. Because we only comprehend cause-and-effect, we can't possibly find the origin in a provable way while researching from within existence.

john_b 12y ago

Godel's incompleteness theorems only place restrictions on deductive systems. In mathematics, you can't perform "experiments" and measure what happens. As long as we can observe and measure physical quantities, even if those quantities are only indirect effects of what physicists are actually trying to measure, incompleteness is not a strong limitation of physics.

smokel 12y ago

Your statement that we will never get to the bottom may be true, but the reasoning is flawed. Gödel's incompleteness theorems are about mathematical theories, not about physical theories. It may well be that for physical understanding a very limited arithmetic is sufficient. Also, there may be statements that are unprovable, but these might turn out to be irrelevant to sufficiently understanding the universe. Also, an axiom, by definition, can not be proven. The things that are proven are theorems, statements, etc. An axiom is an assumption. Eventually, it all depends on what level of understanding you want. But Gödel's theorems have little to do with that.

mkaziz 12y ago
Do you not have to start off with a set of axioms though? Assumptions that will never be proven?
- dfox 12y ago
  From the mathematical point of view, physics is about finding smallest set of axioms from which you can mathematically derive complete theory of universe's behavior. Validity of such axioms is in turn validated by experiments (by testing whether results match theory derived from given axioms)
  - dllthomas 12y ago
    It is true that they will never be "proven", but that doesn't mean we can't build a tremendous confidence in them through experimentation. (Which is to say "I agree", but I wanted to put a slightly different spin on it.)
- sp332 12y ago
  The incompleteness theorem describes a tradeoff: A system of axioms cannot be both consistent and complete. But that seems irrelevant, since you could make a system that describes all of physics while not being either consistent or complete. https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems#Background https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_...

kazinator 12y ago

If reality is just math, then it boils down to everything being generated from axioms. Gödel does not tell us that we cannot discover those axioms (and that they are axioms). Where Gödel comes into the picture is that he gives us no right to believe that only those axioms are all there is. If the reality is mathematics, Gödel justifies the Multiverse hypothesis: just because we are objects within some theory doesn't mean there don't exist other theories (perhaps superset of this one). "Unable to prove" in the Gödel sense can be then equated with "unable to peer into another universe". Gödel's sentence becomes analogous to some phenomenon or artifact of another universe which cannot exist in ours because it cannot be derived from its axioms.

Tloewald 12y ago

Not axioms, tautologies (true statements). Godel's incompleteness theorem assumes you know the axioms.

Tloewald 12y ago

Not axioms, tautologies (true statements). Godel's incompleteness theorem assumes you know the axioms. Godel doesn't tell us whether we can discover the axioms, although perhaps it implies that as a corollary.