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Gromit
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Joined: May 20, 2006
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Location: In Cognito
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 Posted: Mon May 12, 2008 6:56 am Post subject: Can a logically inconsistent universe exist? |
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In mathematics, a theorem can be disproven by showing it would lead to a contradiction. A theorem can be proven by showing that there would be a contradiction if it were false.
I am fairly confident that the physical universe must be free of contradictions, that if ever there is a grand unified theory of physics, it can't have contradictory rules that say both that something must happen and can't happen. But I couldn't prove that the universe must be logically consistent in this way. Is there a proof? |
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asplanet
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Joined: Nov 11, 2007
Posts: 1772
Location: Cyberspace, New Zealand
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| Posted: Mon May 12, 2008 7:20 am Post subject: |
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Unless some think happens to indicate otherwise - how can there really be any real proof of the unknown! all theory to me 
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"Believe in your self, we are who we are - as it can feel like an endless task trying to be someone else!" Alyson Bradley ... Aspergers Parallel Planet web site - http://asplanet.info/index.php
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wolphin
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Joined: Aug 16, 2007
Posts: 441
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| Posted: Mon May 12, 2008 7:39 am Post subject: |
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Perhaps, but depends. If you mean logical contradiction - in the sense of, there is some statement A such that both A and not-A are both true, the problem with that is that ultimately that logically implies everything.
That is, the statement ((A and (not A)) implies B) is a tautology - it is always true, regardless of which substatements A and B you choose. Therefore, if you have both A and not A as true, then you can deduce that any other statement is true as well (which doesn't seem to be the case, but could be) |
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Gromit
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| Posted: Mon May 12, 2008 8:42 am Post subject: |
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| wolphin wrote: | | Perhaps, but depends. If you mean logical contradiction - in the sense of, there is some statement A such that both A and not-A are both true |
That is what I mean.
| wolphin wrote: | the problem with that is that ultimately that logically implies everything.
That is, the statement ((A and (not A)) implies B) is a tautology - it is always true, regardless of which substatements A and B you choose. Therefore, if you have both A and not A as true, then you can deduce that any other statement is true as well (which doesn't seem to be the case, but could be) |
So in a universe operating according to rules with at least one contradiction, anything could happen. Does that imply a stronger statement, that a single contradiction would destroy all regularity in that universe? If that second statement is true, then because we can observe regularity in the universe (the existence of life depends on there being regularities), we could conclude there are no logical contradictions.
I can come up with at least one alternative if I use a computer programme as an analogy. I can imagine writing a programme with a logical contradiction, but the programme should run without trouble until it tries to execute the code containing the contradiction. If a computer programme is a valid analogy, I would then reason that either our universe contains no contradictory rules, or that in all the interaction among all the matter and energy in the universe, it hasn't reached a contradiction yet, because if it had, it would have lost all regularity from that moment, or it would have frozen up in a cosmic crash, or it would be going round in an infinite loop (OK, there is the question whether you could spot an infinite loop from inside a programme).
That takes me to a loosely related point. There are non-computable functions. Could a grand unified theory contain non-computable functions? If it could, what would happen if a physical process had to be described by a non-computable function? If the process happens, wouldn't that be equivalent to computing the function, leading to a contradiction? So unless the solution is that the process would take infinitely long to finish (delaying the contradiction infinitely long), does this mean a theory of everything must not contain non-computable functions? |
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toby2
Raven
Joined: Apr 04, 2008
Age: 44
Posts: 100
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| Posted: Mon May 12, 2008 9:09 am Post subject: |
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hi
i believe every thing in the universe has its own given path. |
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Izaak
Squeeky Bathtime Companion
Joined: Jun 11, 2007
Posts: 1154
Location: Perth, Western Australia
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| Posted: Mon May 12, 2008 9:36 am Post subject: Re: Can a logically inconsistent universe exist? |
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| Gromit wrote: | In mathematics, a theorem can be disproven by showing it would lead to a contradiction. A theorem can be proven by showing that there would be a contradiction if it were false.
I am fairly confident that the physical universe must be free of contradictions, that if ever there is a grand unified theory of physics, it can't have contradictory rules that say both that something must happen and can't happen. But I couldn't prove that the universe must be logically consistent in this way. Is there a proof? |
That problem isn't physics. It's Philosophy. More specifically Metaphysics. Aristotle was the first to outline this aspect, and it is called the Law of Identity.
http://www.importanceofphilosophy.com/Metaphysics_Identity.html
As such it is an Axiom. A self-evident truth at the foot of all knowledge. It is proved evidenced each time you do a more complex proof in mathematics. But there is no way to prove the axiom itself. You must assume it (or not) as it stands with the evidence coming from the fact that (as your knowledge of an entity improves) you discover it has no contradictions. That the Law of Identity holds at ALL times. And that apparent contradictions are only an indication of our misunderstanding or lack of knowledge about an entity. |
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Willard
Phoenix
Joined: Mar 24, 2008
Posts: 584
Location: Confederate States of America
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| Posted: Mon May 12, 2008 10:03 am Post subject: Re: Can a logically inconsistent universe exist? |
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| Gromit wrote: | In mathematics, a theorem can be disproven by showing it would lead to a contradiction. A theorem can be proven by showing that there would be a contradiction if it were false.
I am fairly confident that the physical universe must be free of contradictions, that if ever there is a grand unified theory of physics, it can't have contradictory rules that say both that something must happen and can't happen. But I couldn't prove that the universe must be logically consistent in this way. Is there a proof? |
Light is made up of particles.
Light is made up of waves.
Light is not made of waves of particles.
All of these statements are true. Schroedinger's Cat showed us that the universe is not necessarily without internal contradictions.
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"I don't mean to sound bitter, cynical or cruel - but I am, so that's how it comes out."
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slowmutant
Phoenix
Joined: Feb 14, 2008
Age: 29
Posts: 6814
Location: Ontario, Canada
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| Posted: Mon May 12, 2008 11:07 am Post subject: |
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Life, the Universe, and Everything .... hmm.
Full of contradictions as far as I can see. But I suspect this is due to the inadequaqcy of human language and human intellect. If you are only human, a lot whole of things are bound to be head-scratchers. I resign myself peacefully to not knowing everything.
What's the answer here? I don't know.
More people should practise saying that. It's very liberating. |
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twoshots
Honorary Vertebrate
Joined: Nov 27, 2007
Posts: 1812
Location: NJ
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| Posted: Mon May 12, 2008 11:22 am Post subject: |
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Sure. Logical modeling is all just a priori language anyway. It's easy to make a linguistic model of the universe which is contradictory.
You just wouldn't want to. |
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ToadOfSteel
Extremist Moderate
Joined: Sep 24, 2007
Age: 20
Posts: 2402
Location: New Jersey
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| Posted: Mon May 12, 2008 11:27 am Post subject: Re: Can a logically inconsistent universe exist? |
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| Willard wrote: | | Gromit wrote: | In mathematics, a theorem can be disproven by showing it would lead to a contradiction. A theorem can be proven by showing that there would be a contradiction if it were false.
I am fairly confident that the physical universe must be free of contradictions, that if ever there is a grand unified theory of physics, it can't have contradictory rules that say both that something must happen and can't happen. But I couldn't prove that the universe must be logically consistent in this way. Is there a proof? |
Light is made up of particles.
Light is made up of waves.
Light is not made of waves of particles.
All of these statements are true. Schroedinger's Cat showed us that the universe is not necessarily without internal contradictions. |
Ahh, quantum indecision...
Too bad you can't make a cat fly by strapping buttered toast to its back... |
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Gromit
Velociraptor
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Joined: May 20, 2006
Posts: 492
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| Posted: Mon May 12, 2008 11:27 am Post subject: |
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| slowmutant wrote: | | Life, the Universe, and Everything .... hmm. |
No, the physical universe, at the level physicists look at. I deliberately exclude anything to do with human beliefs, which are full of contradictions. I'm sorry if the intention wasn't clear enough.
| slowmutant wrote: | | Full of contradictions as far as I can see. |
In human beliefs, or in how the universe works at the physical level? |
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slowmutant
Phoenix
Joined: Feb 14, 2008
Age: 29
Posts: 6814
Location: Ontario, Canada
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| Posted: Mon May 12, 2008 11:35 am Post subject: |
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Both.  |
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LoveableNerd
Velociraptor
Joined: Apr 24, 2008
Posts: 435
Location: Kentucky, USA
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| Posted: Mon May 12, 2008 12:22 pm Post subject: Re: Can a logically inconsistent universe exist? |
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| Izaak wrote: | That problem isn't physics. It's Philosophy. More specifically Metaphysics. Aristotle was the first to outline this aspect, and it is called the Law of Identity.
http://www.importanceofphilosophy.com/Metaphysics_Identity.html
As such it is an Axiom. A self-evident truth at the foot of all knowledge. It is proved evidenced each time you do a more complex proof in mathematics. But there is no way to prove the axiom itself. You must assume it (or not) as it stands with the evidence coming from the fact that (as your knowledge of an entity improves) you discover it has no contradictions. That the Law of Identity holds at ALL times. And that apparent contradictions are only an indication of our misunderstanding or lack of knowledge about an entity. |
As the above posters alluded to, the Law of Identity breaks down at the quantum level. According to the Law of Identity, a car can be red or blue, or both red and blue but not at the same time and place. However, a photon is both a wave and a particle at the same time.
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Heisenberg is pulled over by a policeman whilst driving down a motorway, the policeman gets out of his car, walks towards Heisenberg's window and motions with his hand for Heisenberg to wind the window down, which he does. The policeman then says ‘Do you know what speed you were driving at sir?’, to which Heisenberg responds ‘No, but I knew exactly where I was.’ |
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ToadOfSteel
Extremist Moderate
Joined: Sep 24, 2007
Age: 20
Posts: 2402
Location: New Jersey
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| Posted: Mon May 12, 2008 1:07 pm Post subject: |
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Here's a paradox for you: What is the simplest reason for Occam's Razor to exist?
PS: come to think of it, the fact that so many paradoxes (sp?) exist is proof that the universe is fundamentally inconsistent. |
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abstrusemortal
Toucan
Joined: Feb 08, 2007
Posts: 286
Location: DC/VA area
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| Posted: Mon May 12, 2008 1:57 pm Post subject: Re: Can a logically inconsistent universe exist? |
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| Willard wrote: | | Gromit wrote: | In mathematics, a theorem can be disproven by showing it would lead to a contradiction. A theorem can be proven by showing that there would be a contradiction if it were false.
I am fairly confident that the physical universe must be free of contradictions, that if ever there is a grand unified theory of physics, it can't have contradictory rules that say both that something must happen and can't happen. But I couldn't prove that the universe must be logically consistent in this way. Is there a proof? |
Light is made up of particles.
Light is made up of waves.
Light is not made of waves of particles.
All of these statements are true. Schroedinger's Cat showed us that the universe is not necessarily without internal contradictions. |
=)
Light has a wave-particle duality as does everything. Even a baseball. Both cannot exist as one in a visual image.
Light has two different faces. A particle face; and a wave face. Young's double slit experiment confirms the wave part. Photoelectric effect; Compton's effect confirm the particle side, etc...
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