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Post by speakertoanimals on Jan 24, 2011 15:39:46 GMT 1
Why do you insist on mixing up the language of mathematical logic (completeness, undecidability), with a totally DIFFERENT subject, which is science probing reality.
Yes, we can never KNOw that the laws we deduce NOW actually operated for all of the lifetime of the universe, and will continue to do so, but that is really no more surprising than we cannot elimiate the possibility that the entire universe started one second ago, just set up (including my memories) to look older.
It's a fairly trivial, and fairly empty statement, that adds nothing to science.
Ditto trying to borrow these concepts from maths, and apply them to physics.
To which my usual retort is -- MATHS concerns itself with proof, physics DOESN'T, in that physics doesn't seek to prove, say, that these ARE the laws to which the universe runs and always did run, but that instead, saying that the universe runs according to these laws explains all that we have seen, and is not cojntradicted by anything we have seen.
Maths if about proof, science is about experiment with experimental observation, a fundamental distinction.
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Post by abacus9900 on Jan 24, 2011 17:45:24 GMT 1
STA, it is perfectly obvious to me and probably others here that either a) you simply have not understood Godel's Incompleteness Theorem or b) you are just messing about and having a game with us.
Let us take a simple analogy. If we represent the whole body of mathematical axioms by the statement 'I am a liar' it should become clearer. If this statement is true then logically it follows that it is false since if I am a seer I am, in fact, telling the truth. However, if I am telling the truth I cannot be a seer so we see that this statement turns out to be self-contradictory and places us in and endless loop that gets nowhere. This simple example is used to show that a limited body of 'ground-rules' inevitably leads, somewhere along the line, to contradictions and, therefore, is unprovable. If you are only given the 'statement' I am a liar', then you will not be able to construct your version of reality outside of it, however, if someone else outside your particular set of axioms (possessing a different set of statements) would be able to construct reality rather differently. But then their set of statements would similarly lead to contradictions at some stage and so on, so we are always forced to make assumptions about what are true statement (in the sense that 'work' at a particular moment in time and space) but cannot be proved to always be that way.
The fact that much of science (especially physics) is based on maths should make it obvious that we can never prove anything about reality, only what seems to 'work' at the time.
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Post by abacus9900 on Jan 24, 2011 17:46:32 GMT 1
I don't know why the word 'seer' appears above, it must be a glitch!
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Post by speakertoanimals on Jan 24, 2011 18:05:02 GMT 1
That's just the 'all cretans are liars' paradox, which is mentioned in mmany pop-sci treatments of Godel, but isn't actually what Godel was talking about!
Third possibility -- that you have no idea what you are talking about, and have just plain misunderstood Godel. Guess which option I prefer?
Or go read Godel, and see what he actually says......................
Another classic misunderstanding. Science doesn't seek to PROVE anything about reality, which is where it is different from maths. You fail to understand this distinction, which is why you keep misapplying what Godel actually says, as do so many woo-woo merchant pages written about Godel.
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Post by petergriffin on Jan 24, 2011 18:17:23 GMT 1
I understand Godel's incompletness theroy, and lets face it it is only a theory.
It does not say that you cannot prove anything, it states clearly there are some things you canot prove, even though the may appear obvoius.
For example between any prime and it double there is always another prime, this cannot be proved mathmatically but it is still true. But I can prove 3^2 + 4^2 = 5^2 mathmatically.
This is the basis of Godel, many people wrongly ascribe the view that Godel said nothing can be proved, he only said some things cannot be proved mathmatically. For enlightenment read Godel's paper is faily easy to understand, or much easier than Russel's principia which takes 1000's of pages to prove the oposite view.
There nneds to be a sepration into mathmatics, logic and physics here, and not using logic as math and physic and logic etc.
The 'I am a liar' statement is a logical paradox not a mathical axoim. Physics uses math as its language but it does not depend on mathmatical axoims to be true to prove the physics is good.
For fun I was aways taught at school, if it moves its biology, if it changes its chemistry and if it doesn't work it physics. I suppose I should add if its not true it math.
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Post by abacus9900 on Jan 24, 2011 18:34:14 GMT 1
I understand Godel's incompletness theroy, and lets face it it is only a theory. It does not say that you cannot prove anything, it states clearly there are some things you canot prove, even though the may appear obvoius. It is widely accepted as being valid by most mathematicians. "Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems for mathematics." wikipedia.org You cannot separate physics, logic and maths as they are all intertwined in descriptions of reality. It was simply used as an example to make things clearer.
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Post by abacus9900 on Jan 24, 2011 18:47:02 GMT 1
You see, you are just making a fool of yourself now because Godel actually demonstrated that nothing in maths (apart from the most trivial axiomatic maths systems) is proveable! What's more most other mathematicians agree!
BTW, you have contradicted yourself here by stating that a) science does not seek to prove anything about reality while also stating that b) maths is proveable. Well, if b) is correct then science MUST be in a position to prove things about reality!
Take a course in logic!
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Post by Progenitor A on Jan 24, 2011 18:49:45 GMT 1
I understand Godel's incompletness theroy, and lets face it it is only a theory. It does not say that you cannot prove anything, it states clearly there are some things you canot prove, even though the may appear obvoius. For example between any prime and it double there is always another prime, this cannot be proved mathmatically but it is still true. But I can prove 3^2 + 4^2 = 5^2 mathmatically. This is the basis of Godel, many people wrongly ascribe the view that Godel said nothing can be proved, he only said some things cannot be proved mathmatically. For enlightenment read Godel's paper is faily easy to understand, or much easier than Russel's principia which takes 1000's of pages to prove the oposite view. There nneds to be a sepration into mathmatics, logic and physics here, and not using logic as math and physic and logic etc. The 'I am a liar' statement is a logical paradox not a mathical axoim. Physics uses math as its language but it does not depend on mathmatical axoims to be true to prove the physics is good. For fun I was aways taught at school, if it moves its biology, if it changes its chemistry and if it doesn't work it physics. I suppose I should add if its not true it math. Hi Peter But doesn't (unless I am mistaken- I haven't read Godel but watched the videos that Abacus provided references to) Godel say that in every 'proof' there lays outside an assumption (or set of assumptions) which themselves may be 'provable' but only by invoking further assumptions. In other words wasn't he saying that real 'proof' is impossible because we are faced with an infinite regression? Take for example the equation that you can 'prove' 3 2 + 4 2 =5 2Now: 3 2 + 4 2 =41 And that apparently contradicts any proof that you may produce Of course I am working in base 6 on planet Og Whereas your assumption is base 10Your assumption is valid as are any other number bases that give a different answer valid But is our understanding of base 10 shared by other civilisations? Assumptions , assumptions. As to Logic OR Mathematics, surely logic is simply a sub-branch of mathematics? Boole was a mathematcian who invented a new algebra called Boolean algebra. No bloody use, until about 1940 it was discovered that it fitted exactly the new binary arithmetic of computers
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Post by abacus9900 on Jan 24, 2011 20:34:29 GMT 1
If we take the basic commutative laws:
The commutative laws state that the order in addition and multiplication does not matter. Thus x+y=y+x and xy = yx. Ok?
Now, how do we know that our universe isn't really a 'multiverse' where the commutative laws do not apply in all cases? How could we possibly find out and test the nature of such universes that do not abide by the commutative laws? It's not so far fetched, as some cosmologists/physicists take the idea of the multiverse quite seriously. Ah, but I hear you say we only have to bring in new axioms to cover these cases. THIS was was Godel was on about when he said even doing this does not mean such new axioms are provable because we are still making assumptions about them we can never prove.
I wonder if STA has got it yet?
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Post by Progenitor A on Jan 24, 2011 20:58:12 GMT 1
If we take the basic commutative laws: The commutative laws state that the order in addition and multiplication does not matter. Thus x+y=y+x and xy = yx. Ok? Now, how do we know that our universe isn't really a 'multiverse' where the commutative laws do not apply in all cases? How could we possibly find out and test the nature of such universes that do not abide by the commutative laws? It's not so far fetched, as some cosmologists/physicists take the idea of the multiverse quite seriously. Ah, but I hear you say we only have to bring in new axioms to cover these cases. THIS was was Godel was on about when he said even doing this does not mean such new axioms are provable because we are still making assumptions about them we can never prove. I wonder if STA has got it yet? I think that I catch your drift, Abacus, but the commutative law is probably not a good example as it does not apply in matrix maths for example, but, as you say, new axioms are brought in for matrices But you may be right, ther may be another universe where th ecommutative law does not apply for ordinary arithmetic. One thing is for sure and that is that there is no proof for the creation of the univers. Indeed physics fails us absolutely at that point - only mathematical models remain and Godel apparently shows that they are not 'proveable'
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Post by abacus9900 on Jan 24, 2011 21:23:05 GMT 1
naymissus, tonight's 'Horizon' is about the lack of public confidence in scientific theories. Gonna watch?
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Post by speakertoanimals on Jan 24, 2011 21:24:44 GMT 1
Physics is ahead of you there! Way ahead!
First, these aren't LAWS they are axioms -- so, if we say, we have numbers, and addition and multiplication are commutative, you get one type of number system -- the real numbers.
If you say you have numbers of some sort, but multiplication is no longer commutative, then you have grassmann numbers. Which are used in quantum theory for fermions.
Which doesn't mean that you could have a universe where the real numbers weren't commutative - they are commutative by definition! If they don't commute, they aren't the real numbers!
So, I can imagine (sort of) a universe that never used the real numbers.
What numbers the universe uses is a question for physics, not maths! They exist, whether the universe uses them or not!
I should add that what godel did was a theorem NOT a theory. So, Godels result is TRUE (and proven to be true), under conditions stated. Whether or not those conditions apply to anything in the physics of our universe is a different question, and even if they didn't, doesn't make godels theorem any less true!
Don't confuse maths and physics! And don't confuse theories in physics, with theorems in maths. And the next person who says 'it's JUST a theory' gets sent to the naughty step with the creationists (who occupy it permanently, and are very boring companions!)...................
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Post by Progenitor A on Jan 24, 2011 21:41:54 GMT 1
naymissus, tonight's 'Horizon' is about the lack of public confidence in scientific theories. Gonna watch? Sure am! Science bcomes quite clear in the absence of STA!
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Post by abacus9900 on Jan 24, 2011 21:46:29 GMT 1
naymissus, tonight's 'Horizon' is about the lack of public confidence in scientific theories. Gonna watch? Sure am! Science bcomes quite clear in the absence of STA! Ahhhhhh, that's so cruel naymissus.
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Post by Progenitor A on Jan 24, 2011 21:51:16 GMT 1
Sure am! Science bcomes quite clear in the absence of STA! Ahhhhhh, that's so cruel naymissus. No it is not. She is a moron that spouts gibberish I will now ignore her - she makes science a dogmatic laughing stock
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