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Basic Logic

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Numsgil:
For the google impaired.


--- Quote ---At this point, I'm going to jump all the way to the end of Gödel's proof, and fill in the middle later. (Thought all math was linear, didn't you?) The critical step is to take the following statement, which Hofstadter calls "sentence G," and translate it into a TNT-string.

Sentence G: This statement is not a theorem of TNT.

Now, ask yourself this question: is sentence G true or false?

If sentence G is false, then it is a theorem of TNT. Then we have a valid theorem which is false, and the whole system falls apart.

So it must be true. But if it is true, then it is not a theorem of TNT. Which means that sentence G is true, but it is not provable within TNT. That is Gödel's "incompleteness." He showed that TNT, although it may be perfectly consistent and always correct, cannot possibly prove every true statement about number theory; there is always something which is true, which the system cannot prove. So we're done!
--- End quote ---

Godel's theorem then doesn't say that you can discredit a system this way, just that any system must be incomplete, because you can arrive at statements that are true but unprovable.

That doesn't affect the creduility of any statements that are both true and provable from within the system.

PurpleYouko:

--- Quote ---Hey PY, are you familiar with Godel's theorem of undefinability of truth? Basically, in any axiomatic system it is possible to create a statement equivalent to "I am lying", therefore creating liar's paradox and discrediting the system.
How is that for basc logic?  Sends it to hell, I say
--- End quote ---

This only applies to our interpretation of the truth, not to the actual truth.

If an event occurs then it occurs. You might say it happened one way and I might say it happened another way but the only way it actually did happen is in its own way.

That is the kind of truth I am talking about.

A theory is never true, only an event can be.

 :D  PY  :D

SyndLig:
We could all fall upon the theory that the universe doesn't really exist, and is the figment of the imagination of one being somewhere within the universe.

Of course, I'm also just a loon.  :)

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