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Any logical system cannot be both consistent and complete. In particular, for any consistent, logical system that proves certain truths, there will always be a statement that is true, but not provable in the theory. | Any logical system cannot be both consistent and complete. In particular, for any consistent, logical system that proves certain truths, there will always be a statement that is true, but not provable in the theory. | ||
| − | Mainly, I am fond of this, because while we know of this result, we also tend to ignore it and keep plodding away at math, acting like it doesn't exist. | + | Mainly, I am fond of this, because while we know of this result, we also tend to ignore it and keep plodding away at math, acting like it doesn't exist. --[[User:Cctroxel|Cctroxel]] 12:24, 22 January 2009 (UTC) |
Revision as of 07:24, 22 January 2009
Godel's Incompleteness Theorem (first one)
Any logical system cannot be both consistent and complete. In particular, for any consistent, logical system that proves certain truths, there will always be a statement that is true, but not provable in the theory.
Mainly, I am fond of this, because while we know of this result, we also tend to ignore it and keep plodding away at math, acting like it doesn't exist. --Cctroxel 12:24, 22 January 2009 (UTC)
