Tit for Tat

The Orthosphere

1No matter which class I am teaching, for quite some time the first reading assigned has been an article on Goedel’s Theorem. The reason is to emphasize that any attempt to make an axiomatic system of any moderate complexity consistent and complete (able to determine whether any statement within the system is either true or false) will fail. This is because, at least when it comes to mathematics, Goedelian propositions will be generated by the system that are true, can be seen to be true, but are not provable. Goedel’s stand-in for all such propositions is the statement “this statement is not provable within this axiomatic system.” If this statement is true, then it is not provable. If it were to be false, and was provable, then it would again be proved that it is not provable, since you would have just proved a statement that says it is…

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Author: Alfred E. Neuman

73 year old geek, ultra-conservative patriot.

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