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Sorry, I forgot to answer your question.

http://en.wikipedia.org/wiki/Incompleteness_theorem

Gödel's first incompleteness theorem states that:

Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true,[1] but not provable in the theory (Kleene 1967, p. 250).

Gödel's second incompleteness theorem can be stated as follows:

For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent.

Logic isn't illogical. It is merely incomplete.