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I always found the study of logic to be very interesting. What I highly recommend reading first, however, is a layman's introduction to Gödel's Incompleteness Theorem [1]. The essential idea is, much like the conclusion in this article, that axioms are chosen and theorems are proven within the systems they create. The caveat is that no system can be proven to be complete.

[1] http://www.amazon.com/Gödels-Proof-Ernest-Nagel/dp/081475837...

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