Godel made his famous discovery in response to a challenge to finding a "consistent" and "complete" system. At the turn of that century Russel and Whitehead published the gigantic work, "Principia Mathematica (PM)" in an attempt to tackle this problem. They created what they believed a water-tight system to include all of the theorems in the field of Mathematics and Logics. Godel codified his ideas into a historical proof that once and for all demolished the idealistic castle so painstakingly constructed by Russel and Whitehead.

In a few simple words, PM is built on the very premise that "every theorem inside PM is provable." Yet, Godel used the very logic inside PM to generate an infinite number of provable theorems that state like this: "I am not provable inside PM." Godel just created an infinite number of the equivalents of the Epimenides paradox, known to logicians also as liar paradox. Godel proved it is futile for any future attempt to create such a "consistent and complete" system. In fact the stronger the system is, the easier it is to find the paradox.

Truth is to language what completeness is to PM: the more we attempt to grab, the more it eludes. I can't help noticing this happens time and again.

With this understanding of inevitability, here comes the debut of my blog.

I intend to write in either English or Chinese but not mixed, depending on the audience and feedback. I will post class summaries regularly after the class. I will tend the spiritual garden our head teacher worked so hard to make happen. But please remember: this is not my garden, rather "OUR" garden. The harvest is for all to share.