Following up on the topic of too much data, I was asked by a friend to write about windbags and blowhards. I guess I was asked because I was assumed to be an authority. It’s nice to be an authority on something; I’m just not sure that this is the something.
What, you might ask, is the difference between a windbag and a blowhard? According to the dictionary, a windbag is a talkative person who communicates nothing of substance or interest and a blowhard is a very boastful and talkative person. So a windbag will talk endlessly on any subject and a blowhard will talk endlessly on any subject because he thinks you are interested. A gasbag is similar to a windbag. To me a gasbag is a windbag with indigestion. In general, I try to limit my articles to less than 500 words. Doesn’t that make me a condensed windbag or abbreviated blowhard, sort of a Reader’s Digest or Cliff Notes version? I didn’t think so.
Do windbags and blowhards know who they are? I honestly believe that they are blissfully unaware of their windbaggery and blowhardedness. So if I’m a windbag and blowhard, how is it that I know that I am one when I should be unaware of it? Isn’t it inconsistent to be aware that you are unaware? I’m glad that I asked me that question so that I can explain it to you by referring to the logic of Gödel’s proof, specifically his first incompleteness theorem, and the ω (omega) inconsistency.
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, but not provable in the theory. 1
An example is the liar paradox, which is the sentence “This sentence is false.” An analysis of the liar sentence shows that it cannot be true (for then, as it asserts, it is false), nor can it be false (for then, it is true). A Gödel sentence G for a theory T makes a similar assertion to the liar sentence, but with truth replaced by provability: G says “G is not provable in the theory T.” The analysis of the truth and provability of G is a formalized version of the analysis of the truth of the liar sentence.1
Thus, by applying this theorem to my statement “As a windbag, I know that windbags don’t know they are windbags” shows that if the statement is true, then it is proven false. Now you might ask …
Hello? Hello? Is anybody there? Hello?