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Logic is inconsistent. I have derived this from the existence of chillies. And no, I did not spell it wrong: I have consulted the Internet, and I am backed by approximately 7,630,000 search results for "chillies" (as of 2012-09-11).

But first things first. When I discussed this proof with a friend, he seemed a little uncomfortable with the claim that I had at first taken for granted. To match the mathematical rigor contained in the remainder of this proof, I shall start by stating, and fully justifying, this claim: Chillies are hot.

I know many of you are used to formulating hand-waving arguments to justify the claims in your fields that deserve a precise, infallible proof. I was going to write "a precise, foolproof proof", but that seemed like a horrible thing to do and I am a good person. In fact, I am so nice as to present to you the most rigorous proving technique currently acknowledged: Proof by Experimental Data and/or Citations from Select Sources. I will demonstrate this technique with the following lemma:

Lemma 1: Chillies are hot [1].

Proof:
[1]: http://news.bbc.co.uk/2/hi/science/nature/1456995.stm ∎


Now let's proceed with the remainder of the proof:

Proposition 1: Chillies are hot.

Proposition 2: When something is hot, it is not chilly.

Proposition 3: Chilly sounds like, and therefore must be equivalent to, chillie.

This is a corollary to the famous quote "If it looks like a duck, swims like a duck, and quacks like a duck, then it probably is a duck." (As an aside, by the law of transitivity, chillie is also equivalent to Chile).

Now then, we have the following:

Proposition 4: Chillies are not chillie,

or equivalently,

Proposition 4*: Chillies iff not chillie.

A perceptive logician may immediately see a problem with this statement. Note that this is a statement of the form "P iff not P". Since there is clearly no way of assigning a truth value to "chillie" without allowing the universe to blow up (along with any remaining logical consistency) by the principle of explosion, this conclusively shows the inconsistency, and therefore the invalidity, of logic itself. ∎


Unless, of course, there is a truth value that has been excluded all along. If such truth value is discovered through more extensive experimental data, I will call it Middle.