James Randi Lecture @ CalTech in 1992.

http://www.youtube.com/watch?v=qWJTUAezxAI

James Randi describes, in a humourous way, a thought experiment, intended to demonstrate that one cannot prove a negative.  He imagines taking 1000 reindeer to the top of the World Trade Centre to push them, one at a time, off the roof. "You're going to test whether or not reindeer can fly."
As expected, they all fall to their deaths. His comedic way is quite entertaining, but tapers off as he gets closer to making his point.

"Now, what have we proven with this experiment?
Have we proven that reindeer cannot fly? No! Of course not.
Think about it now. We've only shown that; on this occasion, under these conditions of atmospheric pressure, temperature, radiation, all these sort of things, at this position geographically, on this season etc. that these 1000 reindeer either could not fly or, chose not to..."

These 1000 reindeer did not fly, however it may have been the "atmospheric pressure" etc, that prevented them from flying? By that same reasoning, you can't prove that dead sparrows or rocks, can't fly because, it may be the atmospheric pressure etc, preventing them from flying.

"Now, if the second, then we know something certainly about the IQ of the average reindeer...
However, we have not proven a negative. We cannot prove a negative, technically, rationally and philosophically speaking.
However, people will often look at this example and say, 'Well, how many reindeer would you have to test?' Now I'm not going to get into the statistics of the thing... I'm not going to get into the arguments on the matter, I will only tell you that you cannot prove a negative and I think that's a rather good example that you might wish to use in illustrating your point.
The other folks who claim that it is so are required to prove it. And, if it's so, it's very easy. Just show me one flying reindeer!
Of course then they come up with the rationalizations and they say, 'Oh no it's only the 8 tiny reindeer who live at the north pole who can and will, on the evening of December the 24th, fly to do that specific job'. In that case you have to throw up your hands and say, 'Well, I don't think that your hypothesis is very testable."

Let's start with his first question; "Now, what have we proven with this experiment?".
Have we proven that reindeer cannot fly? Mr Randi's answer : No!
Have we proven that reindeer can fly? Answer : No!
So what have we proven with this experiment?  Answer : If you throw reindeer off a tall building, they will probably die.
So the rest of his performance is simply to reiterate his assertion that you cannot prove a negative.

What was the point of his thought experiment?
"We cannot prove a negative, technically, rationally and philosophically speaking". Where is the evidence?

Note the association; those who would argue against his "You can't prove a negative" assertion, would also argue that reindeer can fly. And of course, people who would argue that reindeer can fly are stupid, just like those who would argue against his statement.
Like all good comedians, the punchline is stated as a quick one-liner: "The other folks who claim that it is so, are required to prove it. And, if it's so, it's very easy. Just show me one flying reindeer!".

This is a common misdirection technique used by con-men and magicians.
He plays his audience as any professional magician or comedian would. He distracts his audience with the preposterous concept of throwing 1000 reindeer off the (then) world's tallest buildings. While the audience is still visualizing such a ghastly, ridiculous scenario, he quickly slips in his message that he wants the audience to believe.
Now comes the switch. Let everyone know that only those people who believe that reindeer can fly, would also believe that it is possible to prove a negative. So, after watching his show, if you believe that he has proved that "You cannot prove a negative", then you have been conned.

Personally, I'm not sure whether he was there to give a lecture or to be the comic relief. Unfortunately, so many people believe his joke.

Here's the statement that Mr Randi considers to be a fundamental, self-evident truth (an axiom):
"You cannot prove a negative". The statement itself is a negative.
Can you prove that you cannot prove a negative?
If you can, then you have just proven a negative and contradicted your statement.
If you cannot, then the statement is not an axiom.

From Wikipedia - Evidence of absence. As of 23 Sept 2013 :

"In 1992 during a presentation at Caltech, skeptic James Randi uses the phrase "you can't prove a negative". He claims that he cannot prove a negative (such that telepathy does not exist), but he also argues that an individual who claims telepathy exists must prove so. He discusses that induction is often used as a mode of proving a thesis, but if an individual assumes that something is or is not, then the person must prove so. Further, as he says, he does not take an advocacy position, as a lawyer would. He says that he cannot prove that a negative is true, but he could attempt to use evidence and induction to support a claim that he is biased toward, such as a claim that something does not exist (ex. flying reindeer)."

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

Of course Mr Randi should use evidence and induction to support his claim, that reindeer cannot fly, but what he hasn't proven, nor given any evidence to support, is his assertion that one cannot prove a negative.
All in all, Mr Randi has just dismissed his 1000 dead reindeer evidence as inconclusive, simply because he wants to believe that you can't prove a negative.