Skeptical Inquirer magazine published an article last year called "Cinema Fiction vs. Physics Reality: Ghosts, Vampires, and Zombies."  The article is by two physicists, and the section on vampires is a perfect example of how you can prove whatever you want as long as you make the right (or wrong) assumptions.

Here is their conclusion:

We conclude that vampires cannot exist, since their existence would contradict the existence of human beings. Incidently, the logical proof that we just presented is of a type known as reductio ad absurdum, that is, “reduction to the absurd.” Another philosophical principle related to our argument is the truism given the elaborate title, the anthropic principle. This states that if something is necessary for human existence then it must be true since we do exist. In the present case, the nonexistence of vampires is necessary for human existence. Apparently, whoever devised the vampire legend had failed his college algebra and philosophy courses.

How did they reach such a conclusion?  They made the following assumptions:

1. A vampire needs to feed once a month.  (They consider that a conservative assumption.)
2. When a vampire feeds, the human population decreases by one and the vampire population increases by one.
3. The first vampire appeared in the year 1600.

From this, they derive the formula that the number of vampires doubles every month.  They also have a formula for the equivalent decrease in the human population.  Starting with the world population in 1600, they show that the formulas result in the entire human population having been converted to vampires within 30 months.  (For purposes of the illustration, they ignore human birthrate and normal mortality as having a negligibly small impact.)

And so they arrive at their conclusion that since the whole of humanity did not become vampires, vampires do not exist.  Q.E.D.

Very good.

Now let me make the following assumption:

1. A population of rabbits can double in size every six months.  (I consider this a conservative assumption, since Wikipedia says a litter of rabbits can contain up to seven babies and a female can give birth four to five times per year.)
2. The first pair of rabbits appeared in the year 1600.  (Coincidentally the same year we assumed that the first vampire appeared.)

From this, we can derive a formula that shows the number of rabbits will quadruple every year.  I’ve implemented the formula in an Excel spreadsheet:

As you can see, in just thirty years, the number of rabbits would have grown to over 2 quintillion–that’s over 4000 rabbits for every square meter of the Earth’s surface, which would make human life impossible.

I conclude that rabbits cannot exist, since their existence would contradict the existence of human beings.

Now, obviously, rabbits do exist.  They even existed long before 1630.  So there must be something wrong with our assumptions.  What could it be?  Oh, yes: rabbits die.  (And they don’t keep reproducing at the same rate when resources are scarce.)

So there’s at least one hidden assumption in the vampire scenario: vampires don’t die.  But that contradicts the information movies give us about vampires.  Wooden stakes through the heart, decapitation, sunlight, and fire seem to be capable of killing vampires.  I understand there was even a movie and a TV show about someone who was a "slayer of the vampyres."  The authors of the Skeptical Inquirer article completely ignored that information when writing their article, because it was incompatible with their thesis that vampires don’t exist.

Let me make it clear, I don’t believe vampires exist.  But the "proof" in the Skeptical Inquirer proves only that scientists can reason themselves silly when they aren’t careful in examining their assumptions.