Lemma1: All horses are the same color.
Proof (by induction):
Case n=1: In a set with only one horse, it is obvious that all horses in that set are the same color.
Case n=k: Suppose you have a set of k+1 horses. Pull one of these horses out of the set, so that you have k horses.
Suppose that all of these horses are the same color. Now put back the horse that you took out, and pull out a different
one. Suppose that all of the k horses now in the set are the same color. Then the set of k+1 horses are all the same
color. We have k true => k+1 true; therefore all horses are the same color.
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Theorem1: All horses have an infinite number of legs.
Proof (by intimidation):
Everyone would agree that all horses have an even number of legs. It is also well-known that horses have forelegs in
front and two legs in back. 4 + 2 = 6 legs, which is certainly an odd number of legs for a horse to have! Now the only
number that is both even and odd is infinity; therefore all horses have an infinite number of legs.
However, suppose that there is a horse somewhere that does not have an infinite number of legs. Well, that would be a
horse of a different color; and by the Lemma, it doesn't exist.
Corollary 1. Everything is the same colour.
Proof. The proof of lemma 1 does not depend at all on the nature of the object under consideration. The predicate of the antecedent of the universally-quantified conditional 'For all x, if x is a horse, then x is the same colour,' namely 'is a horse' may be generalized to 'is anything' without affecting the validity of the proof; hence, 'for all x, if x is anything, x is the same colour.'
Corollary 2. Everything is white.
Proof. If a sentential formula in x is logically true, then any particular substitution instance of it is a true sentence. In particular
then: 'for all x, if x is an elephant, then x is the same colour' is true. Now it is manifestly axiomatic that white elephants exist (for
proof by blatant assertion consult Mark Twain 'The Stolen White Elephant'). Therefore all elephants are white. By corollary 1 everything is white.
Theorem 2. Alexander the Great did not exist and he had an infinite number of limbs.
Proof. We prove this theorem in two parts. First we note the obvious fact that historians always tell the truth (for historians always take a stand, and therefore they cannot lie). Hence we have the historically true sentence, 'If Alexander the Great existed, then he rode a black horse Bucephalus.' But we know by corollary 2 everything is white; hence Alexander could not have ridden a black horse. Since the consequent of the conditional is false, in order for the whole statement to be true the antecedent must be false. Hence Alexander the Great did not exist.
We have also the historically true statement that Alexander was warned by an oracle that he would meet death if he crossed a certain river. He had two legs; and 'forewarned is four-armed.' This gives him six limbs, an even number, which is certainly an odd number of limbs for a man. Now the only number which is even and odd is infinity; hence Alexander had an infinite number of limbs. We have thus proved that Alexander the Great did not exist and that he had an infinite number of limbs.
*rot werd*
