This is from _A Random Walk in Science_ (by Joel E. Cohen?):

To illustrate the various methods of proof we give an example of a

logical system.

THE PEJORATIVE CALCULUS

Lemma 1. All horses are the same colour.

(Proof by induction)

Proof. It is obvious that one horse is the same colour. Let us assume

the proposition P(k) that k horses are the same colour and use this to

imply that k+1 horses are the same colour. Given the set of k+1 horses,

we remove one horse; then the remaining k horses are the same colour,

by hypothesis. We remove another horse and replace the first; the k

horses, by hypothesis, are again the same colour. We repeat this until

by exhaustion the k+1 sets of k horses have been shown to be the same

colour. It follows that since every horse is the same colour as every

other horse, P(k) entails P(k+1). But since we have shown P(1) to be

true, P is true for all succeeding values of k, that is, all horses are

the same colour.

Theorem 1. Every horse has an infinite number of legs.

(Proof by intimidation.)

Proof. Horses have an even number of legs. Behind they have two legs

and in front they have fore legs. This makes six legs, which is cer-

tainly an odd number of legs for a horse. But the only number that is

both odd and even is infinity. Therefore horses have an infinite num-

ber of legs. Now to show that this is general, suppose that somewhere

there is a horse with a finite number of legs. But that is a horse of

another colour, and by the lemma that does not 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 uni-

versally-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 parti-

cular 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 Ele-

phant'). 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 conse-

quent 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.

- emma: 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.... - Lemma: 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.... - The ark lands after The Flood. Noah lets all the animals out.

Says, "Go and multiply." Several months pass. Noah decides to check up on the animals.... - Proof By Intimidation
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A Horse has an infinite number of legs.

A horse has two legs in back and forelegs in front.... - Facts most people are content to live without knowing

A duck's quack doesn't echo, and no one can explain why.... - Proof By Intimidation
----- -- ------------
A Horse has an infinite number of legs.

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