`Certainly there might. He, also, had better take to football.'

`And neither of these readers,' the Tortoise continued, `is as yet under any logical necessity to accept Z as true?'

`Quite so,' Achilles assented.

`Well, now, I want you to consider me as a reader of the second kind, and to force me, logically, to accept Z as true.'

`A tortoise playing football would be--' Achilles was beginning.

`--an anomaly, of course,' the Tortoise hastily interrupted. `Don't wander from the point. Let's have Z first, and football afterwards!'

`I'm to force you to accept Z, am I?' Achilles said musingly. `And your present position is that you accept A and B, but you don't accept the Hypothetical--'

`Let's call it C,' said the Tortoise.

`--but you don't accept:

(C) If A and B are true, Z must be true.'

`That is my present position,' said the Tortoise.

`Then I must ask you to accept C.'

`I'll do so,' said the Tortoise, `as soon as you've entered it in that note-book of yours. What else have you got in it?'

`Only a few memoranda,' said Achilles, nervously fluttering the leaves: `a few memoranda of--of the battles in which I have distinguished myself!'

`Plenty of blank leaves, I see!' the Tortoise cheerily remarked. `We shall need them all!' (Achilles shuddered.) `Now write as I dictate:

(A) Things that are equal to the same are equal to each other.

(B) The two sides of this triangle are things that are equal to the same.

(C) If A and B are true, Z must be true.

(Z) The two sides of this Triangle are equal to each other.'

`You should call it D, not Z,' said Achilles. `It comes next to the other three. If you accept A and B and C, you must accept Z.'

`And why must I?'

`Because it follows logically from them. If A and B and C are true, Z must be true. You don't dispute that, I imagine?'

`If A and B and C are true, Z must be true,' the Tortoise thoughtfully repeated. `That's another Hypothetical, isn't it? And, if I failed to see its truth, I might accept A and B and C, and still not accept Z, mightn't I?'