XXIX.  But all argumentation, which can be derived from those topics which we have mentioned, ought to be either probable or unavoidable.  Indeed, to define it in a few words, argumentation appears to be an invention of some sort, which either shows something or other in a probable manner, or demonstrates it in an irrefutable one.  Those things are demonstrated irrefutably which can neither be done nor proved in any other manner whatever than that in which they are stated; in this manner:—­“If she has had a child, she has lain with a man.”  This sort of arguing, which is conversant with irrefutable demonstration, is especially used in speaking in the way of dilemma, or enumeration, or simple inference.

Dilemma is a case in which, whichever admission you make, you are found fault with.  For example:—­“If he is a worthless fellow, why are you intimate with him?  If he is an excellent man, why do you accuse him?” Enumeration is a statement in which, when many matters have been stated and all other arguments invalidated, the one which remains is inevitably proved; in this manner:—­“It is quite plain that he was slain by this man, either because of his enmity to him, or some fear, or hope, which he had conceived, or in order to gratify some friend of his; or, if none of these alternatives are true, then that he was not slain by him at all; for a great crime cannot be undertaken without a motive.  But he had no quarrel with him, nor fear of him, nor hope of any advantage to be gained by his death, nor did his death in the least concern any friend of his.  It remains, therefore, that he was not slain by him at all.”  But a simple inference is declared from a necessary consequence, in this way:—­“If you say that I did that at that time, at that time I was beyond the sea; it follows, that I not only did not do what you say I did, but that it was not even possible for me to have done it.”  And it will be desirable to look to this very carefully, in order that this sort of inference may not be refuted in any manner, so that the proof may not only have some sort of argument in it, and some resemblance to an unavoidable conclusion, but that the very argument itself may proceed on irrefutable reasons.

But that is probable which is accustomed generally to take place, or which depends upon the opinion of men, or which contains some resemblance to these properties, whether it be false or true.  In that description of subject the most usual probable argument is something of this sort:—­“If she is his mother, she loves her son.”  “If he is an avaricious man, he neglects his oath.”  But in the case which depends mainly on opinion, probable arguments are such as this:  “That there are punishments prepared in the shades below for impious men.”—­“That those men who give their attention to philosophy do not think that there are gods.”

XXX.  But resemblance is chiefly seen in things which are contrary to one another, or equal to one another, and in those things which fall under the same principle.  In things contrary to one another, in this manner:—­“For if it is right that those men should be pardoned who have injured me unintentionally, it is also fitting that one should feel no gratitude towards those who have benefited me because they could not help it.”