1. One line of positive proof is based upon consideration of the opposite of the thing in question. Observe whether that opposite has the opposite quality. If it has not, you refute the original proposition; if it has, you establish it. E.g. 'Temperance is beneficial; for licentiousness is hurtful'. Or, as in the Messenian speech, 'If war is the cause of our present troubles, peace is what we need to put things right again'. Or-
For if not even evil-doers should Anger us if they meant not what they did, Then can we owe no gratitude to such As were constrained to do the good they did us.
Or-Since in this world liars may win belief, Be sure of the opposite likewise-that this world Hears many a true word and believes it not.
2. Another line of proof is got by considering some modification of the key-word, and arguing that what can or cannot be said of the one, can or cannot be said of the other: e.g. 'just' does not always mean 'beneficial', or 'justly' would always mean 'beneficially', whereas it is not desirable to be justly put to death.
3. Another line of proof is based upon correlative ideas. If it is true that one man noble or just treatment to another, you argue that the other must have received noble or just treatment; or that where it is right to command obedience, it must have been right to obey the command. Thus Diomedon, the tax-farmer, said of the taxes: 'If it is no disgrace for you to sell them, it is no disgrace for us to buy them'. Further, if 'well' or 'justly' is true of the person to whom a thing is done, you argue that it is true of the doer. But it is possible to draw a false conclusion here. It may be just that A should be treated in a certain way, and yet not just that he should be so treated by B. Hence you must ask yourself two distinct questions:
(1) Is it right that A should be thus treated? (2) Is it right that B should thus treat him? and apply your results properly, according as your answers are Yes or No. Sometimes in such a case the two answers differ: you may quite easily have a position like that in the Alcmaeon of Theodectes:
And was there none to loathe thy mother's crime? to which question Alcmaeon in reply says, Why, there are two things to examine here.
And when Alphesiboea asks what he means, he rejoins:
They judged her fit to die, not me to slay her.
Again there is the lawsuit about Demosthenes and the men who killed Nicanor; as they were judged to have killed him justly, it was thought that he was killed justly. And in the case of the man who was killed at Thebes, the judges were requested to decide whether it was unjust that he should be killed, since if it was not, it was argued that it could not have been unjust to kill him.
4. Another line of proof is the 'a fortiori'. Thus it may be argued that if even the gods are not omniscient, certainly human beings are not. The principle here is that, if a quality does not in fact exist where it is more likely to exist, it clearly does not exist where it is less likely. Again, the argument that a man who strikes his father also strikes his neighbours follows from the principle that, if the less likely thing is true, the more likely thing is true also; for a man is less likely to strike his father than to strike his neighbours. The argument, then, may run thus. Or it may be urged that, if a thing is not true where it is more likely, it is not true where it is less likely; or that, if it is true where it is less likely, it is true where it is more likely: according as we have to show that a thing is or is not true. This argument might also be used in a case of parity, as in the lines:
Thou hast pity for thy sire, who has lost his sons:
Hast none for Oeneus, whose brave son is dead?
And, again, 'if Theseus did no wrong, neither did Paris'; or 'the sons of Tyndareus did no wrong, neither did Paris'; or 'if Hector did well to slay Patroclus, Paris did well to slay Achilles'. And 'if other followers of an art are not bad men, neither are philosophers'. And 'if generals are not bad men because it often happens that they are condemned to death, neither are sophists'. And the remark that 'if each individual among you ought to think of his own city's reputation, you ought all to think of the reputation of Greece as a whole'.
5. Another line of argument is based on considerations of time. Thus Iphicrates, in the case against Harmodius, said, 'if before doing the deed I had bargained that, if I did it, I should have a statue, you would have given me one. Will you not give me one now that I have done the deed? You must not make promises when you are expecting a thing to be done for you, and refuse to fulfil them when the thing has been done.' And, again, to induce the Thebans to let Philip pass through their territory into Attica, it was argued that 'if he had insisted on this before he helped them against the Phocians, they would have promised to do it. It is monstrous, therefore, that just because he threw away his advantage then, and trusted their honour, they should not let him pass through now'.
6. Another line is to apply to the other speaker what he has said against yourself. It is an excellent turn to give to a debate, as may be seen in the Teucer. It was employed by Iphicrates in his reply to Aristophon. 'Would you', he asked, 'take a bribe to betray the fleet?' 'No', said Aristophon; and Iphicrates replied, 'Very good: if you, who are Aristophon, would not betray the fleet, would I, who am Iphicrates?' Only, it must be recognized beforehand that the other man is more likely than you are to commit the crime in question.
Otherwise you will make yourself ridiculous; it is Aristeides who is prosecuting, you cannot say that sort of thing to him. The purpose is to discredit the prosecutor, who as a rule would have it appear that his character is better than that of the defendant, a pretension which it is desirable to upset. But the use of such an argument is in all cases ridiculous if you are attacking others for what you do or would do yourself, or are urging others to do what you neither do nor would do yourself.