I. The modes are (1) ad rem, (2) ad hominem or ex concessis. That is to say: We may show either that the proposition is not in accordance with the nature of things, i.e., with absolute, objective truth; or that it is inconsistent with other statements or admissions of our opponent, i.e., with truth as it appears to him. The latter mode of arguing a question produces only a relative conviction, and makes no difference whatever to the objective truth of the matter.
II. The two courses that we may pursue are (1) the direct, and (2) the indirect refutation. The direct attacks the reason for the thesis; the indirect, its results. The direct refutation shows that the thesis is not true; the indirect, that it cannot be true.
The direct course admits of a twofold procedure. Either we may show that the reasons for the statement are false (nego majorem, minorem); or we may admit the reasons or premisses, but show that the statement does not follow from them (nego consequentiam); that is, we attack the conclusion or form of the syllogism.
The direct refutation makes use either of the diversion or of the instance.
(a) The diversion.—We accept our opponent’s proposition as true, and then show what follows from it when we bring it into connection with some other proposition acknowledged to be true. We use the two propositions as the premisses of a syllogism giving a conclusion which is manifestly false, as contradicting either the nature of things, or other statements of our opponent himself; that is to say, the conclusion is false either ad rem or ad hominem. Consequently, our opponent’s proposition must have been false; for, while true premisses can give only a true conclusion, false premisses need not always give a false one.
[Footnote 1: If it is in direct contradiction with a perfectly undoubted, truth, we have reduced our opponent’s position ad absurdum.]
[Footnote 2: Socrates, in Hippia Maj. et alias.]
(b) The instance, or the example to the contrary.—This consists in refuting the general proposition by direct reference to particular cases which are included in it in the way in which it is stated, but to which it does not apply, and by which it is therefore shown to be necessarily false.
Such is the framework or skeleton of all forms of disputation; for to this every kind of controversy may be ultimately reduced. The whole of a controversy may, however, actually proceed in the manner described, or only appear to do so; and it may be supported by genuine or spurious arguments. It is just because it is not easy to make out the truth in regard to this matter, that debates are so long and so obstinate.