XLIX. An argument, as Crinis says, is that which is composed of a lemma or major premiss, an assumption or minor premiss, and a conclusion; as for instance this, “If it is day, it is light;” “But it is day, therefore it is light.” For the lemma, or major premiss, is, “If it is day, it is light.” The assumption, or minor premiss, is, “It is day.” The conclusion follows, “Therefore it is light.” The mode of a proposition is, as it were, a figure of an argument, as for instance, such as this, “If it is the first, it is the second; but it is the first, therefore it is the second.”
A conditional syllogism is that which is composed of both the preceding arguments; as for instance, “If Plato is alive, Plato breathes; but the first fact is so, therefore so is the second.” And this conditional syllogism has been introduced for the sake, in long and complex sentences, of not being forced to repeat the assumption, as it was a long one, and also the conclusion; but of being able, instead, to content one’s self with summing it up briefly thus, “The first case put is true, therefore so is the second.”
Of arguments, some are conclusive, others are inconclusive. Those are inconclusive which are such, that the opposite of the conclusion drawn in them is not necessarily incompatible with the connection of the premisses. As for instance, such arguments as these, “If it is day, it is light; but it is day, therefore, Dion is walking.” But of conclusive arguments, some are called properly by the kindred name conclusions, and some are called syllogistic arguments. Those then are syllogistic which are either such as do not admit of demonstration, or such as are brought to an indemonstrable conclusion, according to some one or more propositions; such for instance as the following: “If Dion walks, then Dion is in motion.” Those are conclusive, which infer their conclusion specially, and not syllogistically; such for instance, as this, “The proposition it is both day and night is false. Now it is day; therefore, it is not night.”
Those again, are unsyllogistic arguments which have an air of probability about them, and a resemblance to syllogistic ones, but which still do not lead to the deduction of proper conclusions. As for instance, “If Dion is a horse, Dion is an animal; but Dion is not a horse, therefore, Dion is not an animal.”