An adjunctive proposition is correct, which begins with a true premiss, and ends in a consequence which follows of necessity, as for instance, “Since it is day, the sun is above the earth.” But it is incorrect when it either begins with a false premiss, or ends with a consequence which does not follow properly; as for instance, “Since it is night, Dion is walking,” for this may be said in the day-time.
A causal proposition is correct, when it begins with a true premiss, and ends in a consequence which necessarily follows from it, but yet does not have its premiss reciprocally consequent upon its conclusion; as for instance, “Because it is day, it is light.” For the fact of its being light, is a necessary consequence of its being day; but the fact of its being day, is not necessarily a consequence of its being light. A causal proposition is incorrect, which either begins with a false premiss, or ends with a conclusion that does not follow from it, or which has a premiss which does not correspond to the conclusion; as for instance, “Because it is night, Dion is walking.”
A proposition is persuasive, which leads to the assent of the mind, as for instance, “If she brought him forth, she is his mother.” But still this is a falsehood, for a hen is not the mother of an egg. Again, there are some propositions which are possible, and some which are impossible; and some which are necessary, and some which are not necessary. That is possible, which is capable of being true, since external circumstances are no hindrance to its being true; as for instance, “Diocles lives.” And that is impossible which is not capable of being true; as for instance, “The earth flies.” That is necessary which, being true, is not capable of being false; or perhaps is intrinsically capable of being false, but still has external circumstances which hinder its being false, as for instance, “Virtue profits a man.” That again, is not necessary, which is true, but which has a capacity of being false, though external circumstances offer no hindrance to either alternative; as for instance, “Dion walks.”
That is a reasonable or probable proposition, which has a great preponderance of opportunities in favour of its being true; as for instance, “I shall be alive to-morrow.” And there are other different kinds of propositions and conversions of them, from true to false, and re-conversions again; concerning which we must speak at some length.
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.”
Again, of arguments, some are true, and some are false. Those are true which deduce a conclusion from true premisses, as, for instance, “If virtue profits, then vice injures.” And those are false which have some falsehood in their premisses, or which are inconclusive; as, for instance, “If it is day, it is light; but it is day, therefore, Dion is alive.”
There are also arguments which are possible, and others which are impossible; some likewise which are necessary, and others which are not necessary. There are too, some which are not demonstrated from their not standing in need of demonstration, and these are laid down differently by different people; but Chrysippus enumerates five kinds, which serve as the foundation for every kind of argument; and which are assumed in conclusive arguments properly so called, and in syllogisms, and in modes.