The Lives and Opinions of Eminent Philosophers, Diogenes Laërtius [the gingerbread man read aloud TXT] 📗

for instance “It both is day, and it is light.” That is a disjunctive proposition which is disconnected by the disjunctive conjunction, “or” (ἤτοι), as for instance, “It is either day or night.” And this proposition professes that one or other of these propositions is false. That is a causal proposition which is connected by the word “because;” as for instance “Because it is day, it is light.” For the first is, as it were, the cause of the second. That is an augmentative proposition which explains the greater, which is construed with an augmentative particle, and which is placed between the two members of the proposition, as for instance “It is rather day than night.” The diminutive proposition is, in every respect, the exact contrary of the preceding one; as for instance “It is less night than day.” Again, at times, axioms or propositions are opposed to one another in respect of their truth and falsehood, when one is an express denial of the other; as for instance “It is day” and “It is not day.”

Again, a conjunctive proposition is correct when it is such that the opposite of the conclusion is contradictory of the premise; as for instance the proposition “If it is day, it is light,” is true; for “It is not light,” which is the opposite to the conclusion expressed, is contradictory to the premise “It is day.” And a conjunctive proposition is incorrect when it is such that the opposite of the conclusion is not inconsistent with the premise, as for instance “If it is day, Dion is walking.” For the fact that Dion is not walking is not contradictory of the premise “It is day.”

An adjunctive proposition is correct which begins with a true premise 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 premise 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 daytime.

A causal proposition is correct when it begins with a true premise and ends in a consequence which necessarily follows from it, but yet does not have its premise 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 premise or ends with a conclusion that does not follow from it, or which has a premise 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 favor of its being true; as for instance, “I shall be alive tomorrow.” 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.

An argument, as Crinis says, is that which is composed of a lemma or major premise, an assumption or minor premise, 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 premise, is “If it is day, it is light.” The assumption, or minor premise, 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 oneself 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 premises. 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