Vitae philosophorum

Symbolical argument is a combination of full argument and mood; e.g. If Plato is alive, he breathes; but the first is true, therefore the second is true. This mode of argument was introduced in order that when dealing with long complex arguments we should not have to repeat the minor premiss, if it be long, and then state the conclusion, but may arrive at the conclusion as concisely as possible: if A, then B.

Of arguments some are conclusive, others inconclusive. Inconclusive are such that the contradictory of the conclusion is not incompatible with combination

Of conclusive some are denoted by the common name of the whole class, conclusive proper, others are called syllogistic. The syllogistic are such as either do not admit of, or are reducible to such as do not admit of, immediate proof in respect of one or more of the premisses; e.g. If Dion walks, then Dion is in motion; but Dion is walking, therefore Dion is in motion. Conclusive specifically are those which draw conclusions, but not by syllogism; e.g. the statement It is both day and night is false: now it is day; therefore it is not night. Arguments not syllogistic are those which plausibly resemble syllogistic arguments, but are not cogent proof; e.g. If Dion is a horse, he is an animal; but Dion is not a horse, therefore he is not an animal.

Further, arguments may be divided into true and false. The former draw their conclusions by means of true premisses; e.g. If virtue does good, vice does harm; but virtue does good, therefore vice does harm.[*](The example is badly chosen, confusing contrary with contradictory.) Those are false which have error in the premisses or are inconclusive; e.g. If it is day, it is light; but it is day, therefore Dion is alive. Arguments may also be divided into possible and impossible, necessary and not necessary. Further, there are statements which are indemonstrable because they do not need demonstration; they are employed in the construction of every argument. As to the number of these, authorities differ; Chrysippus makes them five. These are assumed alike in reasoning

The first kind of indemonstrable statement is that in which the whole argument is constructed of a hypothetical proposition and the clause with which the hypothetical proposition begins, while the final clause is the conclusion; as e.g. If the first, then the second; but the first is, therefore the second is.[*](Cf. Sext. Emp. Pyrrh. Hyp. ii. 157 sq.) The second is that which employs a hypothetical proposition and the contradictory of the consequent, while the conclusion is the contradictory of the antecedent; e.g. If it is day, it is light; but it is night, therefore it is not day. Here the minor premiss is the contradictory of the consequent; the conclusion the contradictory of the antecedent. The third kind of indemonstrable employs a conjunction of negative propositions for major premiss and one of the conjoined propositions for minor premiss, concluding thence the contradictory of the remaining proposition; e.g. It is not the case that Plato is both dead and alive; but he is dead, therefore Plato is not alive.

The fourth kind employs a disjunctive proposition and one of the two alternatives in the disjunction as premisses, and its conclusion is the contradictory of the other alternative; e.g. Either A or B; but A is, therefore B is not. The fifth kind is that in which the argument as a whole is constructed of a disjunctive proposition and the contradictory of one of the alternatives in the disjunction, its conclusion being the other alternative; e.g. Either it is day or it is night; but it is not night, therefore it is day.

From a truth a truth follows, according to the Stoics, as e.g. It is light from It is day; and