Vitae philosophorum

A notion or object of thought is a presentation to the intellect, which though not really substance nor

Species is that which is comprehended under genus: thus Man is included under Animal. The highest or most universal genus is that which, being itself a genus, has no genus above: namely, reality or the real; and the lowest and most particular species is that which, being itself a species, has no species below it, e.g. Socrates.

Division of a genus means dissection of it into its proximate species, thus: Animals are either rational or irrational (dichotomy). Contrary division dissects the genus into species by contrary qualities: for example, by means of negation, as when all things that are are divided into good and not good. Subdivision is division applied to a previous division: for instance, after saying, Of things that are some are good, some are not good, we proceed, and of the not good some are bad, some are neither good nor bad (morally indifferent).

Partition in logic is (according to Crinis) classification or distribution of a genus under heads: for instance, Of goods some are mental, others bodily.

Verbal ambiguity arises when a word properly, rightfully, and in accordance with fixed usage denotes two or more different things, so that at one and the same time we may take it in several distinct senses: e.g. in Greek, where by the same verbal expression may be meant in the one case that A house has three times fallen, in the other that a dancing-girl has fallen.

Posidonius defines Dialectic as the science dealing with truth, falsehood, and that which is neither true

To the department dealing with things as such and things signified is assigned the doctrine of expressions, including those which are complete in themselves, as well as judgements and syllogisms and that of defective expressions comprising predicates both direct and reversed.[*](Direct Predicate answers to our Active Verb, Predicate reversed to our Passive; cf. supra, 43.)

By verbal expression they mean that of which the content corresponds to some rational presentation. Of such expressions the Stoics say that some are complete in themselves and others defective. Those are defective the enunciation of which is unfinished, as e.g. writes, for we inquire Who? Whereas in those that are complete in themselves the enunciation is finished, as Socrates writes. And so under the head of defective expressions are ranged all predicates, while under those complete in themselves fall judgements, syllogisms, questions, and inquiries.

A predicate is, according to the followers of Apollodorus, what is said of something; in other words, a thing associated with one or more subjects; or, again, it may be defined as a defective expression which has to be joined on to a nominative case in order to yield a judgement. Of predicates some are adjectival [and so have personal subjects], as e.g. to sail through rocks.[*](We should expect τὰ δὲ παρασυμβάματα to follow (cf. Luc. Vit. Auct. 21). By παρασύμβαμα is meant an impersonal verb with subject in oblique case, as μέλει μοι. For other conjectures see Zeller, Phil. der Gr. iii. 13, 89 note 2, 90.) Again, some predicates are direct, some reversed, some neither. Now direct predicates are those that are constructed with one of the oblique cases, as hears, sees, converses;

for here the agent includes himself in the sphere of his action. The oblique cases are genitive, dative, and accusative.

A judgement is that which is either true or false, or a thing complete in itself, capable of being denied in and by itself, as Chrysippus says in his Dialectical Definitions: A judgement is that which in and by itself can be denied or affirmed, e.g. It is day, Dion is walking. The Greek word for judgement (ἀξίωμα ) is derived from the verb ἀξιοῦν, as signifying acceptance or rejection; for when you say It is day, you seem to accept the fact that it is day. Now, if it really is day, the judgement before us is true, but if not, it is false.

There is a difference between judgement, interrogation, and inquiry, as also between imperative, adjurative, optative, hypothetical, vocative, whether that to which these terms are applied be a thing or a judgement. For a judgement is that which, when we set it forth in speech, becomes an assertion, and is either false or true: an interrogation is a thing complete in itself like a judgement but demanding an answer, e.g. Is it day? and this is so far neither true nor false. Thus It is day is a judgement; Is it day? an interrogation. An inquiry is something to which we cannot reply by signs, as you can nod Yes to an interrogation;

An imperative is something which conveys a command: e.g.

Go thou to the waters of Inachus.[*](Nauck, T.G.F.2, Adesp. 177; cf. Galen, xiii. p. 363 K.)

Most glorious son of Atreus, Agamemnon, lord of men.[*](Iliad ix. 96.)

Yea, fair indeed the Parthenon!
1. How like to Priam’s sons the cowherd is

There is also, differing from a proposition or judgement, what may be called a timid suggestion, the expression of which leaves one at a loss, e.g.

Can it be that pain and life are in some sort akin?

The followers of Chrysippus, Archedemus, Athenodorus, Antipater and Crinis divide propositions into simple and not simple. Simple are those that consist of one or more propositions which are not ambiguous, as It is day. Not simple are those that consist of one or more ambiguous propositions.

They

With simple propositions are classed those of negation, denial, privation, affirmation, the definitive and the indefinitive; with those that are not simple the hypothetical, the inferential, the coupled or complex, the disjunctive, the causal, and that which indicates more or less. An example of a negative proposition is It is not day. Of the negative proposition one species is the double negative. By double negative is meant the negation of a negation, e.g. It is not not-day. Now this presupposes that it is day.

A denial contains a negative part or particle and a predication: such as this, No one is walking. A privative proposition is one that contains a privative particle reversing the effect of a judgement, as, for example, This man is unkind. An affirmative or assertory proposition is one that consists of a noun in the nominative case and a predicate, as Dion is walking. A definitive proposition is one that consists of a demonstrative in the nominative case and a predicate, as This man is walking. An indefinitive proposition is one that consists of an indefinite word or words and a predicate, e.g. Some one is walking, or There’s some one walking; He is in motion.

Of propositions that are not simple the hypothetical, according to Chrysippus in his Dialectics and Diogenes in his Art of Dialectic, is one that is formed by means of the conditional conjunction If. Now this conjunction promises that the second of two things follows consequentially upon the first, as, for instance,

A coupled proposition is one which is put together by certain coupling conjunctions, e.g. It is day-time and it is light. A disjunctive proposition is one which is constituted such by the disjunctive conjunction Either, as e.g. Either it is day or it is night. This conjunction guarantees that one or other of the alternatives is false. A causal proposition is constructed by means of the conjunction Because, e.g. Because it is day, it is light. For the first clause is, as it were, the cause of the second. A proposition which indicates more or less is one that is formed by the word signifying rather and the word than in between the clauses, as, for example, It is rather day-time than night.

Opposite in character to the foregoing is a proposition which declares what is less the fact, as e.g. It is less or not so much night as day. Further, among propositions there are some which in respect of truth and falsehood stand opposed to one another, of which the one is the negative of the other, as e.g. the propositions It is day and It is not day. A hypothetical proposition is therefore true, if the contradictory of its conclusion is incompatible with its premiss, e.g. If it is day, it is light. This is true. For the statement It is not light, contradicting the conclusion, is incompatible with the premiss It is day. On the other hand, a hypothetical

An inferential proposition is true if starting from a true premiss it also has a consequent conclusion, as e.g. Since it is day, the sun is above the horizon. But it is false if it starts from a false premiss or has an inconsequent conclusion, as e.g. Since it is night, Dion is walking, if this be said in day-time. A causal proposition is true if its conclusion really follows from a premiss itself true, though the premiss does not follow conversely from the conclusion, as e.g. Because it is day, it is light, where from the it is day the it is light duly follows, though from the statement it is light it would not follow that it is day. But a causal proposition is false if it either starts from a false premiss or has an inconsequent conclusion or has a premiss that does not correspond with the conclusion, as e.g. Because it is night, Dion is walking.

A probable judgement is one which induces to assent, e.g. Whoever gave birth to anything, is that thing’s mother. This, however, is not necessarily true; for the hen is not mother of an egg.

Again, some things are possible, others impossible; and some things are necessary, others are not necessary. A proposition is possible which admits of being true, there being nothing in external circumstances to prevent it being true, e.g. Diocles is alive. Impossible is one which does not admit of being true, as e.g. The earth flies. That is necessary which besides being true does not admit of being

A reasonable proposition is one which has to start with more chances of being true than not, e.g. I shall be alive to-morrow.

And there are other shades of difference in propositions and grades of transition from true to false— and conversions of their terms—which we now go on to describe broadly.

An argument, according to the followers of Crinis, consists of a major premiss, a minor premiss, and a conclusion, such as for example this: If it is day, it is light; but it is day, therefore it is light. Here the sentence If it is day, it is light is the major premiss, the clause it is day is the minor premiss, and therefore it is light is the conclusion. A mood is a sort of outline of an argument, like the following: If the first, then the second; but the first is, therefore the second is.

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.