Zeno · 5

A term is, as stated by Antipater in his first book On Terms, a word which, when a sentence is analysed, is uttered with complete meaning; or, according to Chrysippus in his book On Definitions, is a rendering back one’s own.[34] Delineation is a statement which brings one to a knowledge of the subject in outline, or it may be called a definition which embodies the force of the definition proper in a simpler form. Genus (in logic) is the comprehension in one of a number of inseparable objects of thought: e.g. Animal; for this includes all particular animals.

61. A notion or object of thought is a presentation to the intellect, which though not really substance nor attribute is quasi-substance or quasi-attribute.[35] Thus an image of a horse may rise before the mind, although there is no horse present.

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).”

62. 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 nor false; whereas Chrysippus takes its subject to be signs and things signified. Such then is the gist of what the Stoics say in their theory of language.

63. 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.[36]

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.

64. 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 [37], as e.g. “to sail through rocks.”[38] 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”; while reversed are those constructed with the passive voice, as “I am heard,” “I am seen.” Neutral are such as correspond to neither of these, as “thinks,” “walks.” Reflexive predicates are those among the passive, which, although in form passive, are yet active operations,[39] as “he gets his hair cut”:[40] 65. 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. 66. 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; but you must express the answer in words, “He lives in this or that place.”

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

Go thou to the waters of Inachus.[41]

An adjurative utterance is something... A vocative utterance is something the use of which implies that you are addressing some one; for instance:

Most glorious son of Atreus, Agamemnon, lord of men.[42]

A quasi-proposition is that which, having the enunciation of a judgement, yet in consequence of the intensified tone or emotion of one of its parts falls outside the class of judgements proper, e.g.

Yea, fair indeed the Parthenon!

How like to Priam’s sons the cowherd is![43]

68. 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?

Interrogations, inquiries and the like are neither true nor false, whereas judgements (or propositions) are always either true or false.

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. 69. They may, that is, consist either of a single ambiguous proposition, e.g. “If it is day, it is day,” or of more than one proposition, e.g. “If it is day, it is light.”

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.

70. 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.”

71. 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, “If it is day, it is light.” An inferential proposition according to Crinis in his Art of Dialectic is one which is introduced by the conjunction “Since” and consists of an initial proposition and a conclusion; for example, “Since it is day-time, it is light.” This conjunction guarantees both that the second thing follows from the first and that the first is really a fact. 72. 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.” 73. 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 proposition is false, if the contradictory of its conclusion does not conflict with the premiss, e.g. “If it is day, Dion is walking.” For the statement “Dion is not walking” does not conflict with the premiss “It is day.”

74. 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.” 75. 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 false or, while it may admit of being false, is prevented from being false by circumstances external to itself, as “Virtue is beneficial.” Not necessary is that which, while true, yet is capable of being false if there are no external conditions to prevent, e.g. “Dion is walking.” 76. 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.”

77. 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.