De nuptiis Philologiae et Mercurii, Book IV (De arte dialectica), part 3 of 3 (about §§ 389-423)
The third person, however, is not of man only but of other things also, and when it is said it is not at once understood, unless perhaps something is said of God which can be understood of him alone, as when we say pluit (it rains): it can then be true or false, though we add no noun; for it is known who rains. But when we say disputat (he disputes), though it already signifies something, it cannot be called true or false if a noun is not added. And although this can be understood only of a man, because it cannot be said of one only, the noun must necessarily be supplied. And resistit (he resists), when we say it, is a third person of the verb and demands a noun not of man only but of anything that can resist. The first and second persons, then, can be understood of man only, and said alone can be called true or false, because with them nouns are also understood. The third, however, not every one can be said alone, nor is it understood of man only. What, then, is joined from the nominative case of a noun and the third person of a verb is called a PROPOSITION, so that it is now necessarily either true or false or doubtful. For “man is an animal” we all judge true, and “every animal is a man” we all judge false. “He disputes” is doubtful: although he necessarily either disputes or does not dispute, yet to us it is doubtful. We understand that one of these is necessary, but we do not know which is true. Where there are those verbs which are called impersonal, the sentence is not completed from the nominative case but takes other cases: as when disputatur is said, the sentence is complete if you add the ablative, that is, a Cicerone. And when paenitet is said, the sentence is complete if you add the accusative, that is, Ciceronem. [And there are many others.] This, however, is agreed: that personal verbs do not complete a sentence except with the nominative case and the third person of the verb. There are also sentences which, though they consist of noun and verb, cannot be affirmed or denied. These some have been pleased to call not propositions but ELOQUIA (utterances), such as the imperative mood. When we say curre (run), it is already a full sentence. For what you say can not only be understood but also done. Yet it cannot be denied. For he who says “do not run” does not deny it. For this is not opposed to what was said, curre, so that one is true and the other false. [So that a question may arise. For about affirmation and negation a question undoubtedly arises, as “he runs” and “he does not run”: the question is whether he runs. But “run” and “do not run” raise no question whether he runs. No question can be understood here as to whether he ought to run. For this is born from affirmation and negation, “he ought to run” and “he ought not to run.” The optative mood does this too. For while it is a full sentence when we say “would that I might write,” “would that I might not write,” no question can arise from it whether he writes. But there are many such; let these suffice for example.] What is joined, then, from noun and verb, if the noun be full and the verb full, necessarily makes a sentence but does not necessarily make a proposition. For if it is [what already is], it can be affirmed and denied. And we said above that many things are said in a full sentence which yet cannot be affirmed and denied. A full proposition, then, is “every man is an animal”; and although nature requires that first the noun and then the verb be said, as has been said, it does not cease to be a true proposition even if you say “is an animal every man.” Whatever is added to this sentence, one must carefully see to which part it is added. For there are two parts of a proposition. That which is in the noun is called SUBJECTIVE, that in the verb DECLARATIVE. For what a thing is is subjoined, and what can be understood of it is declared. When we say, then, “Cicero disputes,” if there is added to this sentence “in the Tusculan villa,” it is added declaratively; if “a Roman,” subjectively. Likewise if “prudently and copiously” is added, declaratively. Likewise if it is said “with Cato,” it was added declaratively. Whatever is added to the nominative case, then, is added subjectively. Whatever is added declaratively is added in various cases and modes. For to the subjective other cases cannot be added; to the declarative none but others, with the nominative excepted. This, however, should be known: that it can happen that a verb is in the subjective, a noun in the declarative, but the verb in the subjective in such a way as to hold with it some pronoun in place of a noun. So also the noun is in the declarative so as to hold with it some verb by which it fills its place. As if we say “he who disputes is Cicero”: “who disputes” is subjective, “is Cicero” declarative, but the pronoun makes the one subjective, the verb the other declarative. In this part, then, we say how they are joined and yet cannot make a full sentence; and if they do, how sentences, though full, are not subject to falsity and truth, and how one arrives at what is now not only a full sentence but also necessarily true or false.
The third part follows, in which we must now speak of propositions themselves, to the understanding of which we came in the part above. Propositions, then, have differences in twos, in quantity and in quality. The difference of QUANTITY is that some are universal, some particular, some indefinite. UNIVERSAL, as “every man is an animal.” PARTICULAR, as “a certain man walks.” INDEFINITE, as “man walks.” What we say indefinitely, then, we necessarily take particularly, not necessarily universally. And since that is chiefly to be enumerated which has a safe understanding, the indefinite is taken for the particular. There will be, then, two differences in quantity, in that one proposition is universal, another particular. In quality likewise two, of which one is AFFIRMATIVE, the other NEGATIVE. The affirmative is “every pleasure is a good,” the negative, “every pleasure is not a good.”
Conversion, then, does not necessarily follow the universal affirmative. For it is not so that if every man is an animal, every animal is a man. But conversion necessarily follows the universal negative. For if no pleasure is a good, no good is a pleasure; and if no man is a mute animal, no mute animal is a man. The particular affirmative necessarily has conversion. For if a certain man is an animal, a certain animal is a man. The particular negative has no necessary conversion. For it is not so that if a certain animal is not rational, a certain rational thing is not an animal. The universal affirmative and the particular negative, then, do not necessarily run back. But the universal negative and the particular affirmative are necessarily converted, yet so that, the conversion made, the negation remains in the declarative part. For conversion is made so that what was the declarative part becomes the subjective. When I say, then, “every pleasure is not a good,” “every pleasure” is subjective, “is not a good” declarative. If I convert it, “every good is not a pleasure,” what was declarative has indeed become subjective, but the negation holds this part, which has become declarative. And if I wish to say it thus, “no pleasure is a good,” it must be converted thus, “no good is a pleasure.” But because of the two propositions which we said are not necessarily converted, we ought to attend to everything that is attributed to propositions, through which they can be rightly or wrongly proposed, so as to show true or false. These are five, already shown above: genus, species, difference, accident and property. Of these, two make those propositions run back, the other three in no way. For as every man is a rational mortal animal, so every rational mortal animal is a man; and as every man is risible, so every risible thing is a man. Again, in the particular negative one must see what it is not to be a property. For as it is the property of man to be risible, so it is a property of the risible not to be apart from man. If, then, we propose the particular negative thus, “a certain risible thing is not apart from man,” it runs back without doubt, “a certain thing apart from man is not risible.” Likewise, “a certain inanimate, irrational, immortal thing is not a man”; “a certain man is not inanimate, irrational, immortal.” There are also other conversions, which make the same parts of propositions indefinite, even with the negation changing its place. For indefinite parts are made in this way: man, not-man; animal, not-animal; and it is indefinite because you deny only that this is, and do not say what it is. When I say, then, “every man is an animal,” if I wish to convert rightly, I apply negations, so that the parts become indefinite. For if “every man is an animal” is true, “every not-animal is not a man” is also true. Cicero used this conversion in his rhetorical works: “Then, if a constitution, and any part of a constitution, is a repelling of the charge, whatever is not a repelling of the charge is neither a constitution nor a part of a constitution.” The particular negative too can be converted in this way: “for if a certain animal is not a man, a certain not-man is an animal”; and in this conversion it is to be observed that where there is no negation when we propose directly, there is one when we convert. This conversion in turn is received by the two propositions which did not necessarily receive that first. Only the universal negative does not receive that other. For the sake of teaching, let that first be called the first conversion, this the second. How these propositions are related to one another will appear more clearly in this way. Let a square figure be drawn with four lines. At the first corner of the upper line let the universal affirmative be written, and at the other corner of the same line the universal negative; likewise below, at the first corner of the lower line the particular affirmative, at the remaining corner the particular negative; then let diagonal lines be drawn from the universal affirmative to the particular negative and from the universal negative to the particular affirmative. The two upper ones, then, cannot be affirmed together, but can be denied together. For it cannot be true together that “every pleasure is a good” and “every pleasure is not a good.” But “not every pleasure is a good” and “not every pleasure is not a good” can be together. The two lower ones, in turn, cannot be denied together, but can be affirmed together. For it surely cannot be that “a certain pleasure is a good” and “a certain pleasure is not a good” are both denied. But it can be that “a certain pleasure is a good” and “a certain pleasure is not a good.” The diagonal ones can be neither affirmed together nor denied together. For if “every pleasure is a good” is true, “a certain pleasure is not a good” is false. Likewise if “every pleasure is not a good” is false, “a certain pleasure is a good” is true. The same happens if you name the particular first: for if “a certain pleasure is not a good” is true, “every pleasure is a good” is false. Likewise if “a certain pleasure is a good” is true, “every pleasure is not a good” is false. Likewise the universal affirmative, if affirmed, necessarily affirms its particular; if denied, does not necessarily deny it. For if “every pleasure is a good” is true, “a certain pleasure is a good” is necessarily true. But if we deny the upper one in this way, “not every pleasure is a good,” it can be that “a certain pleasure is a good.” The particular affirmative likewise, if affirmed, does not necessarily affirm its universal; if denied, it necessarily denies it. For if “a certain pleasure is a good” is true, it does not follow that every pleasure is a good. But if “a certain pleasure is not a good,” “every pleasure is a good” is false. In the two remaining you will observe this. When we have proposed a full sentence, wishing to effect something from it, it is called a PREMISE (sumptum) when it has been conceded. To this one sentence another must be joined by a certain reasoning, and surely for the sake of that which we wish to infer it must be conceded; and when this has been conceded, it is called a premise. From two premises joined together to each other by reason the INFERENCE is made. This inference cannot be called a premise, for the reason that you do not expect your adversary to concede it to you also, but it follows even against his will, provided it has been inferred with the reasoning preserved. And that this may be plain by example, let us suppose the question is whether pleasure is useful. If we propose thus, “every pleasure is a good,” it is indeed a full sentence; a premise is made if the adversary concedes it. This conceded, another sentence must be adjoined: “every good, however, is useful.” If he has conceded this also, a premise is made. From these two premises, even against his will, it follows: “therefore every pleasure is useful.”
This whole, which consists of two premises and an inference, is called by us RATIOCINATION, by the Greeks syllogismos. A ratiocination, then, is a necessary arrival from two or more conceded points at that which is not conceded. There may therefore be more premises, but there cannot be fewer than two. And indeed the ratiocination is complete if, to that which we wish to show, that pleasure is useful, we wish to arrive even with three premises: “every pleasure is according to nature; everything according to nature is good; every good is useful; therefore every pleasure is useful.” From this it appears that it is permitted to add more if need be. Sometimes also we conclude by inferring not what is made, but what is necessarily made from the very thing we ought to infer, in this way: “every virtue is a good; every good is useful; therefore no virtue harms.” The thing to be inferred was “therefore every virtue is useful”: from that it necessarily follows that it does not harm, for what is useful never harms. This is called by the Greeks symperasma, and by us can be called an adjacent CONCLUSION. A ratiocination, then, whether it has its own proper conclusion or an adjacent one, is divided into two kinds: the predicative and the conditional syllogism.
The PREDICATIVE is that in which the premises are so linked to each other that they are supplemented by something added from outside, as this which was said above: “every pleasure is a good; every good is useful.” We see, then, that not the whole of what was put above is repeated, but one part taken from it, the declarative, which in the second proposition has been made the subjective. This second proposition, in order to fill out the sentence, sought something from outside, that is, “is useful.” Its inference is made from what has been added and from that which is not repeated, that is, “therefore every pleasure is useful.” Of this kind there are three forms. The first is that in which the declarative part of the earlier premise becomes the subjective of the following, or the subjective of the earlier the declarative of the following. The declarative of the earlier becomes the subjective of the following, as in the example proposed above. The subjective of the earlier becomes the declarative of the following if you wish to convert in this way: “every good is useful; every pleasure is a good; therefore every pleasure is useful.” The second form is that in which the declarative of the earlier premise is the same as that of the following one: “a certain just thing is not base; every evil is base; therefore a certain just thing is not evil.”
The FIRST MODE of the third form is that in which a direct particular affirmative is concluded from two universal affirmatives, as: “every just thing is honorable; every just thing is good; therefore a certain honorable thing is good.” The SECOND MODE is that in which a direct particular affirmative is concluded from a particular affirmative and a universal affirmative, as: “a certain just thing is honorable; every just thing is good; therefore a certain honorable thing is good.” The THIRD MODE is that in which a direct particular affirmative is likewise concluded from a universal affirmative and a particular affirmative, as: “every honorable thing is just; a certain honorable thing is good; therefore a certain just thing is good.” The FOURTH MODE is that in which a direct particular negative is concluded from a universal affirmative and a universal negative, as: “every just thing is honorable; no just thing is evil; therefore a certain honorable thing is not evil.” The FIFTH MODE is that in which a direct particular negative is concluded from a particular affirmative and a universal negative: “a certain just thing is honorable; no just thing is evil; therefore a certain honorable thing is not evil.” The SIXTH MODE is that in which a direct particular negative is concluded from a universal affirmative and a particular negative, as: “every just thing is honorable; a certain just thing is not evil; therefore a certain honorable thing is not evil.” All the modes, then, hold a certain order, and the reason of the order is the same which was shown in the forms themselves.
A CONDITIONAL syllogism is one whose proposition contains both the full argument and the full matter about which the question is, so that, the argument being assumed, what the question was about can now be inferred with certainty, in this way. Let us suppose the question to be whether rhetoric is useful, and that we wish to prove it useful; let us take the argument from its definition, which is the science of speaking well. From the argument and from that question a conditional syllogism is set down thus: “if rhetoric is the science of speaking well, it is useful.” We assume the argument: “but rhetoric is the science of speaking well.” Whoever has conceded these two must, even against his will, concede that rhetoric is useful, which was doubtful before the proposition and assumption were conceded. Yet nothing was added from outside in the assumption, which is proper to the predicative syllogism. This is called by the dialecticians the FIRST MODE, which is FROM ANTECEDENTS, for the reason that the argument, as it is proposed, so is it assumed, differing only in that it is posited with a condition and assumed without a condition. The SECOND MODE is that which is called FROM CONSEQUENTS, in which the argument itself follows the question, not the question the argument, in this way: “if rhetoric is useful, it is the science of speaking well.” The argument is assumed from the contrary, that is, through negation, thus: “but it is not the science of speaking well; therefore it is not useful.” The THIRD MODE is that which is called FROM INCOMPATIBLES, in which it is shown that this cannot be at the same time as that is not, in which, when one has been assumed, the other is necessarily removed, as when being has been assumed, not-being is removed, in this way: “rhetoric is not the science of speaking well and is not useful; but it is the science of speaking well; therefore it is useful”: “to be useful” is concluded, by removing that which was proposed, “not to be useful.” These three modes can be made from one argument and can all prove one thing. Nor does it matter in the proposition which part you put first, whether of the argument or of the question, provided the reasoning of the condition is preserved. When you have said “if rhetoric is the science of speaking well, it is useful,” you can also propose thus: “rhetoric is useful if it is the science of speaking well.” This may also be tried in the other two. The FOURTH MODE is said to be that which is made through DISJUNCTION, so that, one being assumed, the other is necessarily denied, in this way: “either he is healthy or he is infirm; he is healthy; therefore he is not infirm.” The FIFTH MODE is that which is also made through DISJUNCTION, so that, one being denied, the other is necessarily affirmed, in this way: “either he is healthy or infirm; he is not healthy; therefore he is infirm.” Two other modes have been added, which can be made from the argument of these two, yet not through disjunction but through negation. The SIXTH MODE, then, is that in which it is shown that this and that cannot be together. It is assumed by the affirmation of one, concluded by the denial of the other, in this way: “he is not both healthy and infirm; he is healthy; therefore he is not infirm.” The SEVENTH MODE is proposed thus and in it is assumed as in the fifth, and so concluded. To make the matter more easily understood, certain forms are joined to these so that the force of reasoning may be understood in the things themselves, not in what is said. The form of the FIRST mode is this: “if the first, the second; but the first; therefore the second.” Of the SECOND this: “if not the first, not the second; but the second; therefore the first.” Of the THIRD this: “not both the first and not the second; but the first; therefore the second.” Of the FOURTH this: “either the first or the second; but the first; therefore not the second.” Of the FIFTH this: “the first or the second; but not the first; therefore the second.” Of the SIXTH this: “not both the first and the second; but the first; therefore not the second.” Of the SEVENTH this: “not both the first and the second; but not the first; therefore the second.” It must be known, however, that from one argument can be made the three upper modes and from one argument the other four. The reason of this order is that the first mode is that which is called from antecedents, because what precedes is surely first; the second, from consequents, by the same reasoning, so that by its very name it seems to show that it ought to follow the first also in order. There remains the third in the same argument, from incompatibles. For it cannot leap to disjunction, which can no longer be made from the same argument. The fourth mode will be, as it were, the first for another argument. And there surely that ought to come first in which assumption is made by affirmation. For affirmation is prior to negation. The fifth ought to be the same but through disjunction, but after it, because in it assumption is made by affirmation, in this by negation. This may be understood in the two remaining.
Syllogisms are mingled with each other in many ways, so that in one ratiocination you may recognize the forms both of the predicative kind and of the conditional, in this way. If the question is whether dialectic itself is useful, one should propose: “if to argue well is useful, the science of arguing well is useful; but to argue well is useful; therefore dialectic is useful.” In the predicative syllogism it is certainly to be seen that the assumption claims something for itself from the proposition. For it is clear that it receives something from outside. In that which it claims for itself, as we said, from the proposition, one must look to see whether it claims rightly, by reason of the forms preserved and mentioned. For it comes about that what in the proposition seemed to pertain to the declarative part is shown in the assumption to pertain to the subjective. And likewise if you assume otherwise, this very thing will pertain to the declarative, in this way. It is known that in the first form assumption is made so that either the declarative of the proposition is the subjective of the assumption, or the subjective of the proposition the same and the declarative of the assumption, as if you propose thus: “every art is to be practised by frequent exercise; but declamation is the exercise of rhetoric; therefore rhetoric is to be practised by frequent declamation.” In the proposition exercise seemed to pertain to the declarative part; in the assumption exercise itself pertains thus to the declarative. In what way, then, has the form been preserved? Namely, because something is left in the declarative of the proposition which has not come into the declarative of the assumption, whence the conclusion can be made, that is, “is to be practised.” For if I wished to assume thus, “but rhetoric is an art,” the whole would be preserved for the conclusion: “therefore rhetoric is to be practised by frequent exercise.” From this it appears that there are many common things which could be adjoined either subjectively or declaratively, according as the assumption has been.
While Dialectic was pressing on with such matters and hastening to certain things no less inextricable than obscure, Pallas, at the nod of Maia’s son, who was in haste, intervened: “Skilled in speech, check now your progress, lest your tangled teaching bind us with twisted knots and Hymen long refuse to endure manifold windings. Whatever the learned disputation has with decorum brought together, to be built up with a great volume, has been set forth in compendium; enough is the decorous fountain of deep science, which brings forth hidden things, discoursing without tedium, flying past, and leaving nothing unknown. For what remain are sown with much fraud, by which deception goes round the captured with falsehoods, while with feigned circumlocution you build sophisms in advance, snares of captious play, deceitful sorites, and when you gradually heap up the forms, which truth approves as faults, let her not prate it sinfully under the ears of the Thunderer, and a dire crime; for the highest dwellers in heaven hate every falsehood in a base woman. For if you turn it over, what is crueller than cavil? Having spoken long ago as an indecent mountebank you will become, if you add more, a trap. Let then versatile profundity depart, and leave the rest of the time to the sisters.” Hearing these things, Dialectic, hesitating a little, yet about to obey the goddess’s precepts, replied: “Following the words of one to be honored and revered, I shall carry back my foot at your command, and though I have begun, I shall be silent. Though it was fitting to allow one fault to the one commanded, that the report of bringing in yielded to the price of honor, so that Bromius, by whom the people of the well-cloaked sons of Cecrops conceived to know insults and to grieve, might rather know what he had believed to be viperous, and the sluggish Marsian long since become a conjuress, and might not see me drowsy or drunken, babbling jests here and there under Jovian beginnings: yet to you alone, maiden, I must be a servant. We are silent.” Saying this, as though restrained, she fell silent, and several of the gods who at the beginning had mocked her shuddered at her.