De Syllogismo Categorico

ANICIUS MANLIUS SEVERINUS BOETHIUS, TWO BOOKS ON THE CATEGORICAL SYLLOGISM.

BOOK ONE.

The ancient Greeks left many things to their posterity in most carefully reasoned treatises, in which, before they come to matters shrouded in dense darkness, they first play, as it were, with a certain struggle of understanding; hence through introduction the teaching is made easier and more learnable; hence through those things which they call (what we may call things foretold or to be foretold), a readier path to understanding is secured. Therefore, not disdaining this foresight, I too have decided to place, as it were, a kind of bridge over the most obscure matters, touching on each point in moderate fashion, so that if anything has been said too briefly, we may extend it to understanding by fuller treatment; and if anything has been obscured by Aristotle through a change of nouns and words, let us, serving understanding, bring it back to customary vocabulary; but if he, writing for the learned and touching only the highest points, has indicated anything by mere designation, let us investigate it in the manner of an introduction, with some treatment of those matters set out in order. But if any have set themselves to reading this work, let it be asked of them that they not immediately presume to judge matters which they have never touched; and that they not consider as sacrosanct whatever they have received in boyish studies, since the more serious treatment of philosophy often discards things suited to tender ears.

But if anything in these matters does not appear [clear], let them not at once clamor, but, with reason consulted, let them judge with a truer sharpness of mind and a more subtle reasoning what they themselves think and what we maintain. And these men indeed [do so] thus. For we, as I judge, have sufficiently induced those commentaries from which we have brought forth these things to be tasted, perhaps drawn by the bland savor of subtlety; although they are unrestrained and untamed creators, nevertheless they will acquiesce in the unassailable authorities of the ancients. But if anyone is devoid of Greek speech, he will toil over these things, or whatever similar things there are of others. And so this will be the law of this preface, that no one who will not understand our forum should inspect it, and for that reason blame it. But lest time be wasted on prefaces that bring nothing, we must begin after first driving away that danger, lest our speech be blamed by anyone as barren. For we pursue not compositions of eloquence but plainness; and in this matter, if we accomplish this, even speaking however inelegantly, our intention also is perfected for us. But since the structure of syllogisms is to be explained by us in this work, and the proposition is prior to syllogisms, the treatment of propositions will be had in this little book. And since the parts of a proposition are the noun and the verb, and a part is prior to that of which it is a part, let the first disputation be placed concerning the noun and the verb, which are first.

A name is a vocal sound significant by convention, without time, of which no part is significant separately; and it is called a vocal sound because vocal sound is the genus of names. Every definition, moreover, is drawn from the genus, so that if you define man, you say animal, that is, the genus; afterwards, rational, that is, the differentia. It is called significant, moreover, because there are certain vocal sounds that signify nothing, as syllables do. A name, however, designates that of which it is the name. By convention, moreover, because no name signifies anything by itself, but by the convention of the one who establishes it. For each thing is called that which pleased him who first impressed that name upon the thing. For there are vocal sounds that signify naturally, as the barking of dogs signifies the anger of dogs, and a certain other vocal sound of theirs signifies their fawning; but they are not names, for they do not signify by convention, but by nature. Without time, moreover, because verbs are indeed significant vocal sounds and by convention, but they differ in that names are without time, verbs with time. Of which no part is significant separately: a name is distinguished from a sentence, because a sentence is itself also a vocal sound, and significant, and by convention, and sometimes without time, but the parts of a sentence are significant, whereas the parts of names are not at all. For in the name Cicero no part is significant separately, neither ci nor ce nor ro. Nor if names are made from two whole [words]. For what signifies in one [word] does not signify separately. For in the name magister, magis and iter signify together, because it is magister.

But if it is removed, the signification of something will no longer exist—unless it pleases you to give this name to another. For all names are not by nature, but are imposed by convention. But concerning this, it has been said in the commentary on Aristotle's book, and the treatment of that matter is greater than can now be dispatched. Let us return, therefore, to the name. But since there are certain vocal sounds which are both designative and by convention and without time, whose nature is doubtful, as is "not-man

[non-man], for this signifies something and is imposed by convention; for it is doubtful to what it may be subordinated, for it cannot be a name—for every name signifies something definite, but "non-man" destroys what is definite; and it cannot be called a phrase, for every phrase consists of names and verbs, but "non-man" consists neither of names nor of verbs; but much more it cannot be a verb, for every verb is with time, but "non-man" is without time. What it is, therefore, must be seen thus; and since "non-man" signifies a certain utterance, but what it signifies is not contained in man himself (for "non-man" can be a horse and a stone and a house, and whatever is not a man, since the things it can signify are infinite, it is called an infinite name); and since there are certain utterances that are both designative and by convention, and definite, and whose parts signify nothing outside themselves, as are the cases of names, as "of Cicero" and "by Cicero" and the rest, these will not be names. For every name joined with a verb shows either true or false. As if you say, "It is day," this is either true or false. But if you join a case, you make neither true nor false. For if you say, "It is of the day," you have shown nothing that is or is not. And so from this you will make neither true nor false. And rightly does it seem to have been said. For that which, when they first imposed names on things, they called a word, that alone will rightly be called a name.

For he who first imposed the name "circus" on the circus seems to have said: let this be called "circus." And for this reason this first case is called the nominative, because it is the name. But the other cases of other names they called not cases of the name. Therefore we must begin again from the top: the word was called a voice because voice is the genus of names; designative, because there are certain voices that designate nothing, so that it may be separated from those voices that signify nothing; by convention, so that it may be separated from those voices that signify naturally, as do the sounds of cattle. "Without time" was said in distinction to the verb, which is with time; "of which no part signifies separately," so that it might be divided from speech, whose parts are names and verbs, which do signify; finite, so that it might be separated from infinitives; straight, so that it might be distinguished from the cases. And in the verb nearly all the same things concur. For a verb is a significative voice by convention with time, of which no part signifies separately; and because it is a certain significative voice by convention with time, of which a part signifies nothing, as "does not whiten" (for "whitens," which when uncombined signifies together, alone does not signify), and because it shows nothing definite (for what does not whiten can also grow red, can also grow black, can also grow pale, and whatever else does not whiten), therefore it was called an infinite verb. But "was making" and "about to make," as above in the case of the name, are not verbs but cases of verbs.

Therefore we must repeat from the beginning: that the word is said to be a vocal utterance, by genus; significative, so that it may be divided from non-significative utterances; by convention, so that it may be separated from those utterances which are significative by nature; with time, so that it may be divided from the noun; to signify something present, so that it may be disjoined from the cases of the verb; finite, so that it may be distinguished from infinitives. It remains, then, now to say what a sentence is. For this seems to be composed of noun and verb; but first let us consider whether noun and verb alone are parts of the sentence, or also the other six, as the opinion of the grammarians holds, or whether some of these are turned into the rights of the verb and the noun; for unless this is first established, the whole account of propositions, and thereafter that of syllogisms which is composed from propositions, will waver. For if it is not known from what genus the terms are, the whole will be unknown. Noun and verb alone are to be thought the two parts; for the rest are not parts, but supplements of the sentence: for just as the reins or thongs of a four-horse chariot are not parts, but certain bindings in a manner, and, as has been said, supplements rather than parts, so conjunctions and prepositions and other things of this kind are not parts of the sentence, but certain ligaments. But what is called the participle will be placed in the place of the verb, since it is demonstrative of time. But the adverb is a noun; for it is of a certain definite signification without time, and if it is not inflected through cases, nothing prevents it.

For it is not a property of the noun to be inflected through cases. For there are certain nouns which cannot be inflected, which are called by the grammarians monoptota, but this belongs more to grammar than to the present consideration. A sentence is a significative vocal utterance by convention, whose parts signify something extra, as a word does, not as an affirmation does. And it is common to a sentence with a noun and a verb that it is a vocal utterance, and significative, and by convention. For those things whose parts are by convention, that thing itself is also by convention. But the parts of a sentence are the noun and the verb. But these are by convention; therefore the sentence is by convention. But the terms of a sentence are called by the dialecticians nouns and verbs. But they are called terms because the resolution of the parts of a sentence is made only as far as the verb and the noun, lest anyone attempt to resolve a sentence all the way to the syllables of nouns or verbs, which are no longer significative. But a sentence differs from a noun or a verb in that their parts signify something extra, whereas the parts of a verb and a noun signify nothing extra. But a word is the utterance of one simple vocable, or a simple affirmation. And therefore it was said that the parts of a sentence signify as a word, that is, as the utterance of a simple vocable. For in the sentence Socrates walks, each part signifies something extra as much as the utterance of a simple vocable can designate. But how it does not signify as a simple affirmation, I have explained in the commentary On Interpretation. But what affirmation and negation are, we shall explain a little later.

There are, however, five species of speech in the narrowest division: interrogative, as "Do you think the soul is immortal?"; imperative, as "Take the book"; optative or deprecative, as "May God grant it"; vocative, as "Be present, O God"; and enunciative, as "Socrates walks." But in those four there is neither truth nor falsity; only the enunciative alone contains either the true or the false. And from this propositions arise. Enunciation, moreover, will be cut into two parts: into affirmation and negation. Affirmation is the enunciation of something toward something. Negation is the enunciation of something away from something. And affirmation is, for example, "Plato is a philosopher." Negation: "Plato is not a philosopher." For affirmation enunciates some philosophy toward Plato, that is, that Plato is a philosopher. But negation, by enunciating, takes away some philosophy from Plato, that is, it enunciates that Plato is not a philosopher. Of enunciative speeches, therefore, some are simple, others not simple. Simple ones are, as if you were to say, "It is day," "It is light.

Not simple, as, for instance, "If it is day, there is light." But affirmations and negations that are simple are either universal, or particular, or indefinite. Universal ones are those that either affirm universally, as "Every man is an animal," or deny universally, as "No man is an animal"; particular ones are those that either affirm some [subject] or deny some [subject], as "Some man is an animal," "Some man is not an animal"; indefinite ones are those that neither affirm nor deny universally, nor particularly, as "Man is an animal," "Man is not an animal." But a simple proposition is divided into two parts: into subject and predicate, as in "Man is an animal," "man" is the subject, but "animal" is predicated of man; and these parts are called terms. We define them thus: Terms are the parts of a simple proposition into which the proposition is principally divided. For the second division of a universal simple proposition is such that in the proposition "Every man is an animal," "every man" is one term, and the other is "is an animal." But this is in the second place, that in the principal place. For the primary terms are subject and predicate. For "is" and "is not" are not more designative of affirmation or negation than "every" or "no" or "some" are terms than they are designative of definitions, whether something has been said particularly or universally. Therefore, as has been said, the proposition is divided into that which is the subject and into that which is predicated.

I call the subject, for instance, "man" in the proposition "every man is an animal," and what is predicated I call "animal." And always what is predicated either exceeds and surpasses the subject or is equal to it. A predicate less than its subject will never be found. But let us demonstrate what we have said with various examples. The predicate exceeds the subject whenever some genus is predicated of something, as if you say "every man is an animal." For you cannot convert it so as to say "every animal is a man," because animal is more than man and exceeds him. But the predicate is equal to the subject whenever some property is predicated of something, as "every man is risible"; for you can convert it: "every risible thing is a man." But that what is predicated be less cannot happen. The predicate is also said to precede, and the subject to follow. For the predication is more suitable for constituting a proposition than is the subject.

Of simple propositions, however, some share nothing with one another, as are "every man is an animal," and "virtue is good," and other propositions of this kind; but others do share. Of those that share, some share in both terms, others in one; and those that share in one term do so in three ways, but those in both do so in two ways. Let us therefore show by examples how they share in one term in three ways. For a term is common when in one proposition it is the subject and in the other the predicate, as is "every man is an animal" and "every animal is animate." For in the former proposition "animal" is predicated of "man," and in the latter "animate" is predicated of "animal," and "animal" becomes the subject. And this is the first way among those that share in one term. The second way, however, is that in which the common term is predicated in both propositions, as if someone says "every snow is white" and "every pearl is white." For in the first and second proposition "white" is predicated, in the first of snow, in the second of pearl. And this is the second way of those sharing in one term. The third way, however, is whenever in both propositions the common term is a sub-

jected, as if you say, "virtue is good, virtue is just." For in both, virtue is the subject with respect to just and to good. They are therefore participants of the other term in these three ways: either when in one proposition the term is predicated and in the other it is subject; or when it is predicated in both; or when it is subject in both. But of those which participate in both terms there are two modes. For some are according to the same order, others according to a change of order. According to the same order are those which demonstrate the same thing about the same thing, either affirmatively or negatively, either universally or particularly: "every pleasure is good," "no pleasure is good"; and again particularly, "a certain pleasure is good," "a certain pleasure is not good." According to a change of order are those whenever the term which is subject in one is predicated in the other, as "every good is just," and "every just is good." For in the former, good is the subject and just the predicate; in the latter, just is the subject and good the predicate.

Now therefore, since some [propositions] belong to the same order and others to a change of order, we shall first speak of those which participate in the same order by both terms; and since some propositions are affirmative, others negative, some universal, others particular, others indefinite, there are two of those which differ in quality, and three which differ in quantity. Those which differ in quality are the affirmative and the negative; those which differ in quantity are the universal, the particular, and the indefinite. For in affirmatives and negatives it is shown what kind of thing is or is not; in the universal, particular, and indefinite, the quantity of all, of none, or of some is shown. From these five differences, therefore—that is, universal, particular, indefinite, affirmative, negative—six combinations are made, in such a way that the two which are spoken of with respect to quality are fitted to the three which are spoken of with respect to quantity, and there results the universal affirmative and the universal negative, as "every man is just," "no man is just"; and the particular affirmative and the particular negative, as "a certain man is just," "a certain man is not just"; and the indefinite affirmative and negative, as "a man is just," "a man is not just." There come to be, therefore, from the two which are with respect to quality joined to the three which are with respect to quantity, six combinations; of these we shall separate the indefinite, affirmative, and negative, and let our treatment be of the universal and particular alone.

Let there also be subscribed, of those [propositions] participating in the same order by both terms, two universal propositions, one affirmative and the other negative; and let the universal affirmative be "every man is just," and conversely the universal negative "no man is just." Likewise under these let the particular affirmation and the particular negation be placed, so that under the universal affirmative the particular affirmative is placed, and under the universal negative the particular negative is placed; and let the particular affirmative be "a certain man is just," and conversely the particular negative "a certain man is not just," as the following description demonstrates.

In the above description, therefore, the universal affirmative and the universal negative are contraries; but beneath the contraries are the particular affirmative and the particular negative; and subalterns are said to be the universal affirmative and the particular affirmative, and likewise the universal negative and the particular negative. The angular [propositions] are contradictory, that is, the universal affirmative and the particular negative, and likewise the universal negative and the particular affirmative, as "every man is just," "a certain man is not just," "no man is just," "a certain man is just"; and they can be defined in this way: contraries are those which universally affirm and deny the same thing of the same [subject].

Subcontraries are those which, taken particularly, affirm and deny the same thing of the same subject. Subalterns are those which, as it were, affirm or deny the same thing of the same subject, the one particularly, the other universally. Contrajacents are when one affirms and the other denies the same thing of the same subject, or one denies and the other affirms, the one generally, the other particularly; and they are called contraries, because what the universal affirmation posits, the universal negation removes. But they are called subalterns because what the one posits universally, the other also posits particularly. And they are called subcontraries either because they are naturally placed beneath the contraries themselves, as the description teaches, or because they differ from the contraries and are in a certain way contrary to the contraries themselves. For whereas contraries cannot both be together, but can both wholly not be, subcontraries obtain the contrary power. For that both wholly not be cannot happen, but that both be together can happen, which will be better explained in what follows. They are called contrajacents because the universal affirmation or negation looks, as it were, at an angle toward the particular affirmation or negation.

Since, however, individual propositions have two differences, one with respect to quality and the other with respect to quantity — so that the one which is universal and affirmative has a difference with respect to quantity because it is universal, and another with respect to quality because it is affirmative — in the same way the remaining propositions have two differences, one according to quality and the other according to quantity. Subalterns, as they are, differ by only one difference of quantity, because the one is particular and the other universal. For they retain no difference of quality, since both are affirmative. But those others, that is, contraries and subcontraries, differ with respect to quality, because the one is affirmative and the other negative; for with respect to quantity they do not differ at all. For both contraries are universal, and both subcontraries are particular. But those which are called contradictory differ by both differences. For the one is a universal affirmation and the other a particular negation, and the one is a universal negation and the other a particular affirmation. Now, since it has been said what their differences are according to quality or according to quantity, and in what way they differ, let us explain their properties which are according to truth and falsity. Therefore, of those which are subalterns, if the universal affirmation has been true, the particular affirmation will be true. For if every man is just — which is true — then that which says "some man is just" will also be true. For if every man is just, then also a certain one.

In the same way for negative subaltern propositions: for if the universal negative has been true, the particular negative will also be true, as if "no man is just" has been true, then "a certain man is not just" will also be true. For if no man is just, neither is a certain man. But it cannot be converted, for if the particular has been true, it will not be necessary that the universal also be true. As if "a certain man is just" has been true, it will not be necessary that "every man is just" be true. For it is possible that not all are. And in the same way concerning the negative. For if the particular negative has been true, as is "a certain man is not just," it will not be necessary that the universal "no man is just" be true. For it can happen that certain men are just. Therefore we say that in subaltern propositions, if the universals are true, the particulars must necessarily be true, but it is not converted. For if the particulars have been true, it is not necessary that the universals also be true. But particulars have a contrary conversion to universals. For as above, if the universals were true, the particulars would also be true; and if the particulars were true, the universals would not altogether be true in particulars; if the particulars have been false, the universals will also be false. For if the particular "a certain man is just" has been false, the universal "every man is just" will also be false. For if "a certain man is just" is false, "no man is just" is true.

If "no man is just" is true, "every man is just" is false. Therefore, when the particular is false, the universal will be false. Likewise, if the particular negative is false—that is, "a certain man is not just"—then "no man is just" will also be false. For if it is false that a certain man is not just, it is true that every man is just. If this is true, "no man is just" is false; therefore, when the particular is false, the universal will also be false. But it does not convert, so that if the universals are false, the particulars must necessarily be false: for if the universal "every man is just" is false, it is not necessary that the particular "a certain man is just" be false. For it can happen that, if not every man is just, a certain man is just; and likewise, if the universal negative "no man is just" is false, it will not be necessary that "a certain man is not just" be false. For if "no man is just" is false, it is true that some are just, and true also is the proposition that says "a certain man is not just," because some are also not just. Therefore, repeating from the beginning, let him state what holds in subalterns. If the universals are true, the particulars will also be true. But it does not convert. Likewise, if the particulars are false, the universals will also be false, but it does not convert; contraries, however, can never be true at the same time. But it can happen that at one time both are false, at another one is true and the other false.

Both are false, as if someone says "every man is grammatical"—it is false, for not every man is; and "no man is grammatical"—it is false, for not no man is. But one is true and the other false, as if someone says "every man is two-footed"—this affirmative is true; "no man is two-footed"—this negative is false. And likewise "every man is four-footed" is [false]; this affirmative is false. "No man is four-footed"—this negative is true. Therefore contraries are sometimes both false, sometimes dividing truth and falsehood between themselves; but that both should be true can never happen, whereas subcontraries are subject to the contrary. For they can never be found false. But at other times both are true, as "a certain man is grammatical" is true, and "a certain man is not grammatical"—this too is true. For one man can be grammatical and another not. At other times one is true and the other false. For the affirmation "a certain man is two-footed" is true, but the negation "a certain man is not two-footed" is false. Likewise the affirmation "a certain man is four-footed" is false; the negation "a certain man is not four-footed" is true. But that both should be false can never happen. It remains, therefore, that we speak of the subopposites, which can neither sometimes be false together nor true, but always one is true and the other false—which is more easily clear if one frames for oneself examples of whatever kind.

The matter calls for us to consider certain points about indefinite propositions. For indefinite propositions retain the same force as particular propositions. For it has been said that if universal propositions, whether affirmative or negative, were true in subaltern propositions, the particular propositions would also be true. Now we say that if universal propositions are true, the indefinite propositions will also be true. For if "every man is two-footed" is true, "a certain man is two-footed" is also true, and the indefinite proposition which says "a man is two-footed" will also be true. Likewise it has been said that if particular propositions were false, the universal propositions would also be false; but now it must be said that if an indefinite proposition is false, the universal proposition will also be false. For if the proposition which says "a man is four-footed" is false, the proposition which says "a certain man is four-footed" and "every man is four-footed" will also be false. And the same thing seems to hold also in negative propositions.

From this it is clear that all indefinite propositions contain the same force as particular propositions. Again, it has been said that contradictories—which are particular affirmatives and negatives—can be true at the same time, and can also divide truth and falsehood, but cannot be false at the same time. The same must be expected in indefinite propositions. For they divide between truth and falsehood: as if someone says "man is two-footed," it is true; "man is not two-footed," it is false; and likewise "man is four-footed," it is false; "man is not four-footed," it is true. But they can be found true at the same time: as if someone says "man is grammatical"—if someone says this of Donatus, it is true. Likewise "man is not grammatical"—if someone says this of Cato, it is true—so that they are never found false at the same time. By this it is also shown that indefinite propositions have equal power with particular ones. Furthermore, what has been said—that contrajacents, that is, the universal affirmative and the particular negative, and likewise the universal negative and the particular affirmative, are neither true at the same time nor false, but divide truth and falsehood between themselves—the same also happens in indefinite propositions. For the universal affirmative and the indefinite negative, or the universal negative and the indefinite affirmative, can neither be true at the same time nor false at the same time. But they are divided between themselves as to truth and falsehood: for if you say "every man is two-footed," it is true; and if you say "man is not two-footed," it is false.

Likewise, if you say "a man is four-footed," it is false; if you say "no man is four-footed," it is true. From this too it may be gathered that all indefinite propositions are equal in force and power to particular ones. There are also certain propositions that themselves divide the true and the false, as "God thunders," "God does not thunder." But these divide between true and false only when the same time, the same subject, and the same predicate are involved. What I mean is this: if the subject is equivocal, they do not divide the true and the false. For if someone says "Cato killed himself at Utica," and it is answered "Cato did not kill himself at Utica," both are true. For Cato the Younger killed himself, and Cato the Censor did not kill himself at Utica. But this happens because the name "Cato" is used equivocally, for both Cato the Elder the Censor and Cato the Younger of Utica are called Cato. Likewise, if the predication in the proposition is equivocal, affirmation and negation do not divide the true between them. For if someone says "it shines at night," and it is answered "it does not shine at night," it can happen that both are true. For at night a lamp can shine, and the sun cannot shine; this happens because "to shine" is said equivocally both of the light of a lamp and of the sun. Furthermore, if the time in the subjects and predicates is different, affirmation and negation do not divide the true and the false between them. For if someone says—

Socrates walks," and let the response be "Socrates does not walk": both can be true. For it can happen that Socrates walks at one time and does not walk at another, but instead stands or sits or does anything else. In such propositions, therefore, as are "Socrates walks" and "Socrates does not walk," those propositions divide truth and falsehood between them which are said of the same subject, the same predicate, and the same time. There are also others which are called contradictory, which are of this kind: whenever a particular negation removes a universal affirmation—"every man is just," "not every man is just"—and again "no man is just," and "a certain man is just." For in these the universal determination is removed, but of these elsewhere. And since we have spoken of those which participate in the same order, let us now speak of those which participate by a change of order. Of these propositions too which participate in a change of order there is a twofold mode. For there is conversion by contraposition, as if you say "every man is an animal," "every non-animal is not a man"; and there is simple conversion, as if you say "every man is capable of laughter," and convert it, "every capable of laughter is a man." But in those cases the interchange of terms alone effects the conversion in which neither does the predicate abound over the subject nor the subject over the predicate.

For in this proposition which says "every man is risible," "man" is the subject and "risible" the predicate, and it has equal force, and therefore it can be converted so that "risible" is the subject and "man" the predicate, and it is said "every risible is man." But in those cases where one term exceeds the other, the proposition cannot be converted. For if you say "every man is an animal," it is true; yet it cannot be that this proposition, converted with its terms interchanged, is true: for it is false to say "every animal is man." But why does this happen? Because "animal" exceeds "man." But that conversion which is made by contraposition is made in this way whenever in an affirmative proposition the subject has been changed and made the predicate and is placed with a negative particle, as for example "every man is an animal." Here "man" is the subject and "animal" is predicated of it. But if someone converts by contraposition, and makes "animal" the subject and "man" the predicate, and places a negative particle with "man," he will do it in this way: "every non-animal is not man," and this will be the conversion: "every man is an animal," "every non-animal is not man." But we shall treat of these matters later; now let us return to the simple ones. Since, therefore, there are four propositions, of which the universal ones, that is the affirmative and the negative, are two, and the particular ones, that is the affirmative and the negative, are two, the particular affirmative and the universal negative are converted with themselves when their terms are interchanged.

Those [propositions] are converted, as has been said, whenever, with the terms interchanged, they are either true together or false together. For if someone says "some man is an animal," it is true; and its conversion, "some animal is a man," is true. Again, "some man is a stone" is false, just as also its conversion, "some stone is a man," for that too is false. Therefore the particular affirmative, with its terms interchanged, converts to itself. The universal negative undergoes the same. For if someone says "no man is a stone," it is true, and it can be converted to "no stone is a man," for that too is true. Again, "no man is an orator" is false, and its conversion, "no orator is a man," is false. Therefore among these four propositions, only these two convert to themselves as their own contrapositives, namely the particular affirmative and the universal negative. But the other two do not convert to themselves. For neither the universal affirmative nor the particular negative converts to itself. For if someone says "every man is an animal," it is true; but if someone converts it, "every animal is a man," it is false. It cannot therefore convert to itself, since when converted it does not receive the truth of the prior proposition. Nor indeed does the particular negative convert to itself.

For if someone says "some man is not a grammarian," it is true; but if he converts it, "some grammarian is not a man," it is false; for every grammarian is a man. It must therefore be repeated from the beginning that, since there are four propositions—universal affirmation, universal negation, particular affirmation, particular negation—the particular affirmation and the universal negation, which are subcontraries, can be converted with themselves. But the universal affirmation and the particular negation, which are themselves subcontraries, can never be converted with themselves. Nor let it disturb us that certain universal affirmations and certain particular negations can be converted. For it can be said "every man is risible," and "every risible thing is a man," and both are true. And likewise "every man is neighing" is false, and "every neighing thing is a man" is also false. Likewise in particular negation, "some man is not a stone" is true, and "some stone is not a man" is true. Likewise "some man is not risible" is false, and "some risible thing is not a man" is also false. Therefore universal affirmations and particular negations seem able to be converted, and they are indeed converted, but not universally. But I say generally that propositions can be converted whenever they are converted universally, that is, in all cases. But these can be converted in only two matters.

For if someone predicates the property of any species to that very species of which it is the property, as to a subject, he can convert it. For since "capable of laughter" is a property of man, if you predicate "capable of laughter" and subordinate "man," as in "every man is capable of laughter," you can in turn subordinate "capable of laughter" and predicate "man," as if you say "every capable-of-laughter thing is man." But in those cases the conversions of universal affirmations are likewise false in which that which is predicated cannot at any time be truly said of the subject, as if someone says "every man is a stone," it is false. And again, "every stone is a man," this is false, since at no time will either "man is a stone" or "stone is a man" be truly predicated. In particular negatives the contrary is the case; for they are false either when the proper term is the subject or the predicate, as if someone says "some man is not capable of laughter," it is false. Likewise "some capable-of-laughter thing is not a man," and this too is false. In those cases they are true when that which by affirming cannot at any time be truly predicated is predicated of the subject, as if you say "some man is not a stone," it is true. Again "some stone is not a man," it is true. Therefore universal affirmations are converted with one another so as to be true when they predicate a property, and they are converted with one another so as to be false when that which can at no time be truly said of the subject is predicated.

Likewise in particular negatives, they are sometimes false when they predicate a property, and sometimes true when they predicate that which can at no time be truly said. In these cases, then, only they can be converted. But in others they cannot be converted. And for this reason they are not converted universally; it remains, therefore, that in all other cases, as was said above, they are not converted. But this must be observed: that a particular affirmation, which converts with itself, can be converted per accidens to a universal affirmation, which does not convert with itself. And likewise the particular negation, which is the contradictory of the universal affirmation and does not convert with itself, can be converted per accidens to the universal negation, which does convert with itself. But we have shown how the particular affirmation and the universal negation convert with themselves. Now, however, it must be demonstrated how the particular affirmation is converted per accidens to the universal affirmation, or how the particular negation is converted per accidens to the universal negation. It was said above that if the universal affirmation is true, the particular is also true, and the particular would follow the universal. For if "every man is an animal" is true, "some man is an animal" is also true. For if every, then also some; but the particular affirmation converts with itself, so it is also converted to the universal affirmation. For if every man is an animal, some man is also an animal.

But this is converted to itself in this way: if some man is an animal. Therefore particular affirmation, which is "some man is an animal," can be converted to the universal affirmation "every man is an animal," and it is converted, as if you say "a certain animal is a man"; for both are true, both the one which says "every man is an animal" and the one which says "a certain animal is a man." But the particular affirmation is said to be converted to the universal affirmation per accidens, because the particular affirmation is converted to itself principally, but in the second place it is converted to the universal affirmation. It remains, therefore, that we show how the particular negation, which is not converted to itself, is converted per accidens to the universal negation, which is converted to itself; and here the same reasoning applies. For since, if the universal negation is true, the particular is also true, and the universal negation is converted to itself, the particular negation can be converted to the converted universal negation. For let us convert the universal negation, that is, "no man is neighing," so that it becomes "no neighing thing is a man.

But that proposition, that is, the universal negative which is "no man is neighing," is followed by the particular negation which is "some man is not neighing." Therefore convert the universal which is "no man is neighing," and make "no neighing thing is a man"; convert to this the particular negation which is "some man is not neighing," and make "some neighing thing is not a man"; both are true. For both "no neighing thing is a man," which is the conversion of the universal negation, is true, and "some neighing thing is not a man," which is the conversion of the particular negation. But why it is said to be converted by accident has been stated above. It is clear, therefore, that such is the conversion by accident: for what the universal affirmation has, the opposed particular negation also has, since both cannot be converted to themselves; but what the universal negation has, the opposed particular affirmation also has, since both can be converted to themselves. Therefore, joining those which can be converted to themselves and those which cannot be converted to themselves, so that what can be converted to itself is joined to that which cannot be converted to itself, and what cannot be converted to itself is joined to that which can be converted to itself, they make the conversions by accident which have been demonstrated above.

It remains for us to speak of those conversions which are made by contraposition, and first their arrangement is set out in the description below. For the conversion by contraposition of the universal affirmation which says "every man is an animal" is the one which says "every non-animal is a non-man." Likewise the conversion by contraposition of the universal negation which says "no man is an animal" is "no non-animal is a non-man." Likewise the conversion by contraposition of the particular affirmation which says "a certain man is an animal" is the one which says "a certain non-animal is a non-man." Likewise the conversion by contraposition of the particular negation which says "a certain man is not an animal" is the one which says "a certain non-animal is a non-man," which the description below demonstrates: Every man is an animal; No man is an animal; A certain man is an animal; A certain man is not an animal; Every non-animal is a non-man; No non-animal is a non-man; A certain non-animal is a non-man; A certain non-animal is not a non-man. These things being thus posited, as was said above in the simple conversion of terms—that the particular affirmation and the universal negation are converted into themselves, but the universal affirmation and the particular negation are not converted into themselves—here in conversions by contraposition it is the opposite. For the universal affirmation is converted into itself by contraposition, and the particular negation is converted into itself.

But the universal negation and the particular affirmation are not converted to themselves by contraposition. We shall prove that this is so by these examples. For if the universal affirmation which says "every man is an animal" is true, its conversion by contraposition which says "every non-animal is not a man" will be true. For what is not an animal will not be a man. And if the universal affirmation which says "every animal is a man" has been false, its conversion by contraposition which says "every non-man is not an animal" will also be false; for it can happen that what is not a man is an animal. For that [conversion] denies that to be an animal which has not been a man. But if, when the universal affirmative is true, its conversion by contraposition is true, and if, when the universal affirmation is false, its conversion by contraposition is false, there is no doubt that the universal affirmation can itself be converted there. Likewise it must now be shown how the particular negation is converted to itself by contraposition. For if that which says "a certain man is not an animal" is false, its conversion by contraposition which says "a certain non-animal is not a man" will also be false.

For this proposition seems to say this, as if you were to say that certain things which are not animal are man—for he who says "not-man is not" signifies that man is that which is not animal. But this is plainly false; for every man is an animal. And if the particular negation which says "a certain animal is not man" has been true, its conversion by contraposition which says "a certain non-man is not non-animal" will also be true. For it is equivalent to saying that a thing which is not man is not non-animal, but is an animal—as a horse is not a man, and is not non-animal. Therefore, if when the particular negation is false, its conversion by composition is also false, and if when the particular negation is true, its conversion by contraposition is true, there is no doubt that the particular negation can be converted to itself by contraposition. Now, since we have shown that the universal affirmation and the particular negation can be converted to themselves by contraposition, let us show that the universal negation and the particular affirmation cannot be converted to themselves by contraposition. And first we must speak of the universal negation. For if the universal negation is true, it will not be necessary that its converse by contraposition be true. But if it has been false, its converse by contraposition must also necessarily be false.

For if the proposition that says "no man is an animal" is false, then perhaps its conversion by contraposition, which says "no non-animal is a non-man," will be false. For it is equivalent to saying "there is no thing that is not an animal and is a non-man," which means "every thing that does not have a soul is a man," which is plainly false. Likewise, if the universal negation has been true, its conversion by contraposition will be false. For if the proposition that says "no man is a stone" is true, its conversion by contraposition, which says "no non-stone is a non-man," will be false. For it is equivalent to saying "there is no thing that, while it is not a stone, is a non-man," which means "every thing whatsoever that is not a stone is a man," which is false. For you will find countless things that are not stones and are not men. Therefore, since if the universal negation has been false, its conversion by contraposition is false, or if the same has been true, its conversion by contraposition will be false, there is no doubt that the universal negation cannot be converted to itself by contraposition, because what fails in some case cannot be gathered universally. It remains, therefore, that we show what is left: that the particular affirmation cannot be converted to itself by contraposition. For when the particular affirmation has been true, its conversion by contraposition will also be true.

For if the proposition that says "a certain man is an animal" is true, its conversion by contraposition is true: "a certain non-animal is not a man." For it is equivalent to saying "a certain thing that does not have a soul is not a man," which is true. For a stone does not have a soul, and yet it is not a man. Likewise, if the particular affirmation that says "a certain stone is a man" is false, its conversion by contraposition will be true, which says "a certain non-man is not a stone." For it is equivalent to saying "a certain thing that is not a man is not a stone," which is true. For a horse is not a man, and yet it is not a stone. Therefore, if when the particular affirmation is true in some cases, its conversion by contraposition will be true, and if when the particular affirmation is false in some cases, its conversion by contraposition will be true, there is no doubt that particular affirmations cannot be converted by contraposition. For general negation and particular affirmation, which are contraposed, undergo the opposite in conversions by contraposition. For in general negatives, whether the general negatives are true or false, the conversions by contraposition are always false; but in particular affirmatives, whether the particular affirmation is true or false, its conversion by contraposition is true.

We must therefore return to the earlier points and confirm that in simple conversions of terms, the particular affirmation and the universal negation can be converted with each other. But the universal affirmation and the particular negation cannot be converted with each other. In those conversions, however, which are made by contraposition, the opposite holds; for the universal affirmation and the particular negation can be converted with each other by contraposition, but the universal negation and the particular affirmation cannot be converted with each other by contraposition, and the universal negation and the particular affirmation, which are opposed in the distance between truth and falsity (as has been demonstrated), suffer contrariety toward each other in turn. Let these things said about the categorical propositions of categorical syllogisms suffice. But if any things have been omitted in these matters, they have been treated more diligently and more subtly in the commentary on Aristotle's Peri Hermeneias.

BOOK TWO.

The course of the previous volume, which pertained to the propositions of categorical syllogisms, has been explained. Now, however, as far as the temperament of an introduction allows, we shall treat of the very reasoning of categorical syllogisms; and since the firmness or defect of all composites is found chiefly either in those things of which the composite consists, or the praise and blame of it is held in relation to the good or bad composition of it: for a house, if constructed of strong or weak stones, is itself also strong or weak; moreover, if it has obtained from its builder a composition that is even and skillful, that very construction will deservedly be a praiseworthy foundation of stability; but if the composition be less skillful, the whole, though ordered from good stones, will totter, bearing no stability in its fabric. We too, following this same image, have first explained those things of which the syllogism itself consists, that is, the propositions. Now, however, we shall treat of the very conjunction and composition of syllogisms with one another. But you must remember this, that in introducing these matters I have provided things to be taught, not things already introduced. And first I shall show in a few words what it is to be in every or not to be. For if any thing is of another genus, it will contain every species within itself, and the species will be said to be in that whole genus. For let the genus be animal, and man the species. Man, therefore, since he is less than animal, will be said to be in the whole animal. For every man is an animal.

If anyone therefore says that some thing is predicated of every other thing, conversely there is no difference. For just as man is in the whole animal, so also animal is predicated of every man. But to not be in the whole is, whenever one thing is disjoined from every other: as if you say, animal is in no stone, for no animal is a stone; and if you say, animal is predicated of any stone, for animal is said of no stone. We define therefore to be in the whole, or to not be in the whole, thus: to be in the whole, or to be predicated of every, is said whenever nothing of the subject can be found of which that which is predicated cannot be said. For nothing of man is found of which animal cannot be said. But to not be in the whole, or to be predicated of none, is said whenever nothing of the subject can be found of which that which is predicated can be said. For nothing of stone can be found of which animal can be predicated. But it must be noted that to be in the whole is said conversely. For if something is predicated of every something, that of which it is predicated is said to be in the whole of that which is predicated, as animal is said of every man. But man is in the whole, that is, as it were a certain part lies hidden within the whole animal. And if anything is in every other, that thing is said to be in that whole of which it was said above, as the same animal, since it is in every man and is predicated of every one of them, man is in the whole animal.

These things therefore having been set down, whenever we speak in such a way that we set letters in place of terms, we do this for brevity and compendiousness, and what we wish to demonstrate universally through letters, we demonstrate. For perhaps in some terms it may be necessary that something false be introduced. But in letters we are never deceived, since for this purpose we use letters as though we were setting down terms. But in the letters themselves, unless the conjunction of terms is firm and valid in itself, neither truth nor falsity will be found. Therefore, whenever we wish to show that one thing is predicated of every other, we set it down thus: let the first term be a, the second b, and let a be predicated of every b. But understand this as if we had set down a as animal and b as man. In the same way also with negatives. For if we say that a is predicated of no thing, this is as if we were to say that a, which is animal, is predicated of no stone, which is b, and whatever other things are similar to these. But every simple syllogism is demonstrated and concluded with three terms. But first let us look at the figures of the syllogisms themselves, afterwards we shall treat of their modes and orders. With three terms therefore so set down that they are near to one another and connected to one another, it is necessary that no more than three combinations be made, in this way: for let a be, let b be, let c be; for either a is predicated of b and of c, or certainly a will be predicated both of b and of c, or the term a and c will appear to be subject to the same things.

Let a be good, let it be just, let it be virtue. For either a, that is good, will be in every b, that is just, and it will be said, every just thing is good; likewise just in every c, that is virtue, and it will be said, every virtue is just. And propositions of this kind will be: every just thing is good, and every virtue is just; or a, that is good, will be predicated of b, which is just, and of c, which is virtue, so that if every just thing is good, every virtue is good; or certainly a, good, will be subject to just and to virtue, so that it is said, every good thing is just, and every good thing is virtue. For in this combination it is predicated of the term a alone. But where a is predicated of every term, and likewise is predicated of every c. This figure I call the first, which is defined thus: the first figure is that in which the term that is subject is predicated of another. For b, which is subject to the term a, is predicated of another term likewise. But I call the extremes of this figure that which is predicated and that which is subject, that is, a and c. For a is predicated of a term, but a term is subject to a term. But I call that the middle which is subject to one and predicated of another, that is, b. For the term a is subject to a term, but is predicated of a term. But the major extreme is that which is predicated first, that is, a. For the same a is predicated of a term. But the minor is that which is subject to the middle term, that is, c, for the term c is subject to the middle term, that is, b; for the middle term is said of it.

But the major term is so called, that is, the one which is predicated, because every predicate is greater than that of which it is predicated. And in the conclusion, just as in the first proposition, the term a is always predicated; for a, namely good, is predicated of just, and it is said, every just thing is good; but the middle term is predicated of c, and it is said, every virtue is just. From these, therefore, it is concluded in the syllogism, every virtue is good, and a, good, will be named of virtue, and therefore it is called by us the major extreme. But we must remember that those things which are equal can be reversed and predicated of each other in turn, and just as that which is predicated is in that which is subject in every case, so again, when converted, that which was subject will be in that which was previously predicated in every case. For if two terms are so equal to each other that neither is greater than the other, when you have predicated one, the term will be in every term. But if you convert and predicate the term of the term, again the term will be in every term. For let f be risible, and let it be man. Therefore if you predicate risible and make man the subject, risible is found in every g. For every man is risible. But if you predicate man of risible, man is found in every risible. For every risible thing is man. But what terms are, or what predication or subjection is, has been sufficiently said in the earlier book on propositions. But lest perhaps we err, [consider] that a universal affirmation seems to be converted.

For it was said about this too above. But now we wish to show only this, that those things which are in a whole are alone converted. This, however, is useful for the demonstration of syllogisms which is made in a circle, which we discussed in the Analytics. And about the first figure of categorical syllogisms it has been set out. But the second figure is whenever the term a is predicated of both terms in this way: for if you say that a, the good, is predicated of every just thing, so that the proposition is in this way, "Every just thing is good," and thence a, the good, is predicated of every virtue, so that you say, "Every virtue is good," you have predicated only a of both terms, and this will be the second figure. But the middle term in this figure will be the one which is predicated of both, that is, a. But the extremes are those which are subjects, that is, b and c. But the major extreme is that of which the term a is first predicated, that is, the just; or if it is predicated first of it, the term is found to be the major extreme. For this reason, because that extreme of which the middle term is first predicated, in the conclusion it too will be predicated, as must be demonstrated later. But the minor extreme will be that of which the middle term is predicated later. But the third figure is whenever a and b are predicated of one term. For if someone says that a, that is, the good, is predicated of c, that is, virtue, so that the proposition is of this kind, "Every virtue is good," and likewise it is predicated of c, so that it is, "Every virtue is just," he makes the third figure.

In this figure, however, the middle term will be the one that is subject to both, that is, c. For a is predicated of the term c and of the term. The major extreme is the one that is predicated first, that is, a; the minor is the one that is predicated afterward, that is, b; or if one prefers to predicate a later and b earlier, the major or minor extreme will be found according to the prior and posterior predication, and here too the major extreme in the conclusions, just as in the other figures above, is predicated of the minor. Having therefore set out the three figures of syllogisms, it must be said that a perfect syllogism is one to which nothing is lacking for a complete and proven conclusion from the things taken and set forth above. But the conclusion made in a manner and order, lacking nothing, is terminated through those things which it set forth beforehand. An imperfect syllogism, however, is one to which nothing is equally lacking for perfection, yet in those things which have been taken in the propositions something is lacking, because of which it seems to be so. But all these definitions will become clear later. Now, however, it must briefly be explained whence these figures arise. For the things from which they arise are again resolved into the same. But the second and third figures seem to arise and be produced from the first figure. For let a be a term in every term, and let it be predicated of every one, and let the true term be predicated of every term. This, as was said, is the first figure of syllogisms.

If anyone therefore converts the major extreme and the proposition, and makes what was previously the predicate the subject, he will produce the second figure. For just as the term a is predicated of the term [b], so it is predicated of c. If therefore a conversion is made, and it comes about that the term [b] is predicated of the term a, the term that was previously the middle is found, and the term a is made subject, while it is predicated of the term c—we have said that it is predicated of both terms. Come now: since good was predicated of just, and just was predicated of virtue, the proposition was: every just thing is good, every virtue is just. With the proposition that is, every virtue is just, remaining, let the first proposition, that is, every just thing is good, be converted, and let it become: every good thing is just. The propositions are therefore found thus: every good thing is just, every virtue is just, and just, that is, [the term] is predicated of a and the terms. Therefore, with the major extreme of the first figure converted, the second figure of syllogisms is produced. But the third figure is born when the minor proposition is converted. For if good is predicated of just, as

is predicated, so every just thing is good, and truly "just" is predicated of virtue, so that it is said, every virtue is justly, if, with the former proposition remaining, that is, every just thing is good, the second, which is, every virtue is just, is converted, and it becomes, every just thing is virtue, all the propositions will be found thus: every just thing is good, every just thing is virtue, and both terms are predicated of "just," and the connection of the third figure is made. Therefore, when the first and last extremes of the first figure are converted, the third or the second figure is born. But each of these three figures has under it several modes of syllogisms, so that the modes are under the figures as species are under their genera. For the first figure has under it, according to Aristotle as author, four modes; but Theophrastus or Eudemus add five other modes to these four, with Aristotle giving the principle in the second book of the Prior Analytics, which will be explained better afterwards. But the second figure has under it four modes; the third, however, according to Aristotle as author, six; others also add one, as Porphyry himself does, following the earlier ones.

And since (as was said in the previous book) some propositions are affirmative and some negative, and of these some are universal and others particular, it is according to these very propositions that the conclusions of syllogisms are joined together. For the first mode of the first figure is the one that is made from two universal affirmatives, inferring a universal affirmative. For if the term a is in every term b, and if term b is predicated of every term c, then term a will be predicated of every term c. For if "good" is predicated of every just thing, so that it is "every just thing is good," and truly "just" is predicated of virtue, so that it is "every virtue is just," it is necessarily concluded that the extremes are predicated of each other, that is, a and c, so that it is "every virtue is good." Are there, then, propositions and a conclusion of this kind? If a is in every b, and b is in every c, then term a will be predicated of every c, that is, "every just thing is good," "every virtue is just"; and the conclusion, "therefore every virtue is good," and this is the first mode of the first figure. But the second mode of the first figure is whenever from a first universal negative and a second universal affirmative a conclusion is inferred by a universal negation. For if a is evil, b is good, c is just, term a will be predicated of no term b. For no good is evil, but term b will be predicated of every term c; for every just thing is good.

Therefore it is concluded that no just thing is evil, as in this way: if term a is predicated of no term, while term b is predicated of every term, then term a will be predicated of no term, as for instance: no good thing is evil, every just thing is good; therefore no just thing is evil. But the third mode of the first figure is whenever a particular affirmative is concluded from a universal affirmative and a particular affirmative. For if a, virtue, is predicated of every b, that is, of good, and good has been predicated particularly of some c, that is, of just, then the conclusion will also be particular, in this way, so that a, virtue, is predicated particularly of some just thing. If therefore term a is in every b, and term b is in some thing particularly, then term a will be in some thing particularly, as for instance: every good thing is virtue. Some just thing is good. Therefore some just thing is virtue. The fourth mode of the first figure is such whenever a particular negative is concluded from a universal negation and a particular affirmation. For if term a is predicated of no term, while term b is predicated of some term, then term a will not be predicated of some term, which the description set out below shows. For the propositions are of this kind: no good thing is evil. Some just thing is good. Therefore some just thing is not evil. These four modes, then, in the first figure Aristotle set down in his Analytics.

But the remaining five modes Theophrastus and Eudemus added, with which Porphyry, a man of the gravest authority, seems to have agreed; they are of this sort. For since a particular affirmative converts with itself, whoever has shown in the conclusion that term a is predicated particularly of a certain term c, has in that same conclusion shown that term c is in turn predicated particularly of term a. For if a particular proposition converts with itself in the conclusion, if term a is in a certain term c, term c will be predicated of a certain term a. Likewise, whoever has proved a universal negative in the conclusion, it is necessary that he has also proved its conversion in the same conclusion. For a universal negative always converts with itself. For if someone has proved that term a is predicated of no term, there is no doubt that in this conclusion that also has been proved, that the term is predicated of no term a. For always, as has been said, a universal negative converts with itself. A universal affirmative is also contained in a double conclusion; for whoever shows that term a is predicated of every term, shows also that the term is predicated particularly of a certain term a. For if someone has proved that animal is predicated of every man, saying thus, every man is an animal, he has also necessarily shown particularly that a certain animal is a man.

Thus a universal negation, a universal affirmation, and a particular affirmative are always concluded in two ways. For some convert with themselves: the particular one particularly, the universal one universally. Others, although a universal affirmative itself, convert with itself particularly. But a particular negation never converts with itself, and therefore it retains a simple conclusion. What we have just said is shown by Aristotle in the second book of the Prior Analytics: namely, that Theophrastus and Eudemus, taking this as their starting point, set their minds to adding to the other syllogisms in the first figure, which are of the kind called kata anaklasin, that is, by a certain refraction and conversion of the proposition. And the fifth mode is from two universal affirmations, drawing a particular affirmative conclusion in this way: if a is in every b, and b is in every c, it could indeed be concluded that a is in every c. But since that universal proposition, as has been said, converts particularly, setting aside the fact that the term a is predicated of every c, the conclusion is said to be that the term is predicated of some a. This must be shown by this example: for if the propositions are thus, every just thing is good, every virtue is just, it could indeed be concluded that every virtue is good.

But since a proposition converts with itself in such a way that it becomes "a certain good is a virtue" particularly, a particular syllogism and conclusion is gathered from two universal affirmatives. Its form is such: the term a is in every b, the term c is in every b, therefore the term c is in a certain a, as for example: Every just thing is good. Every virtue is just. A certain good is just. It is said to be by conversion and refraction, because what was concluded universally, when converted, is concluded particularly. The sixth mode of the first figure is the one that comes from a universal negative and a universal affirmative, gathering a universal conclusion through conversion. For if the term a is in no c, and the term c is in every b, it could indeed be concluded that the term a is in no b; but since the universal negative converts, we say that the term b is in no a, as in this way: No good is evil. Every just thing is good. It could be concluded: No just thing is evil; but from these by conversion we conclude: No evil is just.

The seventh mode of the first figure is the one which, from a universal affirmative and a particular affirmative, gathers an affirmative conclusion through particular conversion. For if the term A is in every B, and the term C is predicated of a certain term, then the term A can be predicated of a certain term. But since a particular affirmation converts with itself, the conclusion is made through conversion, and the term is said to be predicated of a certain A, so that it is thus: every good is a virtue, a certain just thing is a good. It could indeed be concluded that a certain just thing is a virtue, but because a particular affirmation converts, we say that a certain virtue is just. The eighth mode of the first figure is whenever a particular conclusion is gathered from a universal affirmation and a universal negation. For if the term A has been predicated of every term, but the term B is predicated of no term, it could not be concluded that the term A is predicated of no term. But why it cannot be, has been said in the Resolutorics. But since a universal negative converts with itself, it can be said and converted that the term is predicated of no A, but the term B is said of a certain A, since a universal affirmative converts particularly with itself; wherefore the term will not be predicated of a certain A. So that it is thus: every good is just, no evil is good, it could not be concluded that no evil is just, but it is converted thus: no good is evil.

A certain just thing is good. Therefore a certain just thing is not evil. The ninth mode of the first figure is the one which, from a particular affirmative and a universal negative, gathers a particular negative through conversion. For if the term A is predicated of a certain term, and the term B is predicated of no term, it cannot indeed be said that the term A will not be predicated of a certain term. But why it cannot be, we have also said this in the Resolutions; but since a universal negation can be converted, it is said that the term B is predicated of no term, and the term A is predicated of a certain B; therefore the term B will not be predicated of a certain A, so that it may be thus: A certain good thing is just. No evil thing is good. Therefore a certain just thing is not evil. Having therefore set out the nine modes of the first figure, let us come to the four modes of the second figure. Let only this be established, that just as in the first figure, through the nine modes set out above, both a universal affirmation and a universal negation, and a particular affirmation and a particular negation, are gathered in the conclusion, so in the second figure neither a universal nor a particular affirmative can be gathered, but only negatives, either particularly or universally, are gathered. Now the first mode of the second figure is this: whenever, from a universal negation and a universal affirmation, a universal negative is gathered.

For if the term a is predicated of no term and of every term, the term b will be predicated of no term. For let a be good, let b be evil, let c be just. If anyone therefore speaks thus: No evil is good; every just thing is good; he concludes: No just thing is evil. It is clear, therefore, that the greater extreme is predicated of the lesser in the conclusion. But all the syllogisms of the second figure, although they are true, are not nevertheless proved true from themselves, but are completed from the modes of the first figure. For if the term a is predicated of no term and is in every term, it has not yet been proved that the term is altogether predicated of no term. But if anyone makes from this first mode of the second figure the second mode of the first figure, the whole syllogism and its conclusion are proved through conversion. For if anyone, by this syllogism which is "the term a is in no b, and the same term a is predicated of every [term]," converts the proposition so as to make it "a is in every [term]"—for every universal negative is converted—if anyone therefore says that the term a is predicated of no term, and therefore [b] will be predicated of no term a, but the term a will be predicated of every term. There is made, therefore, the second mode of the first figure, gathering a universal negative from a universal negative and a universal affirmative, so that the conclusion may be: It is predicated, therefore, of no term c. By these conversions, therefore, every syllogism and conclusion of the second and third figure is gathered and proved.

And therefore, since they are not proved from themselves but are established from higher ones—that is, from the moods of the first figure—whatever syllogism is found in the second or third figure is called imperfect. But the second mood of the second figure is when, from a universal affirmative and a universal negative with their terms transposed, a universal negative is again concluded. For if the term a is in every term and is predicated of no term, the term b will be predicated of no term. For let a be good, let b be just, let c be evil. If anyone therefore speaks thus: Every just thing is good; no evil thing is good; he concludes: No evil thing is therefore just. But this combination and conjunction of propositions has a double conversion. For it is shown from the second mood of the first figure thus: For if the term a is in every term and is predicated of no term, this universal negative is converted. It will therefore be that the term b is predicated of no term a. But if this is so, the syllogism will be of this kind: the term b is predicated of no term a; the term a is in every term c; therefore the term b will be predicated of no term c.

Behold, one conversion of a negative proposition has been made. But since we have said that the conclusion is not "in no b" but "in no term," here the universal negative conclusion is converted: and just as it was concluded that a term is predicated of no term, so it is concluded that of no term a term is predicated. The third mood of the second figure is whenever a particular negative is inferred from a universal negative and a particular affirmative. For if term a is predicated of no term, and is in some term, then a term will not be predicated of some term. For let a be good, and let the terms be evil, just. If anyone therefore speaks thus: No evil is good; but something just is good; it necessarily concludes: Some just thing is evil. Here too the syllogism is proved by conversion in this way. For if term a is predicated of no term, then a term will be predicated of no a. But term a is predicated of some term. Therefore the fourth mood of the first figure returns, which is from a universal negation and a particular affirmation, collecting a particular negative, as in this syllogism also. For here too it collects a particular negative, that is, that a term is not predicated of some term. The fourth mood of the second figure is that which from a universal affirmation and a particular negation collects a particular negative. For if term a is in every term, and is not predicated of some term, then a term will not be predicated of some term.

For let a be good, just, evil. If someone therefore says: Every just thing is good; some evil thing is not good, he concludes: Therefore some evil thing is not just. But this combination and order of propositions cannot be approved by conversion. For a universal affirmative cannot be converted with itself. Therefore this syllogism is demonstrated from the first figure not through conversion, but through impossibility, since if the particular negative conclusion is not concluded in this syllogism, some incongruous and impossible thing results. But this impossibility will be demonstrated through the first figure. For I say that if term a is predicated of every term, and is not in some term, such a conclusion is inferred, that a term is not predicated of some term. For if this is false, the proposition opposed to it will be true. But universal affirmatives are opposed to particular negatives, as we taught in the earlier book. If therefore this particular negation is not the conclusion, there will be a universal affirmation. For let the affirmation be universal, and let term a be predicated of every term; but term a is predicated of every term, and term b is said to be predicated of every term; therefore term a is predicated of every term, which cannot happen. For we posited the proposition a earlier in such a way that we said term a is not predicated of some term. This therefore has been shown through the first mode of the first figure.

Therefore in the second figure every syllogism is imperfect, and its proof is either reduced to the first figure through conversion, or by a hypothetical arrangement through impossibility it is shown that the first figure cannot be otherwise; and indeed all the others are proved through impossibility, which will be demonstrated a little later. It remains for us to explain the knots and orders of the third figure. But before we do this, that must first be seen, that in the modes of the third figure a universal conclusion is never collected. But whether the collections are negative or affirmative, they will always be particular, never general. Now the first mode of the third figure is this, which from two universal affirmations collects a particular affirmation. For if a and the terms are predicated of every term, the term a will be predicated of some term through conversion. For if a term is predicated of every term, and a universal affirmation is converted particularly to itself, the term c is predicated of some term. But if this is so, the third first mode of the figure is made, which is from a universal and a particular affirmation, and collects that the term a is predicated of some term. For let a be just, virtue, good. For if someone speaks thus: Every good thing is just. Every good thing is virtue, the conclusion is made: A certain virtue is just.

Others change the terms and wish to make a mood in the second figure, so that a is virtue, b just, c good, as in this syllogism: Every good is virtue; every good is just; and let it be concluded: A certain just thing is virtue. But Aristotle does not separate this from the superior mood; he thinks the two are one mood, and for that reason we have said, doubting, that there are seven moods of the third figure; but Aristotle is rather to be followed, and therefore let us say that there is another mood which can be seen wholly as the second. The second mood of the third figure, then, is whenever a particular negation is inferred from a universal negation and a universal affirmation. For if the term a is predicated of no term, and the term b is predicated of every term, the term a will not be predicated of a certain term. For if the term a is predicated of no term, and b is predicated of every c, the term a will be predicated of a certain term. For a universal affirmative is converted particularly. It is concluded, therefore, in the fourth mood of the first figure, that the term a is not predicated of a certain term. For let a be evil, b just, c good. If someone says thus: No good is evil; every good is just; he must conclude: Therefore a certain just thing is not evil. From this it is to be considered that the major extreme is predicated in the conclusion. The third mood of the third figure is whenever a particular affirmation is concluded from a particular and a universal affirmative.

For if term a is predicated of some c, and term b is predicated of every term, it is concluded that term a is predicated of some term through a double conversion. For since term b is predicated of every term, and term a is predicated of some term, and a particular affirmative always converts with itself, term b will be predicated of some a. The propositions are therefore as follows: term b is predicated of every term, and term b is predicated of some a; and if this is so, it is inferred in the third mode of the first figure that term b is predicated of some a. And thus the particular affirmative is converted, and term a will be predicated of some term, and there will be double conversions, one of the proposition, the other of the conclusion. For let a be just, b virtue, c good. If anyone therefore says thus: Some good is just; every good is virtue; he must conclude: Some virtue is just. This is the fourth mode of the third figure, whenever a particular affirmative is inferred from a universal affirmative and a particular affirmative. For if term a is predicated of every term, and term b is in some term, it is concluded that term a is predicated of some term through conversion.

For if a term is predicated of some term, etc., and a term is predicated of some term, since a particular affirmative converts with itself, it becomes a syllogism in the third mode of the first figure, which is formed from a universal affirmative and a particular affirmative, concluding a particular affirmative, so that the syllogism is as follows: term a is in every c, and term b is in some c; therefore term a is in some b. Let a be virtue, b just, c good. If someone therefore says thus: Every good is virtue, some good is just, he will conclude that: some just thing is virtue. The fifth mode of the third figure is whenever from a particular negative and a universal affirmative a particular negative is concluded. But this mode cannot be proved by conversion, but by impossibility, just as the fourth mode of the second figure was proved. For if term a is not predicated of some term c, but term b is predicated of every term, term a will not be predicated of some term; for if this is not so, it will be true that term a is predicated of every term; but term b is predicated of every term; therefore term a will be predicated of every term, which cannot happen. For term a was posited earlier in such a way that it was not predicated of some term c.

But if the general affirmation is not in the conclusion of the syllogism, so that a term is predicated of every term, its contradictory opposite will be the particular negation, so that the term a is not predicated of some term. For let a be evil, and let the term be just, and the term good. If anyone therefore speaks thus: Some good is not evil, Every good is just, he must conclude: Therefore some evil is not [just]. The sixth mode of the third figure is whenever a particular negation is inferred from a universal negative and a particular affirmative through conversion. For if the term a is in no term, but the term b is predicated of some term, the conclusion comes about that the term a is not predicated of some term. For if the term a is predicated of no term, and the term b is predicated of some term, and the term is predicated of some term, since the particular affirmative can be converted. There comes about therefore such a syllogism, that the term a is predicated of no term, the term c is predicated of some term, and the term a is not predicated of some term. Let a be evil, just, good. If anyone therefore says: No good is evil, Some good is just, he concludes: Some just is not evil. Having therefore settled these matters, what the syllogism itself is must be defined. It is defined thus: a syllogism is a discourse in which, certain things having been posited and conceded, something other than those things which have been posited and conceded necessarily follows through those things which have been conceded.

We have said that an oration is a syllogism for the reason that every definition is drawn from a general term, and the genus of a syllogism is an oration. But what was said, "with certain things having been posited and conceded," is to be understood as if it had been said thus: "according to which, with things posited and conceded"; for in order that a syllogism be made, something is first said by the one proposing it, which the hearer may concede, and if he has conceded it, he concludes and completes the syllogism, for the reason that doubtful matters are shown through certain things conceded and proved, and a true negation is conceded equally as well. But the other elements in the definition of a syllogism are such as distinguish incomplete syllogisms from the definition of true syllogisms. For what was said, "with certain things having been posited," clearly shows the multitude of things assumed and of propositions. For there are those which are thought to be syllogisms of this kind, in which there is only one proposition and one conclusion. Such as this: you see, therefore you live; you are a man, therefore you are an animal; and other such things, which indeed the ancients did not accept among syllogisms, for a syllogism is a collection of certain things. But a collection is not of fewer than many things, and whoever has posited one proposition, he does not collect. Therefore he will make no syllogism. For a syllogism, to be as narrow as possible, ought to be established by two propositions.

But what was said, that something other than the things themselves which have been conceded must necessarily come about, is because frequently syllogisms of such a kind are made by some people that they conclude in the conclusion the very things they proposed, as is the case here: If you are a man, you are a man; but you are a man, therefore you are a man. For it concluded the same thing which it proposed when granting it. And therefore, for the sake of distinguishing these, it was said that something other than the things which have been conceded ought to come about, as in all the superior syllogisms which we set out in the modes of the three figures and in the demonstration. But syllogisms of the kind just described are utterly ridiculous, because what was conceded beforehand is gathered in the conclusion as if it were something doubtful. For the statement that it must necessarily come about pertains to this, since frequently certain propositions are brought in for the sake of induction whose conclusion is in no way true, as if someone were to say: He who knows music is a musician, and let it be conceded; and he who knows arithmetic is an arithmetician, and he who knows medicine is a physician, and he who knows good is good. When, then, all these have been conceded, let him say: and he who knows evil is evil, which seems similar to the foregoing, but is in every way false: for good men do not guard against things otherwise than by having known evils. And therefore, on account of those conclusions which are reached through those propositions which are stated by induction, it was added that the conclusions in syllogisms come about necessarily, that is, come about by necessity.

There is also another exposition, but it has already been given in our Analytics. But what was said, "through the very things which have been posited," was said on account of those who make such syllogisms in which either something less, or something more, or something other than what ought to have been proposed is proposed. For syllogisms of this kind are made. For if someone says thus: "Socrates is a man, every man is an animal," and concludes, "Therefore Socrates is animate," he has proposed something less, because he did not say that every animal is animate. But if he had proposed it thus, he would rightly conclude that Socrates is animate, by saying: "Socrates is a man, every man is an animal, and every animal is animate; therefore Socrates is animate." But to propose something more is this, as if someone says thus: "Every man is an animal, every animal is animate, but also the sun is in Aries; therefore every man is animate." Here indeed what he interposed, that the sun is in Aries, is superfluous. But some propose something other than what is necessary in this way, as if someone says: "Every man is an animal, but virtue is a good; therefore every man is animate." None, therefore, of these propositions pertains to the matter which he wished to conclude. Having therefore set out the definition of the syllogism, let us come to the nature and resolution of the prior modes, and first let all be arranged in order.

The modes of the first figure.

First: Every just thing is good. Every virtue is just. Therefore every virtue is good.

Second: No good thing is evil. Every just thing is good. Therefore no just thing is evil.

Third: Every good thing is a virtue. Some just thing is good. Therefore some just thing is a virtue.

Fourth: No good thing is evil. Some just thing is good. Therefore some just thing is not evil.

Fifth: Every just thing is good. Every virtue is just. Therefore some good thing is a virtue.

Sixth: No good thing is evil. Every just thing is good. Therefore no evil thing is just.

Seventh: Every good thing is a virtue. Some just thing is good. Therefore some virtue is just.

Eighth: Every good thing is just. No evil thing is good. Therefore some just thing is not evil.

Ninth: Some good thing is just. No evil thing is good. Therefore some just thing is not evil.

The modes of the second figure.

First: No evil thing is good. Every just thing is good. Therefore no just thing is evil.

Second: Every just thing is good. No evil thing is good. Therefore no evil thing is just.

Third: No evil thing is good. Some just thing is good. Therefore some just thing is not evil.

Fourth: Every just thing is good. Some evil thing is not good. Therefore some evil thing is not just.

The modes of the third figure.

First: Every good thing is just. Every good thing is virtue. Therefore some virtue is just.

Second: Every good thing is virtue. Every good thing is just. Therefore some just thing is virtue.

Third: No good thing is evil. Every good thing is just. Therefore some just thing is not evil.

Fourth: Some good thing is just. Every good thing is virtue. Therefore some virtue is just.

Fifth: Every good thing is virtue. Some good thing is just. Therefore some just thing is virtue.

Sixth: Some good thing is not evil. Every good thing is just. Therefore some just thing is not evil.

Seventh: No good thing is evil. Some good thing is just. Therefore some just thing is not evil.

These, then, are all the modes of the three figures, of which the first four of the first figure are called indemonstrable and direct, that is, demonstrated without any conversion; and they are called indemonstrable because they are not demonstrated through others, and perfect because they are proved through themselves. And they are first because they are first in position and nature, and all the rest are resolved into them. The five modes of the first figure are also imperfect and [proved] through conversion. But all [the modes] of the second and third figures are imperfect, since they are proved through the first modes of the first figure, for they are resolved into them: so that we may resolve them through conversion, and through impossibility, as those two were demonstrated above. Let us therefore consider their principles, since that into which they are born is that into which they are resolved. The fifth mode, then, of the first figure is produced from the first mode of the first figure. For with the two prior propositions remaining, the conclusion of the first mode converted particularly makes the fifth syllogism, which is declared in the description set out below. But the sixth mode of the first figure takes its beginning from the second mode of the first figure.

For when the two earlier premises of the second mood remain, with the universal conclusion converted universally, the sixth syllogism is born, as the description set out below teaches.

The seventh mood of the first figure is born from the third mood of the first figure. For when the two earlier premises remain, with the particular affirmative conclusion converted, the arrangement of the seventh mood is produced.

But the eighth and ninth moods of the first figure are resolved into the fourth mood of the first figure, and do not even take their beginning from it. The eighth is resolved into the fourth in this way: for the first premise of the fourth, converted universally into the second of the eighth, and the first premise of the eighth mood converted particularly into the second of the fourth mood, the same conclusion is gathered, that is, a particular negation.

No good thing is evil, a universal negation. Some just thing is good, a particular affirmation. Converted universally: Every good thing is just. Converted universally: No evil thing is good. Some just thing is not evil, the same conclusion: Some just thing is not evil.

But the ninth mood is resolved into the fourth mood thus: the first proposition of the fourth is converted universally into the second proposition of the ninth, and the second of the fourth particularly into the first of the ninth, and the same conclusion remains, a particular negative.

No good is evil, a universal negative. Some just thing is good, a particular affirmative. Converted particularly: some good thing is just. Converted universally: no evil is good. Some just thing is not evil, the same conclusion: some just thing is not evil.

Having therefore resolved the five moods of the first figure in the four above, let us resolve the four moods of the second figure into the four moods of the prior figure, of which three are proved by conversion. But the fourth by impossibility alone. But indeed the first and second moods of the second figure are resolved into the second mood of the prior figure, and the first is resolved thus. For with the first universal negative converted universally, and the second universal affirmative remaining, the same conclusion is born from both.

The second mood of the second figure is resolved into the second mood of the first figure thus: with the second proposition converted and the second of the first remaining, the conclusion is made converted universally.

But the third mood of the second figure is generated from the fourth mood of the first figure. For in order that the universal negation be converted universally into the first proposition, and the second propositions remain the same, the term and proposition of the syllogism are gathered in this way:

The fourth mood of the second figure, since already at the outset, when it was made through conversion, it could not be turned back into the mood of the superior first figure, but was demonstrated through impossibility, here also is reduced to the superior moods through impossibility; and since all the moods of the second figure are shown through impossibility, for that reason let us also, beginning from the fourth, resolve all through impossibility. For the fourth mood of the second figure is resolved into the first mood of the first figure through impossibility, the third into the second, the second into the third, the first into the fourth, which will be clear in this way. If anyone therefore has granted these two propositions, namely, every good is virtue, and a certain just thing is not virtue, he must also grant the conclusion which is, therefore a certain just thing is not good. For if this is false, its contradictory will be true, which is, every just thing is good; but he granted that which is the first of the fourth mood, namely, every good is virtue. From these therefore let him conclude, therefore every just thing is virtue.

But earlier he conceded the second proposition of the fourth mood, which is, "some just thing is not virtue." Now, however, he concedes "every just thing is virtue," and he will conclude two propositions opposed to each other at the same time, which cannot happen. This comes about for the reason that the conclusion of the fourth mood has been converted into the second proposition of the first mood; but if the second proposition of the first mood is not gathered in the conclusion of the fourth, the conclusion of the fourth, that is, the particular negation, will remain. But lest it disturb us that we have posited different terms in resolving the mood than we did above in setting it out, for we are not now laboring over terms, but we are expending our effort on constructing and resolving figures and moods and combinations. In the same way the remaining moods of the second figure are also resolved into the first four.

The third mood of the second figure is resolved into the second mood of the first figure thus: if someone grants the two first propositions of the third mood, he will also conclude the particular negation, which is, "therefore some just thing is not good." For if this is false, its opposite will be true, which is, "every just thing is good." But that proposition has also been conceded, which is, "no good thing is evil." From these, therefore, it is gathered that no just thing is evil. But earlier he had conceded that some just thing is evil; now, however, no just thing is evil. He concedes two propositions opposed to each other at one and the same time, which cannot happen.

Therefore, once the universal conclusion "every just thing is good" is removed, the particular negation remains, which is "some just thing is not good."

The second mood of the second figure is resolved into the third mood of the first figure as follows: if someone has conceded the two propositions of the second figure, he also concedes the conclusion, which is "therefore a just thing is good." For if this is false, its contradictory, the particular affirmation "some just thing is good," will be true. But the same person conceded the proposition "every good thing is virtue"; it necessarily follows that "some just thing is virtue." Yet he who had already conceded the second proposition of the second mood, which is "no just thing is virtue," concedes two contradictories at the same time, which cannot happen.

Likewise, the first mood of the second figure is resolved into the fourth mood of the first figure as follows: whoever concedes the two propositions of the first mood necessarily also concedes the conclusion. For if that is false, its contradictory, the particular affirmative "some just thing is good," will be true. But the same person conceded the proposition "no good thing is evil"; it necessarily follows that "therefore some just thing is not evil." Yet he who had previously conceded the proposition "every just thing is evil" concedes two contradictories at the same time, which cannot happen. Therefore, once the particular affirmation "some just thing is good" is removed, there remains the proposition "no just thing is good.

It remains for us to reduce the moods of the third figure to the first four, of which five are resolved into the first four through conversion and through impossibility, while one alone, that is the fifth, is resolved into the earlier ones through impossibility alone. The first mood of the third figure is resolved into the third mood of the first figure in this way: for if the first proposition of the third mood of the first figure remains, and the second particular proposition of the third mood of the first figure is converted universally, and it becomes the second proposition of the first mood of the third figure, the same conclusion is gathered, that is, a particular affirmation.

Or indeed thus, because above we said such a syllogism with its terms changed, which Aristotle does not consider dissimilar.

The second mood of the third figure is resolved into the fourth mood of the first figure in this way. For if the first propositions of the second mood of the third figure and of the fourth mood of the first figure remain, but the second proposition of the fourth mood of the first figure is converted universally, and it becomes the second proposition of the second mood of the third figure, the same conclusion is produced.

The third mood of the third figure is resolved into the third mood of the first figure. For if the first proposition of the third mood of the first figure and the second proposition of the third mood of the third figure remain, and the second proposition of the third mood of the first figure, being particular, is converted particularly, and becomes the first [proposition] of the third mood of the third figure, the converted conclusion arises particularly.

The fourth mood of the third figure is resolved into the third mood of the first figure: for if the first propositions of both remain, and the second particular [propositions] are converted particularly, the same conclusions arise.

The remaining sixth syllogism of the third figure is generated from the fourth mood of the first figure; for when the first propositions of these remain and the second [propositions] are changed particularly in their particles, the conclusion will remain in each.

But the fifth, which remains, just as it was previously proved through impossibility, so also now it is resolved through impossibility. But just as one was resolved, all must be resolved in the same order. Now the sixth mood of the third figure is resolved into the third mood of the first figure. But the fifth mood of the third figure is resolved into the first [mood] of the first figure. The fourth mood of the third figure is resolved into the fourth mood of the first figure. The third mood of the third figure is resolved into the second mood of the first figure. The second mood of the third figure is resolved into the first mood of the first figure. The first moods of the third figure are resolved into the second moods of the first figure.

But the sixth mood of the third figure is resolved by impossibility into the third mood of the first figure in this way: if, then, anyone has granted the two propositions of the sixth mood of the third figure, he must also grant the conclusion, which is, "a certain just thing is not evil." For if this is false, its contradictory will be true, namely the first proposition of the third mood, which is, "every just thing is evil." But he has also granted the second proposition, which is, "a certain good thing is just." From these, therefore, he must grant, "a certain good thing is evil," who had previously granted the first proposition of the sixth mood of the third figure, which is, "no good thing is evil." At one and the same time he grants two things that are contradictory to each other, which the description declares cannot happen.

In this way all the remaining moods of the third figure are referred back to the first moods of the first figure, which the description set out below declares, in that the earlier fifth mood, which could not be resolved by conversion, has been resolved by impossibility.

In the resolution of the second mood of the third figure into the first mood of the first figure, this impossibility results: that one grants two contraries at one time, which cannot happen. For never are two contraries found to be true at the same time together.

Nor let that disturb us, that in some cases a contrary proposition and conclusion are found, but in others a contradictory. For he has erred equally who has granted both contraries as if both contradictories. For just as contradictories can never be true at one time, so too can contraries not be.

This much concerning the introduction to the Categorical Syllogisms, following Aristotle as much as possible, and having borrowed some things from Theophrastus and Porphyry, as far as the brevity of an introduction permitted, I have expressed. But if anything is lacking, I shall set it forth more thoroughly in my Analytics. Now, however, as far as pertained to the form alone of the Categorical Syllogisms, this work is complete for us here, and elaborated for the accumulation of an introduction. Nor let this disturb us, if some propositions and conclusions here are false, since we have undertaken to discuss not the truths of things, but the connections, figures, and moods of syllogisms. For when these are known, if the subtlety of disputation draws anyone to the perfect study of the discipline of logic, let them first learn about ambiguous disputations; afterwards from these, truth in things and falsehood will be considered.