Aristotle 384 - 322 62  
Categories, Interperetation, Sophistical Refutations
 
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Chapters 46
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1 Categories
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Things are termed homonymous, of which the name alone is common, but the definition (of substance according to the name) is different; thus "man" and "the picture of a man" are each termed "animal," since of these, the name alone is common, but the definition (of the substance according to the name) is different: as if any one were to assign what was in either, to constitute it "animal," he would allege the peculiar definition of each. But those are called synonyms, of which both the name is common, and the definition (of the substance according to the name) is the same, as both "a man" and "an ox" are "animal," for each of these is predicated of as "animal" by a common name, and the definition of the substance is the same, since if a man gave the reason of each as to what was in either, to constitute it "animal," he would assign the same reason. Again, things are called paronyms which, though differing in case, have their appellation (according to name) from some thing, as "a grammarian" is called so from "grammar," and "a courageous man" from "courage."
 
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Of things discoursed upon, some are enunciated after a complex, others after an incomplex, manner; the complex as "a man runs," "a man conquers," but the incomplex as "man," "ox," "runs," "conquers." Likewise also some things are predicated of a certain subject, yet are in no subject, as "the man" is predicated of a subject, i. e. of "some certain man," yet is in no subject. Others, again, are in a subject, yet are not predicated of any subject, (I mean by a thing being in a subject, that which is in any thing not as a part, but which cannot subsist without that in which it is,) as "a certain grammatical art" is in a subject, "the soul," but is not predicated of any; and "this white thing" is in a subject, "the body," (for all "colour" is in "body,") but is predicated of no subject. But some things are both predicated of and are in a subject, as "science" is in a subject—"the soul," but is predicated of a subject, namely, "grammar." Lastly, some are neither in, nor are predicated of, any subject, as "a certain man" and "a certain horse," for nothing of this sort is either in, or individuals predicated of, a certain subject. In short, individuals, and whatever is one in number, are predicated of no subject, but nothing prevents some of them from being in a subject, for "a certain grammatical art" is amongst those things which are in a subject, but is not predicated of any subject.
 
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When one thing is predicated of another, as of a subject, whatever things are said of the predicate, may be also said of the subject, as "the man" is predicated of "some certain man," but "the animal" is predicated of "the man," wherefore "the animal" will be predicated of "some certain man," since "the certain man" is both "man" and "animal." The differences of different genera, and of things not arranged under each other, are diverse also in species, as of "animal" and "science". For the differences of "animal" are "quadruped," "biped," "winged," "aquatic," but none of these, forms the difference of "science," since "science," does not differ from "science," in being "biped." But as to subaltern genera, there is nothing to prevent the differences being the same, as the superior are predicated of the genera under them; so that as many differences as there are of the predicate, so many will there also be of the subject.
 
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Of things incomplex enunciated, each signifies either Substance, or Quantity, or Quality, or Relation, or Where, or When, or Position, or Possession, or Action, or Passion. But Substance is, (to speak generally,) as "man," "horse;" Quantity, as "two" or "three cubits;" Quality, as "white," a "grammatical thing;" Relation, as "a double," "a half," "greater;" Where, as "in the Forum," "in the Lyceum;" When, as "yesterday," "last year;" Position, as "he reclines," "he sits;" Possession, as "he is shod," "he is armed;" Action, as "he cuts," "he burns;" Passion, as "he is cut," "he is burnt." Now each of the above, considered by itself, is predicated neither affirmatively nor negatively, but from the connexion of these with each other, affirmation or negation arises. For every affirmation or negation appears to be either true or false, but of things enun- enunciated without any connexion, none is either true or false, as "man," "white," "runs," "conquers."
 
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Substance, in its strictest, first, and chief sense, is that which is neither predicated of any subject, nor is in any; as "a certain man" or "a certain horse." But secondary substances are they, in which as species, those primarily-named substances are inherent, that is to say, both these and the genera of these species; as "a certain man" exists in "man," as in a species, but the genus of this species is "animal;" these, therefore, are termed secondary substances, as both "man" and "animal." But it is evident, from what has been said, that of those things which are predicated of a subject, both the name and the definition must be predicated of the subject, as "man" is predicated of "some certain man," as of a subject, and the name, at least, is predicated, for you will predicate "man" of "some certain man," and the definition of man will be predicated of "some certain man," for "a certain man" is both "man" and "animal;" wherefore both the name and the definition will be predicated of a subject. But of things which are in a subject for the most part, neither the name nor the definition is predicated of the subject, yet with some, there is nothing to prevent the name from being sometimes predicated of the subject, though the definition cannot be so; as "whiteness" being in a body, as in a subject, is predicated of the subject, (for the body is termed "white,") but the definition of "whiteness" can never be predicated of body. All other things, however, are either predicated of primary substances, as of subjects, or are inherent in them as in subjects; this, indeed, is evident, from several obvious instances, thus "animal" is predicated of "man," and therefore is also predicated of some "certain man," for if it were predicated of no "man" particularly, neither could it be of "man" universally. Again, "colour" is in "body," therefore also is it in "some certain body," for if it were not in "some one" of bodies singularly, it could not be in "body" universally; so that all other things are either predicated of primary substances as of subjects, or are inherent in them as in subjects; if therefore the primal substances do not exist, it is impossible that any one of the rest should exist.

But of secondary substances, species is more substance than genus; for it is nearer to the primary substance, and if any one explain what the primary substance is, he will explain it more clearly and appropriately by giving the species, rather than the genus; as a person defining "a certain man" would do so more clearly, by giving "man" than "animal," for the former is more the peculiarity of "a certain man," but the latter is more common. In like manner, whoever explains what "a certain tree" is, will define it in a more known and appropriate manner, by introducing "tree" than "plant." Besides the primary substances, because of their predicates; subjection to all other things, and these last being either predicated of them, or being in them, are for this reason, especially, termed substances. Yet the same relation as the primary substances bear to all other things, does species bear to genus, for species is subjected to genus since genera are predicated of species, but species are not reciprocally predicated of genera, whence the species is rather substance than the genus.

Of species themselves, however, as many as are not genera, are not more substance, one than another, for he will not give a more appropriate definition of "a certain man," who introduces "man," than he who introduces "horse," into the definition of "a certain horse:" in like manner of primary substances, one is not more substance than another, for "a certain man" is not more substance than a "certain ox." With reason therefore, after the first substances, of the rest, species and genera alone are termed secondary substances, since they alone declare the primary substances of the predicates; thus, if any one were to define what "a certain man" is, he would, by giving the species or the genus, define it appropriately, and will do so more clearly by introducing "man" than "animal;" but whatever else he may introduce, he will be introducing, in a manner, foreign to the purpose, as if he were to introduce "white," or "runs," or any thing else of the kind, so that with propriety of the others, these alone are termed substances. Moreover, the primary substances, because they are subject to all the rest, and all the others are predicated of, or exist in, these, are most properly termed substances, but the same relation which the primary substances bear to all other things, do the species and genera of the first substances bear to all the rest, since of these, are all the rest predicated, for you will say that "a certain man" is "a grammarian," and therefore you will call both "man" and "animal" "a grammarian," and in like manner of the rest.

It is common however to every substance, not to be in a subject, for neither is the primal substance in a subject, nor is it predicated of any; but of the secondary substances, that none of them is in a subject, is evident from this; "man" is predicated of "some certain" subject "man," but is not in a subject, for "man" is not in "a certain man." So also "animal" is predicated of "some certain" subject "man," but "animal" is not in "a certain man." Moreover of those which are, in the subject, nothing prevents the name from being sometimes predicated of the subject, but that the definition should be predicated of it, is impossible. Of secondary substances however the definition and the name are both predicated of the subject, for you will predicate the definition of "a man" concerning "a certain man," and likewise the definition of "animal," so that substance, may not be amongst the number, of those things which are in a subject.

This however is not the peculiarity of substance, but difference also is of the number of those things not in a subject; for "pedestrian" and "biped" are indeed predicated of "a man" as of a subject, but are not in a subject, for neither "biped" nor "pedestrian" is in "man." The definition also of difference is predicated of that, concerning which, difference is predicated, so that if "pedestrian" be predicated of "man," the definition also of "pedestrian" will be predicated of man, for "man" is "pedestrian." Nor let the parts of substances, being in wholes as in subjects, perplex us, so that we should at any time be compelled to say, that they are not substances; for in this manner, things would not be said to be in a subject, which are in any as parts. It happens indeed both to substances and to differences alike, that all things should be predicated of them univocally, for all the categories from them are predicated either in respect of individuals or of species, since from the primary substance there is no category, for it is predicated in respect of no subject. But of secondary substances, species indeed is predicated in respect of the individual, but genus in respect to species and to individuals, so also differences are predicated as to species and as to individuals. Again, the primary substances take the definition of species and of genera, and the species the definition of the genus, for as many things as are said of the predicate, so many also will be said of the subject, likewise both the species and the individuals accept the definition of the differences: those things at least were univocal, of which the name is common and the definition the same, so that all which arise from substances and differences are predicated univocally.

Nevertheless every substance appears to signify this particular thing: as regards then the primary substances, it is unquestionably true that they signify a particular thing, for what is signified is individual, and one in number, but as regards the secondary substances, it appears in like manner that they signify this particular thing, by the figure of appellation, when any one says "man" or "animal," yet it is not truly so, but rather they signify a certain quality, for the subject is not one, as the primary substance, but "man" and "animal" are predicated in respect of many. Neither do they signify simply a certain quality, as "white," for "white" signifies nothing else but a thing of a certain quality, but the species and the genus determine the quality, about the substance, for they signify what quality a certain substance possesses: still a wider limit is made by genus than by species, for whoever speaks of "animal," comprehends more than he who speaks of "man."

It belongs also to substances that there is no contrary to them, since what can be contrary to the primary substance, as to a certain "man," or to a certain "animal," for there is nothing contrary either at least to "man" or to "animal?" Now this is not the peculiarity of substance, but of many other things, as for instance of quantity; for there is no contrary to "two" cubits nor to "three" cubits, nor to "ten," nor to any thing of the kind, unless some one should say that "much" is contrary to "little," or "the great" to "the small;" but of definite quantities, none is contrary to the other. Substance, also, appears not to receive greater or less; I mean, not that one substance is not, more or less, substance, than another, for it has been already said that it is, but that every substance is not said to be more or less, that very thing, that it is; as if the same substance be "man" he will not be more or less "man;" neither himself than himself, nor another "man" than another, for one "man" is not more "man" than another, as one "white thing" is more and less "white" than another, and one "beautiful" thing more and less "beautiful" than another, and "the same thing" more or less than "itself;" so a body being "white," is said to be more "white" now, than it was before, and if "warm" is said to be more or less "warm." Substance at least is not termed more or less substance, since "man" is not said to be more "man" now, than before, nor any one of such other things as are substances: hence substance is not capable of receiving the greater and the less.

It appears however, to be especially the peculiarity of substance, that being one and the same in number, it can receive contraries, which no one can affirm of the rest which are not substances, as that being one in number, they are capable of contraries. Thus "colour," which is one and the same in number, is not "white" and "black," neither the same action, also one in number, both bad and good; in like manner of other things as many as are not substances. But substance being one, and the same in number, can receive contraries, as "a certain man" being one and the same, is at one time, white, and at another, black, and warm and cold, and bad and good. In respect of none of the rest does such a thing appear, except some one should object, by saying, that a sentence and opinion are capable of receiving contraries, for the same sentence appears to be true and false; thus if the statement be true that "some one sits," when he stands up, this very same statement will be false. And in a similar manner in the matter of opinion, for if any one should truly opine that a certain person sits, when he rises up he will opine falsely, if he still holds the same opinion about him. Still, if any one, should even admit this, yet there is a difference in the mode. For some things in substances, being themselves changed, are capable of contraries, since cold, being made so, from hot, has changed, for it is changed in quality, and black from white, and good from bad: in like manner as to other things, each one of them receiving change is capable of contraries. The sentence indeed and the opinion remain themselves altogether immovable, but the thing being moved, a contrary is produced about them; the sentence indeed remains the same, that "some one sits," but the thing being moved, it becomes at one time, true, and at another, false. Likewise as to opinion, so that in this way, it will be the peculiarity of substance, to receive contraries according to the change in itself, but if any one admitted this, that a sentence and opinion can receive contraries, this would not be true. For the sentence and the opinion are not said to be capable of contraries in that they have received any thing, but, in that about something else, a passive quality has been produced, for in that a thing is, or is not, in this, is the sentence said to be true, or false, not in that itself, is capable of contraries. In short, neither is a sentence nor an opinion moved by any thing, whence they cannot be capable of contraries, no passive quality being in them; substance at least, from the fact of itself receiving contraries, is said in this to be capable of contraries, for it receives disease and health, whiteness and blackness, and so long as it receives each of these, it is said to be capable of receiving contraries. Wherefore it will be the peculiarity of substance, that being the same, and one in number, according to change in itself, it is capable of receiving contraries; and concerning substance this may suffice.

 
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Of Quantity, one kind is discrete, and another continuous; the one consists of parts, holding position with respect to each other, but the other of parts, which have not that position. Discrete quantity is, as number and sentence, but continuous, as line, superficies, body, besides place and time. For, of the parts of number, there is no common term, by which its parts conjoin, as if five be a part of ten, five and five, conjoin at no common boundary, but are separated. Three, and seven, also conjoin at no common boundary, nor can you at all take a common limit of parts, in number, but they are always separated, whence number is of those things which are discrete. In like manner a sentence, for that a sentence is quantity is evident, since it is measured by a short and long syllable; but I mean a sentence produced by the voice, as its parts concur at no common limit, for there is no common limit, at which the syllables concur, but each is distinct by itself. A line, on the contrary, is continuous, for you may take a common term, at which its parts meet, namely, a point, and of a superficies, a line, for the parts of a superficies coalesce in a certain common term. So also you can take a common term in respect of body, namely, a line, or a superficies, by which the parts of body are joined. Of the same sort are time and place, for the present time is joined both to the past and to the future. Again, place is of the number of continuous things, for the parts of a body occupy a certain place, which parts join at a certain common boundary, wherefore also the parts of place, which each part of the body occupies, join at the same boundary as the parts of the body, so that place will also be continuous, since its parts join at one common boundary.

Moreover, some things consist of parts, having position with respect to each other, but others of parts not having such position; thus the parts of a line have relative position, for each of them lies some where, and you can distinguish, and set out, where each lies, in a superficies, and to which part of the rest, it is joined. So also the parts of a superficies, have a certain position, for it may be in like manner pointed out where each lies, and what have relation to each other, and the parts of a solid, and of a place, in like manner. On the contrary, in respect of number, it is impossible for any one to show that its parts have any relative position, or that they are situated any where, or which of the parts are joined to each other. Nor as regards parts of time, for not one of the parts of time endures, but that which does not endure, how can it have any position? you would rather say, that they have a certain order, inasmuch as one part of time is former, but another latter. In the same manner is it with number, because one, is reckoned before two, and two, before three, and so it may have a certain order, but you can, by no means, assume, that it has position. A speech likewise, for none of its parts endures, but it has been spoken, and it is no longer possible to bring back what is spoken, so that there can be no position of its parts, since not one endures: some things therefore consist of parts having position, but others of those which have not position. What we have enumerated are alone properly termed quantities; all the rest being so denominated by accident, for looking to these, we call other things quantities, as whiteness is said to be much, because the superficies is great, and an action long, because its time being long, and motion also, is termed, much. Yet each of these is not called a quantity by itself, for if a man should explain the quantity of an action, he will define it by time, describing it as yearly, or something of the sort; and if he were to explain the quantity of whiteness, he will define it by the superficies, for as the quantity of the superficies, so he would say is the quantity of the whiteness; whence the particulars we have mentioned are alone properly of themselves termed quantities, none of the rest being so of itself, but according to accident. Again, nothing is contrary to quantity, for in the definite it is clear there is nothing contrary, as to "two cubits" or to "three," or to "superficies," or to any thing of this kind, for there is no contrary to them; except indeed a man should allege that "much" was contrary to "little," or the "great" to the "small." Of these however, none is a quantity, but rather belongs to relatives, since nothing, itself by itself, is described as great or small, but from its being referred to something else. A mountain, for instance, is called "little," but a millet seed "large," from the fact of the one being greater, but the other less, in respect of things of the same nature, whence the relation is to something else, since if each were called "small" or "great" of itself, the mountain would never have been called "small," nor the seed "large." We say also that there are "many" men in a village, but "few" at Athens, although these last are more numerous, and "many" in a house, but "few" in a theatre, although there is a much larger number in the latter. Besides, "two cubits," "three," and every thing of the kind signify quantity, but "great" or "small" does not signify quantity, but rather relation, for the "great" and "small" are viewed in reference to something else, so as evidently to appear relatives. Whether however any one does, or does not, admit such things to be quantities, still there is no contrary to them, for to that which cannot of itself be assumed, but is referred to another, how can there be a contrary? Yet more, if "great" and "small" be contraries, it will happen, that the same thing, at the same time, receives contraries, and that the same things are contrary to themselves, for it happens that the same thing at the same time is both "great" and "small." Something in respect of this thing is "small," but the same, in reference to another, is "large," so that the same thing happens at the same time to be both "great" and "small," by which at the same moment it receives contraries. Nothing however appears to receive contraries simultaneously, as in the case of substance, for this indeed seems capable of contraries, yet no one is at the same time "sick" and "healthy," nor a thing "white" and "black" together, neither does any thing else receive contraries at one and the same time. It happens also, that the same things are contrary to themselves, since if the "great" be opposed to the "small," but the same thing at the same time be great and small, the same thing would be contrary to itself, but it is amongst the number of impossibilities, that the same thing should be contrary to itself, wherefore the great is not contrary to the small, nor the many to the few, so that even if some one should say that these do not belong to relatives, but to quantity, still they will have no contrary.

The contrariety however of quantity seems especially to subsist about place, since men admit "upward" to be contrary to "downward," calling the place toward the middle "downward," because there is the greatest distance from the middle, to the extremities of the world; they appear also to deduce the definition of the other contraries from these, for they define contraries to be those things which, being of the same genus, are most distant from each other.

Nevertheless quantity does not appear capable of the greater and the less, as for instance "two cubits," for one thing is not more "two cubits" than another; neither in the case of number, since "three" or "five" are not said to be more than "three" or "five," neither "five" more "five" than "three" "three;" one time also is not said to be more "time" than another; in short, of none that I have mentioned is there said to be a greater or a less, wherefore quantity is not capable of the greater and less.

Still it is the especial peculiarity of quantity to be called "equal" and "unequal," for each of the above-mentioned quantities is said to be "equal" and "unequal," thus body is called "equal" and "unequal," and number, and time, are predicated of as "equal" and "unequal;" likewise in the case of the rest enumerated, each one is denominated "equal" and "unequal." Of the remainder, on the contrary, such as are not quantities, do not altogether appear to be called "equal" and "unequal," as for instance, disposition is not termed entirely "equal" and "unequal," but rather "similar" and "dissimilar;" and whiteness is not altogether "equal" and "unequal," but rather "similar" and "dissimilar;" hence the peculiarity of quantity will especially consist in its being termed "equal" and "unequal."

 
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Such things are termed "relatives," which are said to be what they are, from belonging to other things, or in whatever other way they may be referred to something else; thus "the greater" is said to be what it is in reference to another thing, for it is called greater than something; and "the double" is called what it is in reference to something else, for it is said to be double a certain thing; and similarly as to other things of this kind. Such as these are of the number of relatives, as habit, disposition, sense, knowledge, position, for all these specified are said to be what they are, from belonging to others, or however else they are referrible to another, and they are nothing else; for habit is said to be the habit of some one, knowledge the knowledge of something, position the position of somewhat, and so the rest. Relatives, therefore, are such things, as are said to be what they are, from belonging to others, or which may somehow be referred to another; as a mountain is called "great" in comparison with another, for the mountain is called "great" in relation to something, and "like" is said to be like somewhat, and other things of this sort, are similarly spoken of, in relation to something. Reclining, station, sitting, are nevertheless certain positions, and position is a relative; but to recline, to stand, or to sit, are not themselves positions, but are paronymously denominated from the above-named positions.

Yet there is contrariety in relatives, as virtue is contrary to vice, each of them being relative, and knowledge to ignorance; but contrariety is not inherent in all relatives, since there is nothing contrary to double, nor to triple, nor to any thing of the sort.

Relatives appear, notwithstanding, to receive the more and the less, for the like and the unlike are said to be so, more and less, and the equal and the unequal are so called, more and less, each of them being a relative, for the similar is said to be similar to something, and the unequal, unequal to something. Not that all relatives admit of the more and less, for double is not called more and less double, nor any such thing, but all relatives are styled so by reciprocity, as the servant is said to be servant of the master, and the master, master of the servant; and the double, double of the half, also the half, half of the double, and the greater, greater than the less, and the less, less than the greater. In like manner it happens as to other things, except that sometimes they differ in diction by case, as knowledge is said to be the knowledge of something knowable, and what is knowable is knowable by knowledge: sense also is the sense of the sensible, and the sensible is sensible by sense. Sometimes indeed they appear not to reciprocate, if that be not appropriately attributed to which relation is made, but here he who attributes errs; for instance, a wing of a bird, if it be attributed to the bird, does not reciprocate, for the first is not appropriately attributed, namely "wing" to "bird," since "wing" is not predicated of it so far as it is "bird," but so far as it is "winged," as there are wings of many other things which are not birds, so that if it were appropriately attributed, it would also reciprocate; as "wing" is the wing of "a winged creature," and "the winged creature" is "winged" by the "wing." It is sometimes necessary perhaps even to invent a name, if there be none at hand, for that to which it may be properly applied: e. g. if a rudder be attributed to a ship, it is not properly so attributed, for a rudder is not predicated of a ship so far as it is "ship," since there are ships without rudders; hence they do not reciprocate, inasmuch as a ship is not said to be the ship of a rudder. The attribution will perhaps be more appropriate, if it were attributed thus, a rudder is the rudder of something ruddered, or in some other way, since a name is not assigned; a reciprocity also occurs, if it is appropriately attributed, for what is ruddered is ruddered by a rudder. So also in other things; the head, for example, will be more appropriately attributed to something headed, than to animal, for a thing has not a head, so far as it is an animal, since there are many animals which have not a head.

Thus any one may easily assume those things to which names are not given, if from those which are first, he assigns names to those others also, with which they reciprocate, as in the cases adduced, "winged" from "wing," and "ruddered" from "rudder." All relatives therefore, if they be properly attributed, are referred to reciprocals, since if they are referred to something casual, and not to that to which they relate, they will not reciprocate. I mean, that neither will any one of those things which are admitted to be referrible to reciprocals, reciprocate, even though names be assigned to them, if the thing be attributed to something accidental, and not to that to which it has relation: for example, a servant, if he be not attributed as the servant of a master, but of a man, of a biped, or any thing else of the kind, will not reciprocate, for the attribution is not appropriate. If however that, to which something is referred, be appropriately attributed, every thing else accidental being taken away, and this thing alone being left, to which it is appropriately attributed, it may always be referred to it, as "a servant," if he is referred to "a master," every thing else accidental to the master being left out of the question, (as the being "a biped," and "capable of knowledge," and that he is "a man,") and his being "a master" alone, left, here the "servant" will always be referred to him, for a "servant" is said to be the servant of a "master." If again, on the other hand, that to which it is at any time referred is not appropriately attributed, other things being taken away, and that alone left, to which it is attributed, in this case it will not be referred to it. For let a "servant" be referred to "man," and a "wing" to "bird," and let the being "a master" be taken away from "man," the servant will no longer refer to man, since "master" not existing, neither does "servant" exist. So also let "being winged" be taken away from "bird," and "wing" will no longer be amongst relatives, for what is "winged" not existing, neither will "wing" be the wing of any thing. Hence it is necessary to attribute that, to which a thing is appropriately referred, and if indeed a name be already given to it, the application is easy; but if no name be assigned, it is perhaps necessary to invent one; but being thus attributed, it is clear that all relatives are referred to reciprocals.

Naturally, relatives appear simultaneous, and this is true of the generality of them, for "double" and "half" are simultaneous, and "half" existing, "double" exists, and "a master" existing, the "servant" is, and the "servant" existing, the "master" is, and other things are also like these. These also are mutually subversive, for if there is no "double" there is no "half," and no "half" there is no "double"; likewise as to other things of the same kind. It does not however appear to be true of all relatives, that they are by nature simultaneous, for the object of "science" may appear to be prior to "science," since for the most part we derive science from things pre-existing, as in few things, if even in any, do we see science and its object originating together. Moreover, the object of science being subverted, co-subverts the science, but science being subverted, does not co-subvert the object of science, for there being no object of science, science itself becomes non-existent, (since there will be no longer a science of any thing); but on the contrary, though science does not exist, there is nothing to prevent the object of science existing. Thus the quadrature of the circle, if it be an object of scientific knowledge, the science of it does not yet exist, though it is itself an object of science: again, "animal" being taken away, there will not be "science," but still it is possible for many objects of science to be. Likewise also do things pertaining to sense subsist, since the sensible seems to be prior to the sense, as the sensible being subverted co-subverts sense, but sense does not co-subvert the sensible. For the senses are conversant with body, and are in body, but the sensible being subverted, body also is subverted, (since body is of the number of sensibles,) and body not existing, sense also is subverted, so that the sensible co-subverts sense. Sense on the other hand does not co-subvert the sensible, since if animal were subverted, sense indeed would be subverted, but yet the sensible will remain; such for instance as "body," "warm," "sweet," "bitter," and every thing else which is sensible. Besides, "sense" is produced simultaneously with what is "sensitive," for at one and the same time "animal" and "sense" are produced, but the "sensible" is prior in existence to "animal" or "sense," for fire and water, and such things as animal consists of, are altogether prior to the existence of animal or sense, so that the sensible will appear to be antecedent to sense.

It is doubtful however whether no substance is among the number of relatives, as seems to be the case, or whether this happens in certain second substances; for it is true in first substances, since neither the wholes, nor the parts, of first substances are relative. "A certain man" is not said to be a certain man of something, nor "a certain ox" said to be a certain ox of something; and so also with respect to the parts, for a "certain hand" is not said to be a certain hand of some one, but the hand of some one; and some head is not said to be a certain head of some one, but the head of some one, and in most secondary substances the like occurs. Thus man is not said to be the man of some one, nor an ox the ox of some one, nor the wood the wood of some one, but they are said to be the possession of some one; in such things therefore, it is evident, that they are not included amongst relatives. In the case of some secondary substances there is a doubt, as "head," is said to be the head of some one, and "hand," the hand of some one, and in like manner, every such thing, so that these may appear amongst the number of relatives. If then the definition of relatives has been sufficiently framed, it is either a matter of difficulty, or of impossibility, to show that no substance is relative; but if the definition has not been sufficiently framed, but those things are relatives, whose substance is the same, as consists with a relation, after a certain manner, to a certain thing; somewhat, perhaps, in reply to this, may be stated. The former definition, however, concurs with all relatives, yet it is not the same thing, that their being, consists in relation, and that being what they are, they are predicated of other things. Hence it is clear, that he who knows any one relative, definitely, will also know what it is referred to, definitely. Wherefore also from this it is apparent, that if one knows this particular thing to be among relatives, and if the substance of relatives is the same, as subsisting in a certain manner, with reference to something, he will also know that, with reference to which, this particular thing, after a certain manner, subsists; for if, in short, he were ignorant of that, with reference to which, this particular thing, after a certain manner, subsists, neither would he know, whether it subsists, after a certain manner, with reference to something. And in singulars, indeed, this is evident; for if any one knows definitely, that this thing is "double," he will also forthwith know that, definitely, of which it is the double, since if he knows not that it is the double, of something definite, neither will he know that it is "double," at all. So again, if a man knows this thing, to be more beautiful than something else, he must straightway and definitely know that, than which, it is more beautiful. Wherefore, he will not indefinitely know, that this, is better, than that which is worse, for such is opinion and not science, since he will not accurately know that it is better than something worse, as it may so happen that there is nothing worse than it, whence it is necessarily evident, that whoever definitely knows any relative, also definitely knows that, to which it is referred. It is possible, notwithstanding, to know definitely what the head, and the hand, and every thing of the sort are, which are substances; but it is not necessary to know that to which they are referred, since it is not necessary definitely to know whose, is the head, or whose, is the hand; thus these will not be relatives, but if these be not relatives, we may truly affirm no substance to be among relatives. It is, perhaps, difficult for a man to assert assuredly any thing of such matters, who has not frequently considered them, yet to have submitted each of them to inquiry, is not without its use.

 
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By quality, I mean that, according to which, certain things, are said to be, what they are. Quality, however, is among those things which are predicated multifariously; hence one species of quality is called "habit" and "disposition," but habit, differs from disposition, in that it is a thing more lasting and stable. Of this kind too, are both the sciences and the virtues, for science appears to rank among those things, which continue more stable, and are hardly removed, even when science is but moderately attained, unless some great change should occur from disease, or from something of the sort; so also virtue, as justice, temperance, and so forth, does not appear capable of being moved or changed with facility. But those are termed dispositions, which are easily moved and quickly changed, as heat, cold, disease, health, and such things; or a man is disposed, after a manner, according to these, but is rapidly changed, from hot becoming cold, and from health passing to disease, and in like manner as to other things, unless some one of these qualities has, from length of time, become natural, immovable, or at least difficult to be moved, in which case we may term it a habit. But it is evident that those ought to be called habits, which are more lasting, and are with greater difficulty removed, for those persons who do not very much retain the dogmas of science, but are easily moved, are said not to possess a scientific habit, although they are in some manner disposed as to science, either worse or better; so that habit differs from disposition in the one being easily removed, but the former is more lasting, and less easily removed. Habits are dispositions also, but dispositions not necessarily habits, for those who have habits are also, after a manner, disposed according to them, but those who are disposed are not altogether possessed of the habit.

Another kind of quality is, that, according to which, we say that men are prone to pugilism, or to the course, or to health, or to disease, in short, whatever things are spoken of according to natural power, or weakness; for each of these is not denominated from being disposed after a certain manner, but from having a natural power or inability of doing something easily, or of not suffering; thus, men are called pugilistic, or fitted for the course, not from being disposed after a certain manner, but from possessing a natural power of doing something easily. Again, they are said to be healthy, from possessing a natural power of not suffering easily from accidents, but to be diseased, from possessing a natural incapacity to resist suffering easily from accidents: similarly to these, do hard and soft subsist, for that is called "hard" which possesses the power of not being easily divided, but "soft," that which has an impotence as to this same thing.

The third kind of quality consists of passive qualities and passions, and such are sweetness, bitterness, sourness, and all their affinities, besides warmth, and coldness, and whiteness, and blackness. Now that these are qualities, is evident from their recipients being called from them, "qualia," as honey from receiving sweetness, is said to be sweet, and the body white, from receiving whiteness; in like manner in other things. They are called passive qualities, not from the recipients of the qualities suffering any thing, for neither is honey said to be sweet from suffering any thing, nor any thing else of such a kind. In like manner to these are heat and cold called passive qualities, not from the recipients themselves suffering any thing, but because each of the above-mentioned qualities produces passion in the senses, they are denominated passive qualities; for as sweetness, produces a certain passion in the taste, and warmth, in the touch, so also do the rest. Whiteness, and blackness, and other colours are, on the contrary, not called passive qualities in the same manner with the above-mentioned, but from themselves being produced from passion; for that many changes of colours spring from passion is evident, since when a man blushes he becomes red, and when frightened, pale, and so every thing of this sort. Whence also if a man naturally suffers a passion of this nature, he will probably have a similar colour, since the disposition which is now produced about the body when he blushes, may also be produced in the natural constitution, so as that a similar colour should naturally arise. Whatever such symptoms then originate from certain passions difficult to be removed and permanent are called passive qualities. For whether in the natural constitution, paleness, or blackness, be produced, they are called qualities, (for according to them we are called "quales;") or whether through long disease or heat, or any such thing, paleness or blackness happens, neither are easily removed, or even remain through life, these are called qualities, for in like manner, we are called "quales" in respect of them. Notwithstanding, such as are produced from things easily dissolved, and quickly restored, are called passions, and not qualities, for men are not called "quales" in respect of them, since neither is he who blushes, in consequence of being ashamed, called red, nor he who turns pale, from fear, called pale, they are rather said to have suffered something, so that such things are called passions, but not qualities. Like these also are passive qualities, and passions denominated in the soul. For such things as supervene immediately upon birth from certain passions difficult of removal, are called qualities; as insanity, anger, and such things, for men according to these are said to be "quales," that is, wrathful and insane. So also as many other mutations as are not natural, but arise from certain other symptoms, and are with difficulty removed, or even altogether immovable, such are qualities, for men are called "quales" in respect of them. Those which, on the other hand, arise from things easily and rapidly restored, are called passions, as for instance, where one being vexed becomes more wrathful, for he is not called wrathful who is more wrathful in a passion of this kind, but rather he is said to have suffered something, whence such things are called passions, but not qualities.

The fourth kind of quality is figure and the form, which is about every thing, besides rectitude and curvature, and whatever is like them, for according to each of these a thing is called "quale." Thus a triangle or a square is said to be a thing of a certain quality, also a straight line or a curve, and every thing is said to be "quale" according to form. The rare and the dense, the rough and the smooth, may appear to signify a certain quality, but probably these are foreign from the division of quality, as each appears rather to denote a certain position of parts. For a thing is said to be "dense," from having its parts near each other, but "rare," from their being distant from each other, and "smooth," from its parts lying in some respect in a right line, but "rough," from this part, rising, and the other, falling.

There may perhaps appear to be some other mode of quality, but those we have enumerated are most commonly called so.

The above-named therefore are qualities, but "qualia" are things denominated paronymously according to them, or in some other manner from them; most indeed and nearly all of them are called paronymously, as "a white man" from "whiteness," "a grammarian" from "grammar," a "just man" from "justice," and similarly of the rest. Still in some, from no names having been given to the qualities, it is impossible that they should be called paronymously from them; for instance, a "racer" or "pugilist," so called from natural power, is paronymously denominated from no quality, since names are not given to those powers after which these men are called "quales," as they are given to sciences, according to which men are said to be pugilists or wrestlers from disposition, for there is said to be a pugilistic and palæstric science, from which those disposed to them are paronymously denominated "quales." Sometimes however, the name being assigned, that which is called "quale" according to it, is not denominated paronymously, as from virtue, a man is called worthy, for he is called worthy, from possessing virtue, but not paronymously from virtue; this however does not often happen, wherefore those things are called "qualia," which are paronymously denominated from the above-mentioned qualities, or which are in some other manner termed from them.

In quality, there is also contrariety, as justice is contrary to injustice, and whiteness to blackness, and the like; also those things which subsist according to them are termed qualia, as the unjust to the just, and the white to the black. This however does not happen in all cases, for to the yellow, or the pale, or such like colours, though they are qualities, there is no contrary. Besides, if one contrary be a quality, the other, will also be a quality, and this is evident to any one considering the other categories. For instance, if justice be contrary to injustice, and justice be a quality, then injustice will also be a quality, for none of the other categories accords with injustice, neither quantity, nor relation, nor where, nor in short any thing of the kind, except quality, and the like also happens as to quality in the other contraries.

Qualia also admit the more and the less, as one thing is said to be more or less "white" than another, and one more and less "just" than another; the same thing also itself admits accession, for what is "white," can become more, "white." This however, does not happen with all, but with most things, for some one may doubt whether justice, can be said to be more or less justice, and so also in other dispositions, since some doubt about such, and assert that justice cannot altogether be called more and less, than justice, nor health than health, but they say, that one man has less health, than another, and one person less justice, than another, and so also of the grammatical and other dispositions. Still the things which are denominated according to these, do without question admit the more and the less, for one man is said to be more grammatical, than another, and more healthy, and more just, and similarly in other things. Triangle and square appear nevertheless incapable of the more, as also every other figure, since those things which receive the definition of a triangle, and of a circle, are all alike triangles or circles, but of things which do not receive the same definition, none can be said to be more such, than another, as a square, is not more a circle, than an oblong, for neither of them admits the definition of the circle. In a word, unless both receive the definition of the thing propounded, one cannot be said to be more so and so, than another, wherefore all qualities do not admit the more and the less.

Of the above-mentioned particulars then, no one is peculiar to quality, but things are said to be similar, and dissimilar, in respect of qualities alone, for one thing is not like another in respect of any thing else, than so far as it is quale, so that it will be peculiar to quality, that the like and the unlike should be termed so in respect of it.

Yet we need not be disturbed lest any one should say that, proposing to speak of quality, we co-enumerate many things which are relatives, for we said that habits and dispositions are among the number of relatives, and nearly in all such things the genera are called relatives, but not one of the singulars. Science, for example, although it is a genus, is said to be what it is, with respect to something else, for it is said to be the science of a certain thing, but of singulars not one is said to be what it is, with reference to something else, as neither grammar is said to be the grammar of something, nor music the music of something. But even perhaps these, are called relatives, according to genus, as grammar is said to be the science of something, not the grammar of something, and music the science of something, not the music of something; so that singulars are not of the number of relatives. Still, we are called quales from singulars, for these we possess, as we are called scientific from possessing certain singular sciences; so that these may be singular qualities, according to which we are sometimes denominated quales, but they are not relatives; besides, if the same thing should happen to be both a particular quality and a relative, there is no absurdity in its enumeration under both genera.

 
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Action and Passion admit contrariety, and the more and the less, for to make warm, is contrary to making cold; to be warm, contrary to the being cold, to be pleased, contrary to being grieved; so that they admit contrariety. They are also capable of the more and the less, for it is possible to heat, more and less, to be heated, more and less, and to be grieved, more and less; wherefore, to act, and to suffer, admit the more and less, and so much may be said of these. But we have spoken of the being situated in our treatment of relatives, to the effect that it is paronymously denominated, from positions: as regards the other categories, when, where, and to have, nothing else is said of them, than what was mentioned at first, because they are evident; e.g. that "to have," signifies to be shod, to be armed; "where," as in the Lycæum, in the Forum, and the rest which are spoken of these. Of the proposed genera therefore, sufficient has been stated.
 
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We must now speak of opposites, in how many ways opposition takes place. One thing then is said to be opposed to another in four ways, either as relative, or as contrary, or as privation and habit, or as affirmation and negation. Thus speaking summarily, each thing of this kind is opposed, relatively, as "the double" to "the half," contrarily, as "evil" to "good," privatively and habitually, as "blindness" and "sight," affirmatively and negatively, as "he sits," "he does not sit."

Whatever things then are relatively opposed, are said to be what they are with reference to opposites, or are in some manner referred to them, as "the double of the half," is said to be what it is, with reference to something else, for it is said to be the double of something; and "knowledge" is opposed relatively to the object of knowledge, and is said to be what it is, in reference to what may be known, and what may be known, is said to be what it is, in reference to an opposite, namely, "knowledge," for "the object of knowledge" is said to be so, to something, namely, to "knowledge."

Things therefore relatively opposed are said to be, what they are, with reference to opposites, or in whatever manner, they are referrible to each other, but those which are opposed as contraries, are by no means, said to be what they are, with reference to each other, but are said to be contrary to each other, for neither is "good" said to be the "good" of "evil," but the contrary of evil, nor is "white," denominated the "white "of "black," but its contrary, so that these oppositions differ from each other. Such contraries however, as are of that kind, that one of them must necessarily be in those things, in which it can naturally be, or of which it is predicated, these have nothing intermediate; but in the case of those, in which it is not necessary, that one should be inherent, there is something intermediate. For instance, health and disease may naturally subsist in the body of an animal, and it is necessary that one, should be therein, either disease, or health; the odd and even are also predicated of number, and one of the two, either the odd or the even, must necessarily be in number, yet there is nothing intermediate between these, neither between disease and health, nor between the odd and the even. Those contraries, again, have something intermediate, in which one of them need not be inherent, as black and white are naturally in body, but it is not necessary, that one of these, should be inherent in body, for every body, is not white or black. Vileness, also and worth, are predicated of man, and of many others, yet one of these, need not be in those things of which it is predicated, for not all things are either vile or worthy; at least, there is something intermediate, as between white and black, there is dark brown, and pale, and many other colours, but between vileness and worth, that, is intermediate, which is neither vile, nor worthy. In some instances, the intermediates have names, thus, the dark brown, and the pale, and such colours are media between white and black, but in other cases, it is not easy to assign a name to the intermediate, but the latter is defined, by the negation of either extreme, as, for example, whatever is neither good nor bad, nor just nor unjust.

Privation, however, and habit are predicated of something identical, as sight and blindness of the eye, and universally, in whatever the habit is naturally adapted to be produced, of such is either predicated. We say then, that each of the things capable of receiving habit is deprived of it, when it is not in that, wherein it might naturally be, and when it is adapted naturally to possess it; thus we say that a man is toothless, not because he has no teeth, and blind, not because he has no sight, but because he has them not, when he might naturally have them, for some persons from their birth, have neither sight nor teeth, yet they are neither called toothless nor blind. To be deprived of, and to possess habit, then, are not privation and habit, for the sight is habit, but the privation is blindness, but to possess sight is not sight, nor to be blind, blindness, for blindness is a certain privation, but the being blind is to be deprived, and is not privation, for if blindness were the same as being blind, both might be predicated of the same person, but a man is said to be blind, yet he is never called blindness. To be deprived also, and to possess habit, appear to be similarly opposed, as privation and habit, since the mode of opposition is the same, for as blindness is opposed to sight, so likewise is the being blind, opposed to the possession of sight.

Neither is that, which falls under affirmation and negation, affirmation and negation; for affirmation is an affirmative sentence, and negation a negative sentence, but nothing which falls under affirmation and negation is a sentence (but a thing). Still these are said to be mutually opposed, as affirmation and negation, since in them the mode of opposition is the same, for as affirmation is sometimes opposed to negation, for example, "he sits" to "he does not sit," so that thing which is under each is opposed, as "sitting" to "not sitting."

But that privation and habit, are not opposed as relatives, is evident, since what a thing is, is not asserted of its opposite, for sight is not the sight of blindness, nor in any other way spoken in reference to it, so also blindness, cannot be called the blindness of sight, but blindness indeed is said to be the privation of sight, not the blindness of sight. Moreover, all relatives are referred to reciprocals, so that if blindness were relative, it would reciprocate with that to which it is referred, but it does not reciprocate, for sight is not said to be the sight of blindness.

From these things, also, it is manifest that those which are predicated, according to privation and habit, are not contrarily opposed, for of contraries which have no intermediate, one must always necessarily be inherent, wherein it is naturally adapted to be inherent, or of which it is predicated, but between these, there is no intermediate thing wherein it was necessary that the one should be in what was capable of receiving it, as in the case, of disease and health, in odd and the even number. Of those however between which there is an intermediate, it is never necessary that one should be inherent in every thing; for neither is it necessary that every thing capable of receiving it, should be white or black, or hot or cold, since there is no prevention to an intermediate being between them. Again, of these also there was a certain medium, of which it was not requisite that one should be in its recipient, unless where one is naturally inherent, as in fire to be hot, and in snow to be white: still in these, one, must of necessity be definitely inherent, and not in whatever way it may happen, for neither does it happen that fire is cold, nor that snow is black. Wherefore it is not necessary that one of them should be in every thing capable of receiving it, but only in those wherein the one is naturally inherent, and in these, that which is definitely and not casually, one. In privation however, and habit, neither of the above-mentioned particulars is true, since it is not always necessary that one should be inherent in what is capable of receiving it, as what is not yet naturally adapted to have sight, is neither said to be blind nor to have sight; wherefore these things will not be of such contraries as have nothing intermediate. But neither, on the other hand, will they be amongst those which have something intermediate, since it is necessary that at some time, one of them, should be inherent in every thing capable of receiving it: thus when a man is naturally fitted to have sight, then he will be said to be blind, or to have sight, and one of these, not definitely, but whichever may happen, since he need not necessarily be blind, nor see, but either, as it may happen. In respect nevertheless of contraries, which have an intermediate, it is by no means necessary that one, should be inherent in every thing, but in some things, and in these, one of them definitely, and neither casually, so that things which are opposed according to privation and habit, are evidently not in either of these ways opposed, as contraries.

Again, in contraries, when the recipient exists, a change into each other may happen, unless one is naturally inherent in something, as for instance, in fire to be hot. It is possible also for the healthy to be sick, the white to become black, cold to become hot, (and the hot to become cold); from good it is possible to become bad, and from bad good, for he who is depraved, being led to better pursuits and discourses, advances, though but a little, to be better, and if he once makes an advancement ever so little, he will evidently become either altogether changed, or have made a very great proficiency, since he ever becomes more disposed to virtue, even if he has obtained the smallest, increase, from the beginning. Wherefore he will probably acquire greater increase, and this perpetually occurring, he will at last be transformed entirely to a contrary habit, unless he be prevented by time; but in privation and habit, it is impossible for a mutual change to occur, since it may take place from habit to privation, but from privation to habit is impossible, as neither can he who has become blind, again see, the bald again have hair, nor has the toothless ever yet again got teeth.

Whatever things are opposed, as affirmation and negation, are evidently opposed according to none of the above-mentioned modes, since in these alone it is always necessary that one should be true, but the other false: as neither, is it always necessary in contraries that one should be true, but the other false, nor in relatives, nor in habit and privation. For instance, health and disease, are contrary, yet neither of them is either true or false; so also the double and the half are relatively opposed, and neither of them is either true or false; nor in things which are predicated as to privation and habit, as sight and blindness. In short, nothing predicated without any conjunction, is either true or false, and all the above-named are predicated without conjunction. Not but that a thing of this kind may appear, to happen in contraries, which are predicated conjunctively, for "Socrates is well" is opposed to "Socrates is sick," yet neither in these is it always necessary, that one should be true and the other false, for while Socrates lives, one will be true and the other false, but when he is not alive, both will be false, since neither is it true that Socrates is sick, nor that he is well, when he is not in existence at all. In privation and habit, then when the subject is non-existent, neither is true, but when the subject exists, the one is not always true, nor the other false. "Socrates sees" is opposed to "Socrates is blind," as privation and habit, and whilst he exists, one need not be true or false, for when he is not naturally fitted to possess them, both are false, but when Socrates does not exist at all, both will thus be false, that he sees, and that he is blind. In affirmation and negation always, if Socrates be or be not, one will always be false and the other true; for it is evident with respect to these two, "Socrates is sick," and "Socrates is not sick," that when he exists one of them is true and the other false; and in like manner when he does not exist, for in the latter case that he is ill is false, but that he is not ill is true; so that in those things alone which are affirmatively and negatively opposed will it be the peculiarity that one of them is either true or false.

 
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"Evil" is of necessity opposed to good, and this is evident from an induction of singulars, as disease to health, and cowardice to courage, and similarly of the rest. But to evil, at one time, good, is contrary, and at another, evil, for to indigence being an evil, excess is contrary, which is also an evil; in like manner, mediocrity, which is a good, is opposed to each of them. A man may perceive this in respect of a few instances, but in the majority the contrary to evil is always good.

Again, of contraries it is not required, if one is, that the remainder should be; for when every man is well, there will indeed be health, and not disease, and so also when all things are white, there will be whiteness, but not blackness. Besides, if "Socrates is well" be the contrary of "Socrates is ill," and both cannot possibly be inherent in the same subject, it follows, that when one of the contraries exists, the other cannot possibly exist, for "Socrates is well" existing, "Socrates is ill" cannot exist.

Contraries, however, evidently are, by their nature, adapted to subsist about the same thing, either in species or genus, since disease and health naturally subsist in the body of an animal, but whiteness and blackness simply in body, and justice and injustice in the soul of man.

Notwithstanding, it is requisite that all contraries be either in the same genus, or in contrary genera, or be genera themselves; for white and black are in the same genus, as "colour" is the genus of them; but justice and injustice in contrary genera, for "virtue" is the genus of one, but "vice" of the other; lastly, "good" and "bad" are not in a genus, but are themselves the genera of certain things.

 
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A thing is said to be prior to another in four respects: first and most properly, in respect of time, according to which, one is said to be older and more ancient than another, since it is called older and more ancient, because the time is longer. Next, when it does not reciprocate, according to the consequence of existence: thus one is prior to two, for two existing, it follows directly that one exists; but when one is, it is not necessary that two should be, hence the consequence of the remainder's existence does not reciprocate from the existence of the one; but such a thing appears to be prior, from which the consequence of existence does not reciprocate.

Thirdly, the prior is that predicated according to a certain order, as in the instance of sciences and discourses, for in demonstrative sciences, the prior and the posterior, subsist in order, since the elements are prior in order, to the diagrams, and in grammar, letters are before syllables; so also of discourses, as the proem is prior, in order, to the narration.

Moreover, besides what we have mentioned, the better and more excellent appear to be prior by nature. The common people are accustomed to say, that those whom they chiefly honour and especially regard, are prior in their esteem; but this is nearly the most foreign of all the modes, wherefore such are (nearly) the modes of priority which have been enumerated.

Besides the above-mentioned, there may yet appear to be another mode of the prior; as of things reciprocating, according to the consequence of existence, that which in any respect is the cause of the existence of the one, may justly be said to be by nature prior, and that there are, certain things of this kind, is manifest. For that man exists, reciprocates, according to the consequence of existence, with the true sentence respecting him, since if man is, the sentence is true, by which we say, that man is, and it reciprocates, since if the sentence be true, by which we say that man is, then man is. Notwithstanding, a true sentence, is by no means the cause of a thing's existence, but in some way, the thing appears the cause of the sentence being true, for in consequence of a thing existing, or not existing, is a sentence said to be true or false. Wherefore one thing may be called prior to another, according to five modes.

 
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Things are called simultaneous simply and most properly, whose generation occurs at the same time, for neither is prior or posterior; these, therefore, are said to be simultaneous as to time. But by nature those are simultaneous, which reciprocate according to the consequence of existence, although one, is by no means the cause of the existence of the other, as in the double and the half, for these reciprocate; thus the double existing, the half also exists, and the half existing, the double exists, but neither is the cause of existence to the other.

Those, also, which being derived from the same genus, are by division mutually opposed, are said to be naturally simultaneous; but they, are said to have a division opposite to each other, which subsist according to the same division; thus the winged is opposed to pedestrian and aquatic, as these being derived from the same genus, are by division mutually opposed, for animal is divided into these, viz. into the winged, the pedestrian, and aquatic, and none of these is prior or posterior, but things of this kind appear naturally simultaneous. Each of these again, may be divided into species, for instance, the winged, the pedestrian, and the aquatic; wherefore, those will be naturally simultaneous which, derived from the same genus, subsist according to the same division. But genera are always prior to species, since they do not reciprocate according to the consequence of existence; for the aquatic existing, animal exists, but though animal exists, it is not necessary that the aquatic should.

Hence those are called naturally simultaneous, which indeed reciprocate, according to the consequence of existence; but the one is by no means the cause of existence to the other, which is also the case with things that, derived from the same genus, have by division a mutual opposition; those, however, are simply simultaneous whose generation is at the same time.

 
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Of motion, there are six species, generation, corruption, increase, diminution, alteration, and change of place.

The other motions then evidently differ from each other, for neither is generation, corruption, nor increase, diminution, nor alteration, change of place, and so of the rest. In the case of alteration however, there is some doubt, whether it be not sometimes necessary that what is altered, be so, in respect to some one, of the other motions, but this is not true, for it happens that we are altered, as to nearly all the passions, or at least the greater part of them, without any participation of the other motions, for it is not necessary that what is passively moved should be either increased or diminished. Wherefore, alteration will differ from the other motions, since if it were the same, it would be necessary that what is altered, be forthwith increased or diminished. Wherefore, alteration will differ from the other motions, since if it were the same, it would be necessary that what is altered, be forthwith increased or diminished, or follow some of the other motions, but this is not necessary. Similarly, also, what is increased or moved with any other motion, ought to be altered (in quality); but some things are increased which are not so altered, as a square is increased when a gnomon is placed about it, but it has not become altered (in quality); and in like manner with other things of this kind, so that these motions will differ from each other.

Nevertheless simply, rest is contrary to motion, the several rests to the several motions, corruption to generation, diminution to increase, rest in place to change in place; but change to a contrary place seems especially opposed, as ascent to descent, downwards to upwards. Still it is not easy, to define the contrary to the remainder of these specified motions, but it seems to have no contrary, unless some one should oppose to this, rest according to quality, or change of quality into its contrary, just as in change of place, rest according to place, or change to a contrary place. For alteration is the mutation of quality, so that to motion according to quality, will rest according to quality, or change to the contrary of the quality, be opposed; thus becoming white is opposed to becoming black, since a change in quality occurs, there being an alteration of quality into contraries.

 
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To have, is predicated in many modes; either as habit and disposition or some other quality, for we are said to have knowledge and virtue; or as to quantity, as the size which any one has; thus he is said to have the size of three or four cubits; or as things about the body, as a garment or a tunic; or as in a part, as a ring in the hand; or as a part, as the hand or the foot; or as in a vessel, as a bushel has wheat, or a flagon, wine, for the flagon is said to have the wine, and the bushel the wheat; all these therefore are said to have, as in a vessel; or as a possession, for we are said to have a house or land.

A man is also said to have a wife, and the wife a husband, but the mode now mentioned, of "to have," seems the most foreign, for we mean nothing else by having a wife, than that she cohabits with a man; there may perhaps appear to be some other modes of having, but those usually mentioned have nearly all been enumerated.

 
2 Interperetation.
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First we must define the terms ‘noun’ and ‘verb’, then the terms ‘denial’ and ‘affirmation’, then ‘proposition’ and ‘sentence.’
Spoken words are the symbols of mental experience and written words are the symbols of spoken words. Just as all men have not the same writing, so all men have not the same speech sounds, but the mental experiences, which these directly symbolize, are the same for all, as also are those things of which our experiences are the images. This matter has, however, been discussed in my treatise about the soul, for it belongs to an investigation distinct from that which lies before us.
As there are in the mind thoughts which do not involve truth or falsity, and also those which must be either true or false, so it is in speech. For truth and falsity imply combination and separation. Nouns and verbs, provided nothing is added, are like thoughts without combination or separation; ‘man’ and ‘white’, as isolated terms, are not yet either true or false. In proof of this, consider the word ‘goat-stag.’ It has significance, but there is no truth or falsity about it, unless ‘is’ or ‘is not’ is added, either in the present or in some other tense.
 
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By a noun we mean a sound significant by convention, which has no reference to time, and of which no part is significant apart from the rest. In the noun ‘Fairsteed,’ the part ‘steed’ has no significance in and by itself, as in the phrase ‘fair steed.’ Yet there is a difference between simple and composite nouns; for in the former the part is in no way significant, in the latter it contributes to the meaning of the whole, although it has not an independent meaning. Thus in the word ‘pirate-boat’ the word ‘boat’ has no meaning except as part of the whole word.
The limitation ‘by convention’ was introduced because nothing is by nature a noun or name-it is only so when it becomes a symbol; inarticulate sounds, such as those which brutes produce, are significant, yet none of these constitutes a noun.
The expression ‘not-man’ is not a noun. There is indeed no recognized term by which we may denote such an expression, for it is not a sentence or a denial. Let it then be called an indefinite noun.
The expressions ‘of Philo’, ‘to Philo’, and so on, constitute not nouns, but cases of a noun. The definition of these cases of a noun is in other respects the same as that of the noun proper, but, when coupled with ‘is’, ‘was’, or will be’, they do not, as they are, form a proposition either true or false, and this the noun proper always does, under these conditions. Take the words ‘of Philo is’ or ‘of or ‘of Philo is not’; these words do not, as they stand, form either a true or a false proposition.
 
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A verb is that which, in addition to its proper meaning, carries with it the notion of time. No part of it has any independent meaning, and it is a sign of something said of something else.
I will explain what I mean by saying that it carries with it the notion of time. ‘Health’ is a noun, but ‘is healthy’ is a verb; for besides its proper meaning it indicates the present existence of the state in question.
Moreover, a verb is always a sign of something said of something else, i.e. of something either predicable of or present in some other thing.
Such expressions as ‘is not-healthy’, ‘is not, ill’, I do not describe as verbs; for though they carry the additional note of time, and always form a predicate, there is no specified name for this variety; but let them be called indefinite verbs, since they apply equally well to that which exists and to that which does not.
Similarly ‘he was healthy’, ‘he will be healthy’, are not verbs, but tenses of a verb; the difference lies in the fact that the verb indicates present time, while the tenses of the verb indicate those times which lie outside the present.
Verbs in and by themselves are substantival and have significance, for he who uses such expressions arrests the hearer’s mind, and fixes his attention; but they do not, as they stand, express any judgement, either positive or negative. For neither are ‘to be’ and ‘not to be’ the participle ‘being’ significant of any fact, unless something is added; for they do not themselves indicate anything, but imply a copulation, of which we cannot form a conception apart from the things coupled.
 
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A sentence is a significant portion of speech, some parts of which have an independent meaning, that is to say, as an utterance, though not as the expression of any positive judgement. Let me explain. The word ‘human’ has meaning, but does not constitute a proposition, either positive or negative. It is only when other words are added that the whole will form an affirmation or denial. But if we separate one syllable of the word ‘human’ from the other, it has no meaning; similarly in the word ‘mouse’, the part ‘ouse’ has no meaning in itself, but is merely a sound. In composite words, indeed, the parts contribute to the meaning of the whole; yet, as has been pointed out, they have not an independent meaning.
Every sentence has meaning, not as being the natural means by which a physical faculty is realized, but, as we have said, by convention. Yet every sentence is not a proposition; only such are propositions as have in them either truth or falsity. Thus a prayer is a sentence, but is neither true nor false.
Let us therefore dismiss all other types of sentence but the proposition, for this last concerns our present inquiry, whereas the investigation of the others belongs rather to the study of rhetoric or of poetry.
 
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The first class of simple propositions is the simple affirmation, the next, the simple denial; all others are only one by conjunction.
Every proposition must contain a verb or the tense of a verb. The phrase which defines the species ‘man’, if no verb in present, past, or future time be added, is not a proposition. It may be asked how the expression ‘a footed animal with two feet’ can be called single; for it is not the circumstance that the words follow in unbroken succession that effects the unity. This inquiry, however, finds its place in an investigation foreign to that before us.
We call those propositions single which indicate a single fact, or the conjunction of the parts of which results in unity: those propositions, on the other hand, are separate and many in number, which indicate many facts, or whose parts have no conjunction.
Let us, moreover, consent to call a noun or a verb an expression only, and not a proposition, since it is not possible for a man to speak in this way when he is expressing something, in such a way as to make a statement, whether his utterance is an answer to a question or an act of his own initiation.
To return: of propositions one kind is simple, i.e. that which asserts or denies something of something, the other composite, i.e. that which is compounded of simple propositions. A simple proposition is a statement, with meaning, as to the presence of something in a subject or its absence, in the present, past, or future, according to the divisions of time.
 
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An affirmation is a positive assertion of something about something, a denial a negative assertion.
Now it is possible both to affirm and to deny the presence of something which is present or of something which is not, and since these same affirmations and denials are possible with reference to those times which lie outside the present, it would be possible to contradict any affirmation or denial. Thus it is plain that every affirmation has an opposite denial, and similarly every denial an opposite affirmation.
We will call such a pair of propositions a pair of contradictories. Those positive and negative propositions are said to be contradictory which have the same subject and predicate. The identity of subject and of predicate must not be ‘equivocal’. Indeed there are definitive qualifications besides this, which we make to meet the casuistries of sophists.
 
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Some things are universal, others individual. By the term ‘universal’ I mean that which is of such a nature as to be predicated of many subjects, by ‘individual’ that which is not thus predicated. Thus ‘man’ is a universal, ‘Callias’ an individual.
Our propositions necessarily sometimes concern a universal subject, sometimes an individual.
If, then, a man states a positive and a negative proposition of universal character with regard to a universal, these two propositions are ‘contrary’. By the expression ‘a proposition of universal character with regard to a universal’, such propositions as ‘every man is white’, ‘no man is white’ are meant. When, on the other hand, the positive and negative propositions, though they have regard to a universal, are yet not of universal character, they will not be contrary, albeit the meaning intended is sometimes contrary. As instances of propositions made with regard to a universal, but not of universal character, we may take the ‘propositions ‘man is white’, ‘man is not white’. ‘Man’ is a universal, but the proposition is not made as of universal character; for the word ‘every’ does not make the subject a universal, but rather gives the proposition a universal character. If, however, both predicate and subject are distributed, the proposition thus constituted is contrary to truth; no affirmation will, under such circumstances, be true. The proposition ‘every man is every animal’ is an example of this type.
An affirmation is opposed to a denial in the sense which I denote by the term ‘contradictory’, when, while the subject remains the same, the affirmation is of universal character and the denial is not. The affirmation ‘every man is white’ is the contradictory of the denial ‘not every man is white’, or again, the proposition ‘no man is white’ is the contradictory of the proposition ‘some men are white’. But propositions are opposed as contraries when both the affirmation and the denial are universal, as in the sentences ‘every man is white’, ‘no man is white’, ‘every man is just’, ‘no man is just’.
We see that in a pair of this sort both propositions cannot be true, but the contradictories of a pair of contraries can sometimes both be true with reference to the same subject; for instance ‘not every man is white’ and some men are white’ are both true. Of such corresponding positive and negative propositions as refer to universals and have a universal character, one must be true and the other false. This is the case also when the reference is to individuals, as in the propositions ‘Socrates is white’, ‘Socrates is not white’.
When, on the other hand, the reference is to universals, but the propositions are not universal, it is not always the case that one is true and the other false, for it is possible to state truly that man is white and that man is not white and that man is beautiful and that man is not beautiful; for if a man is deformed he is the reverse of beautiful, also if he is progressing towards beauty he is not yet beautiful.
This statement might seem at first sight to carry with it a contradiction, owing to the fact that the proposition ‘man is not white’ appears to be equivalent to the proposition ‘no man is white’. This, however, is not the case, nor are they necessarily at the same time true or false.
It is evident also that the denial corresponding to a single affirmation is itself single; for the denial must deny just that which the affirmation affirms concerning the same subject, and must correspond with the affirmation both in the universal or particular character of the subject and in the distributed or undistributed sense in which it is understood.
For instance, the affirmation ‘Socrates is white’ has its proper denial in the proposition ‘Socrates is not white’. If anything else be negatively predicated of the subject or if anything else be the subject though the predicate remain the same, the denial will not be the denial proper to that affirmation, but on that is distinct.
The denial proper to the affirmation ‘every man is white’ is ‘not every man is white’; that proper to the affirmation ‘some men are white’ is ‘no man is white’, while that proper to the affirmation ‘man is white’ is ‘man is not white’.
We have shown further that a single denial is contradictorily opposite to a single affirmation and we have explained which these are; we have also stated that contrary are distinct from contradictory propositions and which the contrary are; also that with regard to a pair of opposite propositions it is not always the case that one is true and the other false. We have pointed out, moreover, what the reason of this is and under what circumstances the truth of the one involves the falsity of the other.
 
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An affirmation or denial is single, if it indicates some one fact about some one subject; it matters not whether the subject is universal and whether the statement has a universal character, or whether this is not so. Such single propositions are: ‘every man is white’, ‘not every man is white’;’man is white’,’man is not white’; ‘no man is white’, ‘some men are white’; provided the word ‘white’ has one meaning. If, on the other hand, one word has two meanings which do not combine to form one, the affirmation is not single. For instance, if a man should establish the symbol ‘garment’ as significant both of a horse and of a man, the proposition ‘garment is white’ would not be a single affirmation, nor its opposite a single denial. For it is equivalent to the proposition ‘horse and man are white’, which, again, is equivalent to the two propositions ‘horse is white’, ‘man is white’. If, then, these two propositions have more than a single significance, and do not form a single proposition, it is plain that the first proposition either has more than one significance or else has none; for a particular man is not a horse.
This, then, is another instance of those propositions of which both the positive and the negative forms may be true or false simultaneously.
 
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In the case of that which is or which has taken place, propositions, whether positive or negative, must be true or false. Again, in the case of a pair of contradictories, either when the subject is universal and the propositions are of a universal character, or when it is individual, as has been said,’ one of the two must be true and the other false; whereas when the subject is universal, but the propositions are not of a universal character, there is no such necessity. We have discussed this type also in a previous chapter.
When the subject, however, is individual, and that which is predicated of it relates to the future, the case is altered. For if all propositions whether positive or negative are either true or false, then any given predicate must either belong to the subject or not, so that if one man affirms that an event of a given character will take place and another denies it, it is plain that the statement of the one will correspond with reality and that of the other will not. For the predicate cannot both belong and not belong to the subject at one and the same time with regard to the future.
Thus, if it is true to say that a thing is white, it must necessarily be white; if the reverse proposition is true, it will of necessity not be white. Again, if it is white, the proposition stating that it is white was true; if it is not white, the proposition to the opposite effect was true. And if it is not white, the man who states that it is making a false statement; and if the man who states that it is white is making a false statement, it follows that it is not white. It may therefore be argued that it is necessary that affirmations or denials must be either true or false.
Now if this be so, nothing is or takes place fortuitously, either in the present or in the future, and there are no real alternatives; everything takes place of necessity and is fixed. For either he that affirms that it will take place or he that denies this is in correspondence with fact, whereas if things did not take place of necessity, an event might just as easily not happen as happen; for the meaning of the word ‘fortuitous’ with regard to present or future events is that reality is so constituted that it may issue in either of two opposite directions. Again, if a thing is white now, it was true before to say that it would be white, so that of anything that has taken place it was always true to say ‘it is’ or ‘it will be’. But if it was always true to say that a thing is or will be, it is not possible that it should not be or not be about to be, and when a thing cannot not come to be, it is impossible that it should not come to be, and when it is impossible that it should not come to be, it must come to be. All, then, that is about to be must of necessity take place. It results from this that nothing is uncertain or fortuitous, for if it were fortuitous it would not be necessary.
Again, to say that neither the affirmation nor the denial is true, maintaining, let us say, that an event neither will take place nor will not take place, is to take up a position impossible to defend. In the first place, though facts should prove the one proposition false, the opposite would still be untrue. Secondly, if it was true to say that a thing was both white and large, both these qualities must necessarily belong to it; and if they will belong to it the next day, they must necessarily belong to it the next day. But if an event is neither to take place nor not to take place the next day, the element of chance will be eliminated. For example, it would be necessary that a sea-fight should neither take place nor fail to take place on the next day.
These awkward results and others of the same kind follow, if it is an irrefragable law that of every pair of contradictory propositions, whether they have regard to universals and are stated as universally applicable, or whether they have regard to individuals, one must be true and the other false, and that there are no real alternatives, but that all that is or takes place is the outcome of necessity. There would be no need to deliberate or to take trouble, on the supposition that if we should adopt a certain course, a certain result would follow, while, if we did not, the result would not follow. For a man may predict an event ten thousand years beforehand, and another may predict the reverse; that which was truly predicted at the moment in the past will of necessity take place in the fullness of time.
Further, it makes no difference whether people have or have not actually made the contradictory statements. For it is manifest that the circumstances are not influenced by the fact of an affirmation or denial on the part of anyone. For events will not take place or fail to take place because it was stated that they would or would not take place, nor is this any more the case if the prediction dates back ten thousand years or any other space of time. Wherefore, if through all time the nature of things was so constituted that a prediction about an event was true, then through all time it was necessary that that should find fulfillment; and with regard to all events, circumstances have always been such that their occurrence is a matter of necessity. For that of which someone has said truly that it will be, cannot fail to take place; and of that which takes place, it was always true to say that it would be.
Yet this view leads to an impossible conclusion; for we see that both deliberation and action are causative with regard to the future, and that, to speak more generally, in those things which are not continuously actual there is potentiality in either direction. Such things may either be or not be; events also therefore may either take place or not take place. There are many obvious instances of this. It is possible that this coat may be cut in half, and yet it may not be cut in half, but wear out first. In the same way, it is possible that it should not be cut in half; unless this were so, it would not be possible that it should wear out first. So it is therefore with all other events which possess this kind of potentiality. It is therefore plain that it is not of necessity that everything is or takes place; but in some instances there are real alternatives, in which case the affirmation is no more true and no more false than the denial; while some exhibit a predisposition and general tendency in one direction or the other, and yet can issue in the opposite direction by exception.
Now that which is must needs be when it is, and that which is not must needs not be when it is not. Yet it cannot be said without qualification that all existence and non-existence is the outcome of necessity. For there is a difference between saying that that which is, when it is, must needs be, and simply saying that all that is must needs be, and similarly in the case of that which is not. In the case, also, of two contradictory propositions this holds good. Everything must either be or not be, whether in the present or in the future, but it is not always possible to distinguish and state determinately which of these alternatives must necessarily come about.
Let me illustrate. A sea-fight must either take place to-morrow or not, but it is not necessary that it should take place to-morrow, neither is it necessary that it should not take place, yet it is necessary that it either should or should not take place to-morrow. Since propositions correspond with facts, it is evident that when in future events there is a real alternative, and a potentiality in contrary directions, the corresponding affirmation and denial have the same character.
This is the case with regard to that which is not always existent or not always nonexistent. One of the two propositions in such instances must be true and the other false, but we cannot say determinately that this or that is false, but must leave the alternative undecided. One may indeed be more likely to be true than the other, but it cannot be either actually true or actually false. It is therefore plain that it is not necessary that of an affirmation and a denial one should be true and the other false. For in the case of that which exists potentially, but not actually, the rule which applies to that which exists actually does not hold good. The case is rather as we have indicated.
 
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An affirmation is the statement of a fact with regard to a subject, and this subject is either a noun or that which has no name; the subject and predicate in an affirmation must each denote a single thing. I have already explained’ what is meant by a noun and by that which has no name; for I stated that the expression ‘not-man’ was not a noun, in the proper sense of the word, but an indefinite noun, denoting as it does in a certain sense a single thing. Similarly the expression ‘does not enjoy health’ is not a verb proper, but an indefinite verb. Every affirmation, then, and every denial, will consist of a noun and a verb, either definite or indefinite.
There can be no affirmation or denial without a verb; for the expressions ‘is’, ‘will be’, ‘was’, ‘is coming to be’, and the like are verbs according to our definition, since besides their specific meaning they convey the notion of time. Thus the primary affirmation and denial are ‘as follows: ‘man is’, ‘man is not’. Next to these, there are the propositions: ‘not-man is’, ‘not-man is not’. Again we have the propositions: ‘every man is, ‘every man is not’, ‘all that is not-man is’, ‘all that is not-man is not’. The same classification holds good with regard to such periods of time as lie outside the present.
When the verb ‘is’ is used as a third element in the sentence, there can be positive and negative propositions of two sorts. Thus in the sentence ‘man is just’ the verb ‘is’ is used as a third element, call it verb or noun, which you will. Four propositions, therefore, instead of two can be formed with these materials. Two of the four, as regards their affirmation and denial, correspond in their logical sequence with the propositions which deal with a condition of privation; the other two do not correspond with these.
I mean that the verb ‘is’ is added either to the term ‘just’ or to the term ‘not-just’, and two negative propositions are formed in the same way. Thus we have the four propositions. Reference to the subjoined table will make matters clear:
A. Affirmation. Man is just B. Denial. Man is not just
\ /
/ \
D. Denial. Man is not not-just C. Affirmation. Man is not-just
Here ‘is’ and ‘is not’ are added either to ‘just’ or to ‘not-just’. This then is the proper scheme for these propositions, as has been said in the Analytics. The same rule holds good, if the subject is distributed. Thus we have the table:
A'. Affirmation. Every man is just B'. Denial. Not every man is just
\ /
/ \
D'. Denial. Not every man is not-just C'. Affirmation. Every man is not-just.
Yet here it is not possible, in the same way as in the former case, that the propositions joined in the table by a diagonal line should both be true; though under certain circumstances this is the case.
We have thus set out two pairs of opposite propositions; there are moreover two other pairs, if a term be conjoined with ‘not-man’, the latter forming a kind of subject. Thus:
A". Not-man is just. B". Not-man is not just
\ /
/ \
D". Not-man is not not-just. C". Not-man is not-just.
This is an exhaustive enumeration of all the pairs of opposite propositions that can possibly be framed. This last group should remain distinct from those which preceded it, since it employs as its subject the expression ‘not-man’.
When the verb ‘is’ does not fit the structure of the sentence (for instance, when the verbs ‘walks’, ‘enjoys health’ are used), that scheme applies, which applied when the word ‘is’ was added.
Thus we have the propositions: ‘every man enjoys health’, ‘every man does-not-enjoy-health’, ‘all that is not-man enjoys health’, ‘all that is not-man does-not-enjoy-health’. We must not in these propositions use the expression ‘not every man’. The negative must be attached to the word ‘man’, for the word ‘every’ does not give to the subject a universal significance, but implies that, as a subject, it is distributed. This is plain from the following pairs: ‘man enjoys health’, ‘man does not enjoy health’; ‘not-man enjoys health’, ‘not man does not enjoy health’. These propositions differ from the former in being indefinite and not universal in character. Thus the adjectives ‘every’ and no additional significance except that the subject, whether in a positive or in a negative sentence, is distributed. The rest of the sentence, therefore, will in each case be the same.
Since the contrary of the proposition ‘every animal is just’ is ‘no animal is just’, it is plain that these two propositions will never both be true at the same time or with reference to the same subject. Sometimes, however, the contradictories of these contraries will both be true, as in the instance before us: the propositions ‘not every animal is just’ and ‘some animals are just’ are both true.
Further, the proposition ‘no man is just’ follows from the proposition ‘every man is not just’ and the proposition ‘not every man is not just’, which is the opposite of ‘every man is not-just’, follows from the proposition ‘some men are just’; for if this be true, there must be some just men.
It is evident, also, that when the subject is individual, if a question is asked and the negative answer is the true one, a certain positive proposition is also true. Thus, if the question were asked Socrates wise?’ and the negative answer were the true one, the positive inference ‘Then Socrates is unwise’ is correct. But no such inference is correct in the case of universals, but rather a negative proposition. For instance, if to the question ‘Is every man wise?’ the answer is ‘no’, the inference ‘Then every man is unwise’ is false. But under these circumstances the inference ‘Not every man is wise’ is correct. This last is the contradictory, the former the contrary. Negative expressions, which consist of an indefinite noun or predicate, such as ‘not-man’ or ‘not-just’, may seem to be denials containing neither noun nor verb in the proper sense of the words. But they are not. For a denial must always be either true or false, and he that uses the expression ‘not man’, if nothing more be added, is not nearer but rather further from making a true or a false statement than he who uses the expression ‘man’.
The propositions ‘everything that is not man is just’, and the contradictory of this, are not equivalent to any of the other propositions; on the other hand, the proposition ‘everything that is not man is not just’ is equivalent to the proposition ‘nothing that is not man is just’.
The conversion of the position of subject and predicate in a sentence involves no difference in its meaning. Thus we say ‘man is white’ and ‘white is man’. If these were not equivalent, there would be more than one contradictory to the same proposition, whereas it has been demonstrated’ that each proposition has one proper contradictory and one only. For of the proposition ‘man is white’ the appropriate contradictory is ‘man is not white’, and of the proposition ‘white is man’, if its meaning be different, the contradictory will either be ‘white is not not-man’ or ‘white is not man’. Now the former of these is the contradictory of the proposition ‘white is not-man’, and the latter of these is the contradictory of the proposition ‘man is white’; thus there will be two contradictories to one proposition.
It is evident, therefore, that the inversion of the relative position of subject and predicate does not affect the sense of affirmations and denials.

 
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There is no unity about an affirmation or denial which, either positively or negatively, predicates one thing of many subjects, or many things of the same subject, unless that which is indicated by the many is really some one thing. do not apply this word ‘one’ to those things which, though they have a single recognized name, yet do not combine to form a unity. Thus, man may be an animal, and biped, and domesticated, but these three predicates combine to form a unity. On the other hand, the predicates ‘white’, ‘man’, and ‘walking’ do not thus combine. Neither, therefore, if these three form the subject of an affirmation, nor if they form its predicate, is there any unity about that affirmation. In both cases the unity is linguistic, but not real.
If therefore the dialectical question is a request for an answer, i.e. either for the admission of a premiss or for the admission of one of two contradictories-and the premiss is itself always one of two contradictories-the answer to such a question as contains the above predicates cannot be a single proposition. For as I have explained in the Topics, question is not a single one, even if the answer asked for is true.
At the same time it is plain that a question of the form ‘what is it?’ is not a dialectical question, for a dialectical questioner must by the form of his question give his opponent the chance of announcing one of two alternatives, whichever he wishes. He must therefore put the question into a more definite form, and inquire, e.g.. whether man has such and such a characteristic or not.
Some combinations of predicates are such that the separate predicates unite to form a single predicate. Let us consider under what conditions this is and is not possible. We may either state in two separate propositions that man is an animal and that man is a biped, or we may combine the two, and state that man is an animal with two feet. Similarly we may use ‘man’ and ‘white’ as separate predicates, or unite them into one. Yet if a man is a shoemaker and is also good, we cannot construct a composite proposition and say that he is a good shoemaker. For if, whenever two separate predicates truly belong to a subject, it follows that the predicate resulting from their combination also truly belongs to the subject, many absurd results ensue. For instance, a man is man and white. Therefore, if predicates may always be combined, he is a white man. Again, if the predicate ‘white’ belongs to him, then the combination of that predicate with the former composite predicate will be permissible. Thus it will be right to say that he is a white man so on indefinitely. Or, again, we may combine the predicates ‘musical’, ‘white’, and ‘walking’, and these may be combined many times. Similarly we may say that Socrates is Socrates and a man, and that therefore he is the man Socrates, or that Socrates is a man and a biped, and that therefore he is a two-footed man. Thus it is manifest that if man states unconditionally that predicates can always be combined, many absurd consequences ensue.
We will now explain what ought to be laid down.
Those predicates, and terms forming the subject of predication, which are accidental either to the same subject or to one another, do not combine to form a unity. Take the proposition ‘man is white of complexion and musical’. Whiteness and being musical do not coalesce to form a unity, for they belong only accidentally to the same subject. Nor yet, if it were true to say that that which is white is musical, would the terms ‘musical’ and ‘white’ form a unity, for it is only incidentally that that which is musical is white; the combination of the two will, therefore, not form a unity.
Thus, again, whereas, if a man is both good and a shoemaker, we cannot combine the two propositions and say simply that he is a good shoemaker, we are, at the same time, able to combine the predicates ‘animal’ and ‘biped’ and say that a man is an animal with two feet, for these predicates are not accidental.
Those predicates, again, cannot form a unity, of which the one is implicit in the other: thus we cannot combine the predicate ‘white’ again and again with that which already contains the notion ‘white’, nor is it right to call a man an animal-man or a two-footed man; for the notions ‘animal’ and ‘biped’ are implicit in the word ‘man’. On the other hand, it is possible to predicate a term simply of any one instance, and to say that some one particular man is a man or that some one white man is a white man.
Yet this is not always possible: indeed, when in the adjunct there is some opposite which involves a contradiction, the predication of the simple term is impossible. Thus it is not right to call a dead man a man. When, however, this is not the case, it is not impossible.
Yet the facts of the case might rather be stated thus: when some such opposite elements are present, resolution is never possible, but when they are not present, resolution is nevertheless not always possible. Take the proposition ‘Homer is so-and-so’, say ‘a poet’; does it follow that Homer is, or does it not? The verb ‘is’ is here used of Homer only incidentally, the proposition being that Homer is a poet, not that he is, in the independent sense of the word.
Thus, in the case of those predications which have within them no contradiction when the nouns are expanded into definitions, and wherein the predicates belong to the subject in their own proper sense and not in any indirect way, the individual may be the subject of the simple propositions as well as of the composite. But in the case of that which is not, it is not true to say that because it is the object of opinion, it is; for the opinion held about it is that it is not, not that it is.
 
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As these distinctions have been made, we must consider the mutual relation of those affirmations and denials which assert or deny possibility or contingency, impossibility or necessity: for the subject is not without difficulty.
We admit that of composite expressions those are contradictory each to each which have the verb ‘to be’ its positive and negative form respectively. Thus the contradictory of the proposition ‘man is’ is ‘man is not’, not ‘not-man is’, and the contradictory of ‘man is white’ is ‘man is not white’, not ‘man is not-white’. For otherwise, since either the positive or the negative proposition is true of any subject, it will turn out true to say that a piece of wood is a man that is not white.
Now if this is the case, in those propositions which do not contain the verb ‘to be’ the verb which takes its place will exercise the same function. Thus the contradictory of ‘man walks’ is ‘man does not walk’, not ‘not-man walks’; for to say ‘man walks’ merely equivalent to saying ‘man is walking’.
If then this rule is universal, the contradictory of ‘it may be’ is may not be’, not ‘it cannot be’.
Now it appears that the same thing both may and may not be; for instance, everything that may be cut or may walk may also escape cutting and refrain from walking; and the reason is that those things that have potentiality in this sense are not always actual. In such cases, both the positive and the negative propositions will be true; for that which is capable of walking or of being seen has also a potentiality in the opposite direction.
But since it is impossible that contradictory propositions should both be true of the same subject, it follows that’ it may not be’ is not the contradictory of ‘it may be’. For it is a logical consequence of what we have said, either that the same predicate can be both applicable and inapplicable to one and the same subject at the same time, or that it is not by the addition of the verbs ‘be’ and ‘not be’, respectively, that positive and negative propositions are formed. If the former of these alternatives must be rejected, we must choose the latter.
The contradictory, then, of ‘it may be’ is ‘it cannot be’. The same rule applies to the proposition ‘it is contingent that it should be’; the contradictory of this is ‘it is not contingent that it should be’. The similar propositions, such as ‘it is necessary’ and ‘it is impossible’, may be dealt with in the same manner. For it comes about that just as in the former instances the verbs ‘is’ and ‘is not’ were added to the subject-matter of the sentence ‘white’ and ‘man’, so here ‘that it should be’ and ‘that it should not be’ are the subject-matter and ‘is possible’, ‘is contingent’, are added. These indicate that a certain thing is or is not possible, just as in the former instances ‘is’ and ‘is not’ indicated that certain things were or were not the case.
The contradictory, then, of ‘it may not be’ is not ‘it cannot be’, but ‘it cannot not be’, and the contradictory of ‘it may be’ is not ‘it may not be’, but cannot be’. Thus the propositions ‘it may be’ and ‘it may not be’ appear each to imply the other: for, since these two propositions are not contradictory, the same thing both may and may not be. But the propositions ‘it may be’ and ‘it cannot be’ can never be true of the same subject at the same time, for they are contradictory. Nor can the propositions ‘it may not be’ and ‘it cannot not be’ be at once true of the same subject.
The propositions which have to do with necessity are governed by the same principle. The contradictory of ‘it is necessary that it should be’, is not ‘it is necessary that it should not be,’ but ‘it is not necessary that it should be’, and the contradictory of ‘it is necessary that it should not be’ is ‘it is not necessary that it should not be’.
Again, the contradictory of ‘it is impossible that it should be’ is not ‘it is impossible that it should not be’ but ‘it is not impossible that it should be’, and the contradictory of ‘it is impossible that it should not be’ is ‘it is not impossible that it should not be’.
To generalize, we must, as has been stated, define the clauses ‘that it should be’ and ‘that it should not be’ as the subject-matter of the propositions, and in making these terms into affirmations and denials we must combine them with ‘that it should be’ and ‘that it should not be’ respectively.
We must consider the following pairs as contradictory propositions:
It may be. It cannot be.
It is contingent. It is not contingent.
It is impossible. It is not impossible.
It is necessary. It is not necessary.
It is true. It is not true.
 
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Logical sequences follow in due course when we have arranged the propositions thus. From the proposition ‘it may be’ it follows that it is contingent, and the relation is reciprocal. It follows also that it is not impossible and not necessary.
From the proposition ‘it may not be’ or ‘it is contingent that it should not be’ it follows that it is not necessary that it should not be and that it is not impossible that it should not be. From the proposition ‘it cannot be’ or ‘it is not contingent’ it follows that it is necessary that it should not be and that it is impossible that it should be. From the proposition ‘it cannot not be’ or ‘it is not contingent that it should not be’ it follows that it is necessary that it should be and that it is impossible that it should not be.
Let us consider these statements by the help of a table:
A. B.
It may be. It cannot be.
It is contingent. It is not contingent.
It is not impossible that it should be. It is impossible that it should be.
It is not necessary that it should be. It is necessary that it should not be.
C. D.
It may not be. It cannot not be.
It is contingent that it should not be. It is not contingent that it should not be.
It is not impossible that it should not be. It is impossible that it should not be.
It is not necessary that it should not be. It is necessary that it should be.
Now the propositions ‘it is impossible that it should be’ and ‘it is not impossible that it should be’ are consequent upon the propositions ‘it may be’, ‘it is contingent’, and ‘it cannot be’, ‘it is not contingent’, the contradictories upon the contradictories. But there is inversion. The negative of the proposition ‘it is impossible’ is consequent upon the proposition ‘it may be’ and the corresponding positive in the first case upon the negative in the second. For ‘it is impossible’ is a positive proposition and ‘it is not impossible’ is negative.
We must investigate the relation subsisting between these propositions and those which predicate necessity. That there is a distinction is clear. In this case, contrary propositions follow respectively from contradictory propositions, and the contradictory propositions belong to separate sequences. For the proposition ‘it is not necessary that it should be’ is not the negative of ‘it is necessary that it should not be’, for both these propositions may be true of the same subject; for when it is necessary that a thing should not be, it is not necessary that it should be. The reason why the propositions predicating necessity do not follow in the same kind of sequence as the rest, lies in the fact that the proposition ‘it is impossible’ is equivalent, when used with a contrary subject, to the proposition ‘it is necessary’. For when it is impossible that a thing should be, it is necessary, not that it should be, but that it should not be, and when it is impossible that a thing should not be, it is necessary that it should be. Thus, if the propositions predicating impossibility or non-impossibility follow without change of subject from those predicating possibility or non-possibility, those predicating necessity must follow with the contrary subject; for the propositions ‘it is impossible’ and ‘it is necessary’ are not equivalent, but, as has been said, inversely connected.
Yet perhaps it is impossible that the contradictory propositions predicating necessity should be thus arranged. For when it is necessary that a thing should be, it is possible that it should be. (For if not, the opposite follows, since one or the other must follow; so, if it is not possible, it is impossible, and it is thus impossible that a thing should be, which must necessarily be; which is absurd.)
Yet from the proposition ‘it may be’ it follows that it is not impossible, and from that it follows that it is not necessary; it comes about therefore that the thing which must necessarily be need not be; which is absurd. But again, the proposition ‘it is necessary that it should be’ does not follow from the proposition ‘it may be’, nor does the proposition ‘it is necessary that it should not be’. For the proposition ‘it may be’ implies a twofold possibility, while, if either of the two former propositions is true, the twofold possibility vanishes. For if a thing may be, it may also not be, but if it is necessary that it should be or that it should not be, one of the two alternatives will be excluded. It remains, therefore, that the proposition ‘it is not necessary that it should not be’ follows from the proposition ‘it may be’. For this is true also of that which must necessarily be.
Moreover the proposition ‘it is not necessary that it should not be’ is the contradictory of that which follows from the proposition ‘it cannot be’; for ‘it cannot be’ is followed by ‘it is impossible that it should be’ and by ‘it is necessary that it should not be’, and the contradictory of this is the proposition ‘it is not necessary that it should not be’. Thus in this case also contradictory propositions follow contradictory in the way indicated, and no logical impossibilities occur when they are thus arranged.
It may be questioned whether the proposition ‘it may be’ follows from the proposition ‘it is necessary that it should be’. If not, the contradictory must follow, namely that it cannot be, or, if a man should maintain that this is not the contradictory, then the proposition ‘it may not be’.
Now both of these are false of that which necessarily is. At the same time, it is thought that if a thing may be cut it may also not be cut, if a thing may be it may also not be, and thus it would follow that a thing which must necessarily be may possibly not be; which is false. It is evident, then, that it is not always the case that that which may be or may walk possesses also a potentiality in the other direction. There are exceptions. In the first place we must except those things which possess a potentiality not in accordance with a rational principle, as fire possesses the potentiality of giving out heat, that is, an irrational capacity. Those potentialities which involve a rational principle are potentialities of more than one result, that is, of contrary results; those that are irrational are not always thus constituted. As I have said, fire cannot both heat and not heat, neither has anything that is always actual any twofold potentiality. Yet some even of those potentialities which are irrational admit of opposite results. However, thus much has been said to emphasize the truth that it is not every potentiality which admits of opposite results, even where the word is used always in the same sense.
But in some cases the word is used equivocally. For the term ‘possible’ is ambiguous, being used in the one case with reference to facts, to that which is actualized, as when a man is said to find walking possible because he is actually walking, and generally when a capacity is predicated because it is actually realized; in the other case, with reference to a state in which realization is conditionally practicable, as when a man is said to find walking possible because under certain conditions he would walk. This last sort of potentiality belongs only to that which can be in motion, the former can exist also in the case of that which has not this power. Both of that which is walking and is actual, and of that which has the capacity though not necessarily realized, it is true to say that it is not impossible that it should walk (or, in the other case, that it should be), but while we cannot predicate this latter kind of potentiality of that which is necessary in the unqualified sense of the word, we can predicate the former.
Our conclusion, then, is this: that since the universal is consequent upon the particular, that which is necessary is also possible, though not in every sense in which the word may be used.
We may perhaps state that necessity and its absence are the initial principles of existence and non-existence, and that all else must be regarded as posterior to these.
It is plain from what has been said that that which is of necessity is actual. Thus, if that which is eternal is prior, actuality also is prior to potentiality. Some things are actualities without potentiality, namely, the primary substances; a second class consists of those things which are actual but also potential, whose actuality is in nature prior to their potentiality, though posterior in time; a third class comprises those things which are never actualized, but are pure potentialities.
 
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The question arises whether an affirmation finds its contrary in a denial or in another affirmation; whether the proposition ‘every man is just’ finds its contrary in the proposition ‘no man is just’, or in the proposition ‘every man is unjust’. Take the propositions ‘Callias is just’, ‘Callias is not just’, ‘Callias is unjust’; we have to discover which of these form contraries.
Now if the spoken word corresponds with the judgement of the mind, and if, in thought, that judgement is the contrary of another, which pronounces a contrary fact, in the way, for instance, in which the judgement ‘every man is just’ pronounces a contrary to that pronounced by the judgement ‘every man is unjust’, the same must needs hold good with regard to spoken affirmations.
But if, in thought, it is not the judgement which pronounces a contrary fact that is the contrary of another, then one affirmation will not find its contrary in another, but rather in the corresponding denial. We must therefore consider which true judgement is the contrary of the false, that which forms the denial of the false judgement or that which affirms the contrary fact.
Let me illustrate. There is a true judgement concerning that which is good, that it is good; another, a false judgement, that it is not good; and a third, which is distinct, that it is bad. Which of these two is contrary to the true? And if they are one and the same, which mode of expression forms the contrary?
It is an error to suppose that judgements are to be defined as contrary in virtue of the fact that they have contrary subjects; for the judgement concerning a good thing, that it is good, and that concerning a bad thing, that it is bad, may be one and the same, and whether they are so or not, they both represent the truth. Yet the subjects here are contrary. But judgements are not contrary because they have contrary subjects, but because they are to the contrary effect.
Now if we take the judgement that that which is good is good, and another that it is not good, and if there are at the same time other attributes, which do not and cannot belong to the good, we must nevertheless refuse to treat as the contraries of the true judgement those which opine that some other attribute subsists which does not subsist, as also those that opine that some other attribute does not subsist which does subsist, for both these classes of judgement are of unlimited content.
Those judgements must rather be termed contrary to the true judgements, in which error is present. Now these judgements are those which are concerned with the starting points of generation, and generation is the passing from one extreme to its opposite; therefore error is a like transition.
Now that which is good is both good and not bad. The first quality is part of its essence, the second accidental; for it is by accident that it is not bad. But if that true judgement is most really true, which concerns the subject’s intrinsic nature, then that false judgement likewise is most really false, which concerns its intrinsic nature. Now the judgement that that is good is not good is a false judgement concerning its intrinsic nature, the judgement that it is bad is one concerning that which is accidental. Thus the judgement which denies the true judgement is more really false than that which positively asserts the presence of the contrary quality. But it is the man who forms that judgement which is contrary to the true who is most thoroughly deceived, for contraries are among the things which differ most widely within the same class. If then of the two judgements one is contrary to the true judgement, but that which is contradictory is the more truly contrary, then the latter, it seems, is the real contrary. The judgement that that which is good is bad is composite. For presumably the man who forms that judgement must at the same time understand that that which is good is not good.
Further, the contradictory is either always the contrary or never; therefore, if it must necessarily be so in all other cases, our conclusion in the case just dealt with would seem to be correct. Now where terms have no contrary, that judgement is false, which forms the negative of the true; for instance, he who thinks a man is not a man forms a false judgement. If then in these cases the negative is the contrary, then the principle is universal in its application.
Again, the judgement that that which is not good is not good is parallel with the judgement that that which is good is good. Besides these there is the judgement that that which is good is not good, parallel with the judgement that that that is not good is good. Let us consider, therefore, what would form the contrary of the true judgement that that which is not good is not good. The judgement that it is bad would, of course, fail to meet the case, since two true judgements are never contrary and this judgement might be true at the same time as that with which it is connected. For since some things which are not good are bad, both judgements may be true. Nor is the judgement that it is not bad the contrary, for this too might be true, since both qualities might be predicated of the same subject. It remains, therefore, that of the judgement concerning that which is not good, that it is not good, the contrary judgement is that it is good; for this is false. In the same way, moreover, the judgement concerning that which is good, that it is not good, is the contrary of the judgement that it is good.
It is evident that it will make no difference if we universalize the positive judgement, for the universal negative judgement will form the contrary. For instance, the contrary of the judgement that everything that is good is good is that nothing that is good is good. For the judgement that that which is good is good, if the subject be understood in a universal sense, is equivalent to the judgement that whatever is good is good, and this is identical with the judgement that everything that is good is good. We may deal similarly with judgements concerning that which is not good.
If therefore this is the rule with judgements, and if spoken affirmations and denials are judgements expressed in words, it is plain that the universal denial is the contrary of the affirmation about the same subject. Thus the propositions ‘everything good is good’, ‘every man is good’, have for their contraries the propositions ‘nothing good is good’, ‘no man is good’. The contradictory propositions, on the other hand, are ‘not everything good is good’, ‘not every man is good’.
It is evident, also, that neither true judgements nor true propositions can be contrary the one to the other. For whereas, when two propositions are true, a man may state both at the same time without inconsistency, contrary propositions are those which state contrary conditions, and contrary conditions cannot subsist at one and the same time in the same subject.
 
3 Sophistical Refutations.
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Concerning sophistical elenchi, and such as appear, indeed, elenchi, yet are paralogisms but not elenchi, let us treat, commencing in natural order, from the first.

That some, then, are syllogisms, but that others which are not, appear (syllogisms), is clear, for as this happens in other things through a certain similarity, so also does it occur in arguments. For some have a good habit, others appear (to have it), being inflated on account of their family, and decorating themselves; some, again, are beautiful on account of beauty, but others appear so from ornament. Likewise, in the case of things inanimate, for of these, some are really silver, and others gold, but others again, though they are not, appear so to sense; for instance, substances like litharge and tin (seem) silvery, others dyed with gall (appear) golden. In the same manner also, syllogism and elenchus, one indeed is (in reality), but the other is not, yet seems so from inexperience, for the inexperienced make their observations as it were, withdrawing to a distance; for syllogism is from certain things so laid down, as that we collect something of necessity, different from the things laid down, through the posita; but an elenchus is a syllogism with contradiction of the conclusion. Some, indeed, do not do this, but appear to do it from many causes, of which this is one place most natural and most popular, viz. through names, for since we cannot discourse by adducing the things themselves, but use names as symbols instead of things, we think that what happens in names, also happens in things, as with those who calculate, but there is no resemblance. For names and the number of sentences are finite, but things are infinite in number, wherefore it is necessary that the same sentence and one name should signify many things. As therefore there, those who are not clever in calculation are deceived by the skilful, in the same manner also, with regard to arguments, those who are unskilled in the power of names are deceived by paralogisms, both when they dispute themselves, and when they hear others, for which reason also, and others which will be assigned, there may be a syllogism and elenchus in appearance, but not in reality. Since, however, to some men it is more the endeavour to seem, than to be, wise, and not to seem, (for the sophistical is apparent but not real wisdom, and a sophist is a trader from apparent and not real wisdom,) it is clearly necessary to these, that they should rather seem to perform the office of a wise man, than to perform it and not to seem to do so. On the other hand, it is the business of him who is skilful in any thing, (that I may compare one thing with one,) not to deceive about what he knows, and to be able to expose another who does deceive; and these consist, the one, in being able to give a reason, and the other in receiving one. Therefore it is necessary, that those who desire to argue sophistically, should investigate the genus of the before-named arguments, since it is to the purpose; for a power of this kind, will cause a man to appear wise, which these happen to prefer.

That there is then, a certain such genus of arguments as this, and that they, whom we call sophists, desire such a power, is evident; but how many species of sophistical arguments there are, and from what number this power consists; also, how many parts there are of this treatise; and concerning the other points, which contribute to this art, let us now speak.

 
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In disputation, there are four genera of arguments, the didactic, the dialectic, the peirastic (or tentative), and the contentious. The didactic, indeed, are those which syllogize from the proper principles of each discipline, and not from the opinions of him who answers, (for it is necessary that he who learns, should believe:) the dialectic are such as collect contradiction from probabilities: the peirastic are those which are (conclusive) from things appearing to the respondent, and which are necessary for him to know, who pretends to possess science, (in what manner, indeed, has been defined elsewhere:) the contentious are those which infer, or seem to infer, from the apparently, but not really, probable. Now concerning the demonstrative, we have spoken in the Analytics, but concerning the dialectic and peirastic in other treatises; let us now, therefore, speak about those which are contentious, and litigious.
 
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We must, in the first place, assume how many are the objects which they aim at, who contend, and strive, in disputations, and these are five in number: an elenchus, the false, the paradox, the solecism, and the fifth, to make their opponent in disputation trifle, (this is to compel him frequently to say the same thing,) or what is not, but seems to be, each of these. They specially indeed, prefer, to appear to confute by an elenchus, next to point out some false assertion, thirdly, to lead to a paradox, and fourthly, to make (their adversary) commit a solecism, (and this is, to make the respondent, from the argument, speak barbarously), in the last place, to make (a person) frequently say the same thing.
 
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The modes of employing elenchus are two, for there are some conversant with diction, but others without diction, those which cause appearance (of elenchus) according to diction, are six in number, which are equivocation, ambiguity, composition, division, accent, and figure of speech. The credibility of this, however, is from induction and syllogism, both whether some other (mode) be assumed, and because we may signify what is not the same in so many ways by the same names and sentences. Such arguments as these are from equivocation, as that those scientifically cognizant, learn, for grammarians learn those things which they recite from memory; for to learn, is equivocal, (signifying) both to understand, by using science, and also to acquire science. Again, also, that things evil, are good, for that things necessary are good, but that things evil are necessary; for necessary is twofold, viz. that which is indispensable, which frequently happens also in evils, for (some evil is indispensable), and again, we say that good things are necessary, (that is, expedient). Moreover, that the same person sits, and stands, and is ill, and well, for he who rose, stands, and he who became well, is well; but he who was sitting, rose, and he who was ill, became well, for that he who is ill, does, or suffers any thing, does not signify one thing, but sometimes signifies him who is now ill, or sitting, sometimes him who was ill before, except that both he who was ill, and being ill, became well, but he is well, not being ill, and he who was ill, not (who is) now, but (who was) before. Such arguments as these however, are from ambiguity:

τὸ βούλεσθαι λαβεῖν με τοὺς πολεμίους,
and

ἆρ’ ὄ τις γινώσκει τοῦτο γινώσκει;
for both he who knows, and what is known, may signify in this sentence, the same thing as knowing; also

ἆρ’ ὄ ὁρᾷ τις, τοῦτο ὁρᾷ—but he sees a pillar, so that the pillar sees: and,
ἆρα ὁ σὺ φῂς εἶναι, τοῦτο σὺ φῂς εἶναι; φῂς δὲ λίθον εἶναι, σὺ ἀρα φῂς λίθος εἶναι
and,

ἆρ’ ἔστι σιγῶντα λέγειν; for σιγῶντα λέγειν is two-fold, signifying both that he who speaks, is silent, and those things which are spoken. There are, however, three modes of the equivocal and ambiguous, one when the sentence or word properly signifies many things, as an eagle and a dog; another when we are accustomed thus to speak; and a third, when the conjoined signifies many things, but separated (is taken) simply, as ἐπίσταται γράμματα, for each ἐπίσταται, and γράμματα, signifies if it should so happen, one thing, but both (conjointly) many things, either that letters themselves have science, or that some one else knows letters.
Ambiguity therefore, and equivocation, are in these modes, but the following belong to composition; as that he who sits, can walk, and that he who does not write, may write. For it does not signify the same if a person speaks separately and conjointly, that it is possible that a person sitting, may walk, and that one not writing, may write, and this in a similar manner, if some one should connect (the words), that he who does not write, writes; since it signifies that he has a power by not writing, of writing. If however he does not join (the words, it signifies), that he has a power, when he does not write, of writing; also he now learns letters, since he learned what he knows; moreover, that he who is able to carry one thing only, is able to carry many.

Concerning division, (the arguments) are such as these, that five is two and three, and odd and even, and that the greater is equal, for it is so much, and something more; for the same sentence divided, and conjoined, does not always appear to signify the same thing; as

"Ἐγὼ σ’ ἔθηκα δοῦλον ὄντ’ ἐλεύθερον,"
and this,

"πεντηκοντ’ ἀνδρῶν ἑκατὸν λίπε διõς Ἀχιλλεύς."
But from accent, in discussions which are not committed to writing, it is not easy to frame an argument, but rather in writings and poems, as, for instance, some defend Homer against those who accuse him as having spoken absurdly,

τὸ μὲν οὖ καταπύθεται ὄμβρῷ,
for they solve this by accent, saying that οὔ is to be marked with an acute accent. Also about the dream of Agamemnon, because Jupiter himself does not say,

δίδομεν δέ οἱ εὖχος ἀρέσθαι,
but commanded the dream διδόναι; such things therefore are assumed from accent.

Those (arguments) occur from figure of speech, when what is not the same, is interpreted after the same manner, as when the masculine is interpreted feminine, or the feminine as masculine, or the neuter as either of these, or again, quantity as quality, or quality as quantity, or the agent as the patient, or the disposed as the agent, and other things as they were divided before. For what is not (in the category) of action, it is possible to signify in the diction, as if it were in it, (action); thus, to be well is asserted in a similar form of speech, as to cut or to build, though that signifies a certain quality, and being disposed in a certain way, but this to do something, and in the same manner also with regard to other things.

 
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The elenchi, then, which belong to diction, are from these places, but the species of paralogism without diction are seven; one from accident; the second on account of what is asserted simply, or not simply, but in a certain respect, or some where, or at some time, or with a certain relation; the third from ignorance of the elenchus; the fourth from the consequent; the fifth from petitio principii; the sixth from placing non-causa pro causâ; the seventh from making many interrogations, one.

Paralogisms, then, which arise from accident, are when it is required to be granted, that any thing is similarly present with a subject and accident, for since there are many accidents to the same thing, it is not necessary that all these should be present with all the predicates, and the subject of which they are predicated. Thus, if Coriscus is different from man, he is different from himself, for he is a man; or if he is different from Socrates, but Socrates is a man, they say that it is granted, that he is different from man, because it happens that that from which he is said to be different is a man.

Other (paralogisms arise) from some particular thing being said to be simply this, or in a certain respect, and not properly, when what is predicated in part, is assumed as spoken simply; e.g. if (some one should infer that if) what is not, is the obiect of opinion, what is not, is, for it is not the same thing to be a certain thing, and to be, simply. Or, again, that being is not being, if some one of the number of beings is not, for instance if man is not, for it is not the same for a certain thing not to be, and not to be simply, but there seems from the affinity of diction, to be but a small difference between a certain thing existing and existence, and a certain thing not existing and non-existence. Likewise, also, (paralogisms arise) from (predication) in a certain respect, and simply, thus, if an Indian, being wholly black, has white teeth, he is white and not white, or if both are present in a certain respect, that contraries are present at the same time. Such a case, however, (of paralogism) it is easy for every body to perceive in certain (sentences), for instance, if assuming the Ethiopian to be black, he should ask whether he is white as to his teeth, if then in this respect he is white, it may be thought syllogistically proved, when he has perfected the interrogation, that (the man) is black and not black. In some (sentences), indeed, (the paralogism) is frequently latent, viz. in those, where when an assertion is made in a certain respect, the simply (being asserted) also seems to follow, and in those wherein it is not easy to perceive, whether the attribution is appropriate. Now such a thing occurs, wherein opposites are similarly inherent, for it seems that either both, or neither, must be granted as simply predicated; e.g. if one half (of a thing) is white, but the other black, whether is it, (the thing itself,) white or black?

Others (arise) from its not being defined what a syllogism is, or what an elenchus, but the definition is omitted, for an elenchus is a contradiction of one and the same, not of a name but of a thing, and of a name not synonymous, but the same (collected) necessarily from the things granted, the original (question) not being co-enumerated according to the same, with reference to the same in a similar manner, and in the same time. In the same way also, falsify about any thing (occurs); some, however, omitting some one of these, appear to employ an elenchus, as that the double and the non-double are the same, for two are the double of one, but not the double of three; or if the same thing is the double and not the double of the same, yet not according to the same, for according to length it is double, but according to breadth it is not double: or if it is (the double) of the same thing, and according to the same, and in a similar manner, yet not at the same time, wherefore there is an apparent elenchus. A person, however, might refer this, too, to those which belong to diction.

Those which are from petitio principii, arise thus, and in as many ways as it is possible to beg the original question; they seem, however, to confute from inability to perceive what is the same, and what is different.

The elenchus on account of the consequent, is from fancying that the consequence reciprocates. For when from the existence of that thing, this necessarily is, they fancy that if this is, the other necessarily is, whence also deceptions from sense about opinion occur. For often men take gall for honey, because a yellow colour is consequent to honey, and since it happens, that the earth when it has rained becomes moist, if it be moist, we think that it has rained, yet this is not necessary. In rhetorical (arguments), the demonstrations which are derived from a sign are from consequent, for when persons desire to show that a man is an adulterer, they assume a consequent, that he is fond of adorning his person, or that he is seen wandering by night, these things, however, are present with many men, but the thing predicated is not present. Likewise, also, in syllogistic (arguments), for instance, the argument of Melissus, that the universe is infinite, assuming the universe to be unbegotten, (for nothing can be generated from what is not,) but what is generated is generated from a beginning; if, therefore, the universe was not generated, it had not a beginning, so that it is infinite. Nevertheless, this does not necessarily happen, for it does not follow, that if whatever is generated has a beginning, whatever has a beginning is also generated, as neither is it necessary, if a man in a fever is hot, that whoever is hot should have a fever.

That which is from what is not a cause, being assumed as a cause, is when what is causeless is taken, as if the elenchus were produced on account of it. Now such a thing happens in syllogisms leading to the impossible, since in these it is necessary to subvert some one of the posita; if then it be reckoned in necessary interrogations, for the impossible to result, the elenchus will often appear to arise on account of this, as that soul and life are not the same, for if generation be contrary to destruction, a certain generation will be to a certain destruction, but death is a certain destruction, and is contrary to life, so that life is generation, and to live is to be generated, but this is impossible, wherefore soul and life are not the same. It is not, however, syllogistically concluded, for the impossible happens even if some one should not say that life is the same as soul, but only that life is contrary to death, which is corruption, and generation to corruption. Such arguments, then, are not simply unsyllogistic, but unsyllogistic as to the thing proposed, and a matter of this kind frequently escapes, no less the observation of the interrogators themselves.

Such, then, are the arguments which result from what is consequent, and from what is not a cause, but others from making two interrogations one, when it escapes notice that there are many, and one answer is given as if there were one (interrogation). In some cases, therefore, it is easy to perceive that there are many (interrogations), and that one answer must not be given, as, whether is the earth sea, or the heaven? in others it is less (easy), and as if there were one interrogation, men either assent, because they do not answer what is asked, or seem to be confuted, as, whether is this person, and this, a man? so that if some one should beat this, and that person, he will beat a man, and not men. Or again, in those things of which some are good, but others not good, are all good or not good? for whatever a man replies, it is possible to appear either to assert an elenchus or what is apparently false; for to say that some one of the things not good is good, or that some one of the things good is not good, is a falsehood. Still, sometimes, there may be a true elenchus from certain assumptions, for instance, if a man should grant that things white, naked, and blind, are similarly called one and many, for if that is blind which has not sight, but is adapted to have it by nature, those also will be blind which have not sight, but are naturally adapted to have it; when therefore, one thing has it, but another has not, both will see or will be blind, which is impossible.

 
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We must either, therefore, thus divide apparent syllogisms and elehchi, or refer them all to ignorance of the elenchus, assuming this as a principle, for it is possible to resolve all the modes mentioned into the definition of the elenchus. In the first place, if they are unsyllogistic, for the conclusion must result from the posita, so that we may say it is of necessity, and not that it appears to be. Next, as to the parts of definition, for of those (paralogisms) which are in diction, some are from two-fold signification, for instance, equivocation, and a sentence (ambiguous) and a similar figure (of speech), (for it is usual with all these to signify this particular thing,) but composition, and division, and accent, (produce false reasoning,) from the sentence not being the same, or the name being different. But it is necessary that this should be the same as the thing is so, if there is to be an elenchus or syllogism; thus, if a garment (is to be concluded), a garment, and not a vestment, ought to be syllogistically concluded: for that is true, indeed, but is not syllogistically inferred, as there is still need of interrogation, that it signifies the same thing by him who investigates the why.

Paralogisms from accident, become evident when the syllogism is defined, for it is necessary that there be the same definition of the elenchus, except that contradiction is added, for the elenchus is a syllogism of contradiction. If then there is not a syllogism of accident, there is not an elenchus, for neither if when these things exist it is necessary that this should be, (but this is white,) is it necessary to be white on account of the syllogism, nor if a triangle has angles equal to two right, but it happens to it to be a figure, either first or the principle, (does it follow) that figure, or principle, or first, is this thing. For the demonstration is not so far as it is figure, nor so far as it is first, but so far as it is triangle, and similarly in other cases. Wherefore, if an elenchus is a certain syllogism, that which is from accident will not be an elenchus, but by this, artists, and the scientific generally, are confuted by the unscientific, for they form syllogisms from accident, against scientific men, but they, not being able to distinguish, either grant when questioned, or not granting, fancy that they have granted.

Those which belong to "in a certain respect," and "simply," (arise) because the affirmation and negation are not of the same thing, for of what is in a certain respect, white, the negation is, that which in a certain respect, is not white, but of what is simply, white, that which is simply, not white. If then, when it is granted that a thing is in a certain respect white, a person assumes it as if said, simply white, he does not produce an elenchus, but he seems to do so, from ignorance of what an elenchus is.

The most evident of all, are those which were before mentioned, from the definition of an elenchus, wherefore they are thus also denominated; as an appearance (of elenchus) is produced from the ellipse of definition, and by those who thus divide, the defect of definition must be laid down, as common to all these.

Those also which are from petitio principii, and from admitting "non-causa," "pro causâ" become manifest by definition, for it is necessary that the conclusion should happen in consequence of these things existing; which is not amongst "non-causes;" and again, the original question not being enumerated, which those paralogisms have not, which subsist from petitio principii.

Those which belong to the consequent, are a part of accident, since what is consequent, happens; still it differs from accident in that it is only possible to assume accident in one thing, as that yellow and honey are the same, also whiteness and a swan, but what follows is always in many things, for those which are the same with one and the same thing, we consider the same with each other, wherefore there is an elenchus from the consequent. Still this is not altogether true, as if it should be from accident, for snow, and swan, are the same, so far as each is white. Or again, as in the argument of Melissus, a person assumes that to have been generated, and to have a beginning, are the same; or that to become equals, is identical with to receive the same magnitude; for because what was generated has a beginning, they require it to be granted, that what had a beginning, was generated, as if both these were the same from having a beginning, viz. that which was generated, and what was finite. Likewise, also in things made equal, if those which receive one, and the same magnitude, become equal, those also which become equal, receive one magnitude, so that the consequent is assumed. Since then, an elenchus which is from accident, subsists in the ignorance of the elenchus, it is clear that this also is the case, with that which is from the consequent, and this is also to be considered in another way.

Notwithstanding, those paralogisms which are from making many interrogations, one, consist in our not distinctly unfolding the definition, of the proposition. For the proposition is one thing of one, since there is the same definition of a thing, one only and simply, as of man, and of one man only, and similarly in other cases. If then, one proposition be that which requires one thing of one, an interrogation of this kind will be simply a proposition, but since a syllogism is from propositions, and the elenchus is a syllogism, an elenchus also will consist of propositions, wherefore if a proposition be one thing of one, it is evident that he (who errs) in the definition of syllogism, is in ignorance of an elenchus, as that seems a proposition, which is not one. If then he gives an answer, as if to one interrogation, it will be an elenchus, but if he does not, yet seems to do so, it will be an apparent elenchus, so that all the places fall into ignorance of the elenchus, those from diction, because there is apparent contradiction, which was the characteristic of an elenchus, but the rest from the definition of syllogism.

 
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Deception of these (paralogisms) from equivocation and (ambiguous) sentence, arises from our not being able to distinguish that which is multifariously predicated, (since it is not easy to divide some things, for instance, the one, being, and the same;) but of those from composition and division, in consequence of fancying there is no difference between a conjoined, and a divided sentence, as is the case in most things. Similarly also with regard to those from accent, for either in nothing, or not in many things, a sentence with intention, and a sentence with remission, appear to signify the same thing. But of those from figure of speech, it is on account of the similarity of diction, for it is difficult to distinguish what things are predicated after the same, and what in a different manner, (since he who is able to do this, almost approaches the perception of truth, and especially knows how to assent,) because we suppose that every thing predicated of a certain thing, is this definite thing, and we admit it as one; for this particular definite thing, and being, seem especially to be consequent to the one, and to essence. Wherefore this mode is to be placed amongst those (fallacies) which belong to diction; first, because deception rather arises to those who consider with others, than by themselves, (for consideration with others, is through discourse, but that by oneself, is no less through the thing itself;) next, it happens that one is deceived by oneself, when one makes the consideration by words; moreover, deception is from resemblance, but resemblance from diction. Of the paralogisms from accident, (there is deception) from our inability to distinguish the same, and different, and one, and many, and to what attributes, and thing, all these are accidental. Likewise also, as to those from what is consequent, for the consequent is a certain part of accident; besides also, in many instances it appears, and is required to be granted thus, that if this thing is not separated from that, neither will that, be separated from this. Nevertheless, of those which are from the defect of definition, and of those from a certain respect, and simply, there is deception from the difference being small, for we concede universally, as if a certain thing, or in a certain respect, or in what manner, or now, signified nothing in addition. Likewise also, in the case of those which assume the original question, and which are not causes, and such as make many interrogations as if they were one, since in all these, the deception arises from smallness, as we do not accurately distinguish either the definition of the proposition, or of the syllogism, on account of the before-named cause.
 
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Since we have assigned the causes from which apparent syllogisms arise, we also have those from which sophistical syllogisms and elenchi may be produced. Now I call a sophistical elenchus and syllogism, not only the syllogism and elenchus which are apparent but not real, but also the real, but which appear (falsely) appropriate to a thing. Such are they which do not confute according to a thing, and expose the ignorant, which was the province of the peirastic art, but the peirastie is a part of the dialectic, which is able syllogistically to conclude the false through the ignorance of him who admits the argument. Sophistical elenchi, on the other hand, though they syllogistically infer contradiction, do not render it evident whether he, (the opponent) is ignorant, for by these arguments, persons impede the man of science.

Now that we obtain these by the same method is evident, for from those things, through which it appears to the hearers, that the subjects of investigation are syllogistically concluded, from these they may appear also to the respondent, so that there will be false syllogisms through either all or some of these, for what a person, not interrogated, thinks he has granted, he will also admit when interrogated, except that in some cases it happens at the same time that what is deficient is questioned, and what is false is detected, as in the paralogisms from diction and solecism. If then, paralogisms of contradiction arise from apparent elenchus, it is clear that false syllogisms will be derived from as many (places) as apparent elenchus. But the apparent is from parts of the true; for when each fails, there may appear an elenchus, as that which is from the conclusion not happening in consequence of the reasoning; that which leads to the impossible; also, that which makes two interrogations, one, from the proposition; and that which assumes what is from accident, instead of what is per se, and a part of this, which is (derived) from what is consequent; besides not to happen in the thing, but in the discussion; then, instead of (assuming) contradiction universally, according to the same, and with reference to the same, and after the same manner, (to assume it) in a certain thing, or according to each of these; further from the original (question), not being reckoned, to assume the original question. Hence, we shall be in possession of those things from which paralogisms occur, since they cannot arise from more, but they will all be from the (places) specified.

A sophistical elenchus, is yet not simply an elenchus, but against some person, and a syllogism likewise, for except it be assumed that what is from the equivocal signifies one thing, and what is from a similar figure of speech, (signifies) this thing only, and the rest in like manner, there will neither be elenchi nor syllogisms, whether simply, or against him who is interrogated, but if this is assumed, there will be, indeed, against him who is interrogated, but simply there will not be, since they do not assume that which signifies one thing, but what appears (to do so) and from this person.

 
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Nevertheless, we should not endeavour to assume from how many places they are confuted, who are confuted by elenchi, without the science of all things, which, however, belongs to no one art, since there are perhaps infinite sciences, so that evidently there are also infinite demonstrations. Still there are also true elenchi, for in whatever it is possible to demonstrate, we may also therein confute him who lays down a contradiction of the truth, as if he asserted the diameter of a square to be commensurate with its side, a person might confute him by showing it incommensurate. Wherefore, it will be necessary to be scientifically cognizant of all, for some (elenchi) will be from geometrical principles, and their conclusions; others from medical principles; others from those of other sciences; moreover, false elenchi are similarly amongst infinites, since according to each art there is a false syllogism, as the geometrical in geometry, and the medical, (false syllogism) in medicine. Now I mean by according to art, that which is according to the principles of that art, therefore it is evident that places are not to be assumed of all elenchi, but of those which belong to dialectic, since these are common to every art and faculty. It is also, indeed, the province of the man of science to investigate the elenchus which is in each science, whether it is only apparent, not real, and if it is, why it is; but that (elenchus) which is from things common, and does not fall under any art, belongs to dialectics. For if we have those particulars from which probable syllogisms about any thing arise, we have those also from which (probable) elenchi are formed, since the elenchus is a syllogism of contradiction, so that an elenchus is either one or two syllogisms of contradiction, therefore we have the number of places from which all such originate, and if we have this, we also possess their solutions, for objections of these are solutions. We have, however, the places from which apparent elenchi arise, not apparent to every one, but to certain persons, for the places are infinite, if any one considers from what they appear to the multitude casually. Hence it appears, that it is the province of the dialectician, to be able to assume from what number of particulars, through common (propositions), either a real, or an apparent elenchus, whether dialectic, or apparently dialectic, or peirastic, is produced.
 
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That however is not a difference of arguments which some state, viz. that some arguments belong to the name, but others to the reason, since it is absurd to suppose that some arguments belong to a name, but others, and not the same, pertain to the reason. For what else is it, not to pertain to the reason, than for the arguer not to employ the name, in (the sense in) which, he who is interrogated, would admit it, fancying that the question was (in that sense) made? still this very thing belongs also to name; but to the reason, when it is understood in the sense, in which it was admitted. If indeed any one, when a name signifies many things, fancies that it signifies one thing, both the questionist and the person questioned, (as perhaps being, or one, signifies many things, but the respondent and the questionist (Zeno), thinking it to be one, interrogate, and the argument is that all things are one,) this discussion will belong to the name, or to the reason of the person interrogated. If however a person thinks that it signifies many things, it evidently does not pertain to the reason; for in the first place, what belongs to name and reason, is conversant with such arguments as signify many things; next it is (adapted) to any one, for to pertain to reason does not consist in argument, but in the respondent being disposed in a certain manner to the things granted. Further, all these arguments may possibly pertain to name, for to belong to name is here not to pertain to reason, for unless all these arguments (may be referred hither), there will be certain others pertaining neither to name nor to reason; but they say that all (belong to one of these), and distinguish all to be either belonging to name or to reason, and that there are no others. Still, whatever syllogisms belong to multifarious signification, some of these belong to name, for it is absurdly said, that all which are from diction are from name; nevertheless, there are certain paralogisms which are not produced, from the respondent being disposed in a certain manner towards these, but because the very argument itself contains such an interrogation as signifies many things.

In short, it is absurd to discuss an elenchus, and not prior to it a syllogism, for an elenchus is a syllogism; so that we must discuss a syllogism prior to a false elenchus, for such an elenchus is an apparent syllogism of contradiction. Wherefore, the cause (of deception) will either be in the syllogism, or in the contradiction, (for it is necessary that the contradiction be added,) sometimes indeed in both, if the elenchus be apparent. But it is in the contradiction and not in the syllogism, when a person asserts that he who is silent speaks; but this is in both, viz. that some one may give what he has not got; but that the poetry of Homer is a figure from being a circle, is in syllogism, and that (which errs) in neither, is a true syllogism.

But (to return), whence the discussion digressed, do mathematical arguments pertain to the reason or not? and if a triangle seems to some one to signify many things, and he grants (not so far as it is figure, of which this is concluded) that it has angles equal to two right, does this discussion belong to the reasoning faculty of his mind or not?

Again, if a name signifies many things, but he does not understand, nor fancy (that it does), how does this disputation not pertain to the reason? or how must we interrogate, unless by granting a distinction, whether any one may inquire if it is possible for him who is silent to speak or not, or whether it partly is not, and partly is, possible? If then, some one should grant that it is by no means possible, but another should contend that it is, will not the disputation be against the reasoning faculty? though the dispute seems to belong to those which are from name; there is not then a certain genus of arguments, which belong to the reason. Nevertheless, some pertain to name, yet not all are such, not (I say) those which are elenchi, but not the apparent elenchi, for there are apparent elenchi, which are not from diction, for instance, those which are from accident, and others.

Notwithstanding, if some one thinks fit to claim a division, I mean that the silent speaks, partly in this and partly in that manner; yet to demand this, is, in the first place, absurd, (for sometimes what is interrogated does not seem to subsist multifariously, and it is impossible to divide that which a man does not conceive). Next, what else will to teach be? for it will render the manner in which a thing subsists evident to him who neither considered, nor knew, nor supposed that it is predicated in another way. Since what prevents this also being done in things which are not double? are then unities equal to duals in four? but the duals are inherent, some in this, but others in that way. Is there also one science of contraries or not? but some contraries are known, others unknown: so that he appears to be ignorant, who requires this, viz. that to teach is different from to discuss, and that it is necessary that the teacher should not interrogate, but himself declare, but that the other should interrogate.

 
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Moreover, to postulate affirmation or denial is not the province of one who demonstrates, but of him who makes a trial, for the peirastic art is a certain dialectic, and considers not the scientific, but him who is ignorant, and who pretends. Whoever therefore considers things which are common really, is a dialectician, but he who does this apparently, is a sophist; the contentious and sophistical syllogism also are, one indeed, apparently syllogistic about things with which the peirastic dialectic is conversant, although the conclusion be true, for it deceives in assigning the why, and (in the other kind are those paralogisms), which not being according to the method of each thing, seem to be according to art. For false descriptions are not contentious, (since paralogisms are according to those things which are subject to art,) neither even if there is a certain false description about the true (conclusion), as that of Hippocrates, viz. the quadrature of the circle through lunulæ, but as Bryso squared the circle, though the circle should be squared, yet, because it is not according to the thing, it is on this account sophistical. Wherefore both the apparent syllogism about these things, is a contentious argument, and the syllogism which seems to be according to the thing, even if it be a syllogism, is a contentious argument, for it appears to be according to the thing, wherefore it is deceptive and unjust. For as injustice, in contest, has a certain form (of justice), and is a certain unjust combat, so in contradiction the contentious is an unjust combat, for both there, those who make conquest entirely the object of their preference, try all things, and here, the contentious do. Those therefore who are such, for the sake of victory itself, seem to be contentious men and lovers of strife; but those who are so for the sake of the glory which tends to gain, are sophists, for the sophistical art, as we said, is a certain art of making money from apparent wisdom, wherefore they desire an apparent demonstration. Those who love strife also, and sophists, employ the same arguments, yet not for the sake of the same things, and the same argument will be both sophistical and contentious, yet not according to the same, but so far as it is for the sake of apparent victory, it is contentious, and so far as it is for (apparent) wisdom, it is sophistical, for the sophistical art is a certain apparent, but not real wisdom. The contentious man however is in a certain respect disposed with reference to the dialectician, as the false describer is to the geometrician, for (the one) paralogizes from the same things with dialectic, and the false describer (subsists in the same way with regard to) the geometrician. Still he is not contentious, because he describes falsely from principles and conclusions which are subject to art, but it will be evident that he who is subject to dialectic, is about other things contentious, as the quadrature of the circle through lunulæ is not contentious, but (the quadrature) of Bryso is contentious, and it is impossible to refer the one except to geometry alone from its being from the proper principles, but (we may refer) the other to many who do not know what is possible and impossible in each thing, for it will accord. Or as Antipho squared the circle, or if a man should not grant it is better to walk after supper on account of the argument of Zeno, it is not medical, for it is common. If then, the contentious person subsists altogether with reference to the dialectician, as he who makes a false description does to the geometrician, there would not be a contentions syllogism about those; now however the dialectician is not in any definite genus, nor does he demonstrate any thing, nor is he such as the universal (philosopher). For neither are all things in one certain genus, nor if they were, is it possible that beings should be under the same principles, so that none of those arts which demonstrate a certain nature is interrogative, for it is not possible to grant each of the parts, for a syllogism does not arise from both. Dialectic however is interrogative, but if it should demonstrate, though not all things, yet it would not interrogate primary things and proper principles; for there being no concession, he would no longer have arguments from which he could discourse against the objection. It is also peirastic, for neither is the peirastic art such as geometry, but even an unscientific man may possess it, since it is possible that he who is ignorant of a thing may make trial of one who is ignorant, if he concedes not from what he knows, nor from properties, but from consequents, which are such as there is nothing to prevent him who knows them, not knowing the art, but it is necessary that he who does not know them, must be ignorant (of the art). Wherefore, it is evident that the peirastic art is the science of nothing definite; hence also, it is conversant with all things, since all arts use certain common things, on which account all men, even idiots, use after a certain manner, the dialectic and peirastic, for all up to a certain point endeavour to form a judgment of such as announce any thing. These however are common, for they know these no less, though they appear to speak very foreign from the purpose. All men therefore confute, for without art they partake of this with which dialectic is artistically conversant, and he is a dialectician who is peirastic in the syllogistic art. Nevertheless, since these are many, and are about all things, yet are not of such a kind as to be in a certain nature and genus, but as negations, other things again are not such, but are properties, it is possible from these to make a trial about all, and that there should be a certain art, and that it should not be such as those are which demonstrate. Wherefore, the contentious person is not one who in all respects thus subsists, as the maker of a false description, for the contentious person will not be paralogistic from a certain definite genus of principles, but will be about every genus.

Such then are the modes of sophistical elenchi, but it is not difficult to perceive that it is the province of the dialectician to investigate these, and to be able to effect them, for the method about propositions comprehends the whole of this theory.

 
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We have treated of the apparent elenchi, but with regard to showing that something is falsely serted, and bringing an argument to something contrary to opinion, (for this was the second object of sophistical preference,) in the first place, this generally happens from a certain manner of inquiry, and through interrogation. For to make an interrogation to nothing definitely laid down, is adapted to the investigation of these things; since those who speak casually commit a greater fault, and they speak casually who have nothing proposed. Both to ask many questions, even if that should be defined against which a discussion is made, and to require a person to assert what appears, produces a certain abundance of argument, so as to lead to what is contrary to opinion, or false; and whether being questioned, he asserts or denies some one of these things, to lead him to those particulars against which an abundance of argument is supplied. They are able however, to injure by these means, less now, than formerly, for they ask what this has to do with the original proposition; still the element of obtaining something false or contrary to opinion, is to question no thesis immediately, but to assert that the question is made from the desire of learning; for this consideration makes a place for argument.

In order to show a false assertion, a proper sophistical place is to bring (the opponent) to those things against which there is an abundance of arguments; but we may do this both well and badly, as was observed before.

Again, to state paradoxes, observe from what genus the disputant is, then ask what that is which such men assert to be contrary to the common opinion, for to each (sect) there is something of this kind. The element however of these is to assume the thesis of the several (sects) in the propositions, but an appropriate solution of these, is adduced to show that what is contrary to opinion does not happen through the argument, and this is always the wish of him who contends.

Moreover, from volitions and apparent nions, since they do not desire and say the same thing, but employ the most seemly words, and desire things which appear profitable; for instance, they say, it is necessary to die well, rather than to live pleasantly, and to he justly poor, than to be basely rich; but they desire the contrary. He therefore who speaks according to volitions, must be brought to apparent opinions, but he who speaks according to these, must be brought to concealed (volitions), for it is necessary in both ways to speak paradoxes, since either they assert what is contrary to apparent or to unapparent opinions.

The place indeed of causing the assertion of paradoxes is very extensive, as Callicles in the Gorgias is introduced, saying, (which also all the ancients consider to happen,) from what was according to nature, and according to law; for they say nature, and law, are contraries, and that justice according to law, is excellent, but according to nature, it is not excellent. Wherefore we must oppose him according to law who speaks according to nature, but lead him to nature who speaks according to law, for to say that it exists in either of these two ways, is paradoxical. But according to them, that which is after nature is true, but what is according to law is that which appears to the multitude; wherefore it is evident that they, as the disputants, now endeavoured either to confute the respondent, or to make him assert paradoxes.

Some questions, indeed, have on both sides an answer contrary to opinion, as whether is it right to obey the wise or a father, and ought we to do things advantageous or just, and is to be injured more eligible than to injure? We ought, however, to lead to conclusions which are opposed to the multitude and the wise, if, indeed, some one speaks as those who are conversant with disputations, we ought to bring him to conclusions contrary to the multitude; but if he speaks as the multitude, (to conclusions contrary) to those who are conversant with disputations. For the one, indeed, say that the happy man is necessarily just, but it seems contrary to the opinion of the many, that a king should not be happy; thus to collect things contrary to opinion, is the same with leading to what is contrary to nature and law, for law is the opinion of the many, but the wise speak after nature and after truth.

 
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Paradoxes, indeed, we must investigate from these places, but with regard to making a man trifle, what we mean by trifling we have already declared, but all such arguments will produce this, if it is of no consequence whether a name or a sentence is stated, but the double and the double and the half are the same, if then, the double is the double of the half, it will be the double of the half of the half. Again, also, if instead of double, we lay down the double of the half, it will be thrice said, the double of the half of the half of the half. And is desire then the desire of the pleasant? but this is the appetite of the pleasant, wherefore desire is the appetite of the pleasant of the pleasant.

All such arguments, then, are among the ber of relatives, where not only their genera, but also the things themselves are predicated with reference to something, and are referred to one and the same thing; thus appetite is the appetite of something, and desire the desire of something, the double also is the double of something, and the double of the half. Those also whose essence is not really amongst relatives, but in short, of which there are habits or passions, or some such thing manifested in their definition which are predicated of these. Thus, the odd is a number having a middle, but there is an odd number, wherefore there is a number number having a middle, and if τὸ σιμον is a concavity of nose, but there is a concave nose, there is then nose nose concave.

They seem to produce (trifling) sometimes which really do not produce it, because the inquiry is not added, whether the double enunciated by itself signifies something or nothing, and if it signifies any thing whether it signifies the same, or something else, but the conclusion is immediately adduced; yet from the name being the same, there seems to be the same thing and the same signification.

 
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Solecism is what we have declared before; sometimes, however, it is possible to produce this, and not producing to seem to do so, and producing it, not to appear to, as Protagoras said, if μὴνις and πήληξ, are of the masculine gender: for he who says οὐλόμενην, commits a solecism according to him, but to others does not seem to, but he who says ὀυλόμενον, seems to solecize but does not. Hence it is clear that a certain art can produce this; wherefore many arguments which do not infer a solecism, seem to infer it as in the elenchi.

Almost all apparent solecisms, indeed, are from hoc, and when the case signifies neither male nor female, but what is between, for hic signifies the masculine, hæc the feminine, and hoc, indeed, ought to signify what is between, but frequently signifies either of these, as, for instance; "What is this?" "Calliope," "wood," "Coriscus." All the cases then of the masculine and feminine differ, but of what is between, some do, and others do not; frequently, therefore, when "hoc" is given, they syllogize as if "hunc" were said, and in like manner take one case for another. Now a paralogism is produced, because "hoc" is common to many cases, for "hoc" at one time signifies "hic," and at another time "hunc;" it is requisite, however, that it should signify alternately with the verb "est," "hic," but with "esse," "hunc," for instance, "est Coriscus," "esse Coriscum." Also in like manner with feminine nouns, and with those which are called σκεύη, (furniture,) but which have a feminine or masculine inflection, for whatever end in ο and ν, have alone the inflection of σκεύη as ξύλον, wood, σχοινίον, a rope, but those which are not thus, (have the inflexion) of the masculine or feminine, some of which we refer to σκεύη, as ἀσκὸς, a bladder, is a masculine noun, but κλίνη, a bed, is feminine; wherefore, likewise, in such things also, "est" and "esse" will produce a difference. In a certain respect too, a solecism is similar to those so called elenchi, from things not similar being similarly assumed, for as in them in things, so in these a solecism is committed in words, for "man" and "white" are both things and words.

It is evident, then, that we must endeavour to infer a solecism from the cases enumerated.

Such, then, are the species of contentious arguments, and the parts of the species and the modes which have been stated; still it makes no slight difference to concealment, if things which belong to interrogation, are arranged in a certain manner, as in the case of dialectics, hence, after the above-mentioned particulars, these must be first discussed.

 
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One thing which contributes to confutation by an elenchus is prolixity, for it is difficult to consider many things at once, and for prolixity we must employ the above-named elements. Another thing is rapidity, for those who are slow, perceive less; anger also, and contention, for all men who are disturbed, have less power of observation. The elements, however, of anger, are for a man to render himself obviously willing to commit injustice, and to conduct himself with thorough impudence. Moreover to arrange the questions alternately, whether a man has many arguments for the same thing, or (to show) that they subsist in one way, and not in another, for at the same time it happens that (the opponent) will guard against many things or such as are contrary. In short, all the things enumerated before as contributing to concealment, are useful also for contentious arguments; for concealment is for the sake of escaping notice, and escaping notice for the sake of deception.

Against those indeed who deny whatever they think contributes to the argument, an interrogation must be made from negation, as if he (the querist) wished the contrary, or by making the interrogation equally; for it not being evident what (the interrogator) wishes to assume, (the respondents) are less indignant. When, too, any one admits the several particulars partially, by making an induction of the universal, frequently an interrogation must not be made, but we must use it as granted, for sometimes they (the respondents) think they have admitted, and appear to the auditors from making mention of induction, as if the particulars had not been questioned in vain; and in those wherein the universal is not signified by name, we must yet use similitude, as may be expedient, for similitude frequently escapes notice. In order also to assume a proposition, we ought to make the inquiry by a comparison of the contrary; as if it should be necessary to assume, that it is right in all things to obey a father, (we must ask) whether it is necessary to obey parents in all things, or to disobey them in all? and, (if it is answered that we ought) frequently (to obey them, we must ask) whether many things are to be conceded to them, or a few? for if it is necessary (to obey them), many things will seem to be conceded, for when contraries are placed by each other, they appear to men to be greater, and great, and worse, and better.

The sophistical false accusation indeed of those who question, when not syllogistically concluding any thing, they do not question the extreme, but conclusively say, as if a syllogism had been made, "it is not so and so;" this very much and frequently causes a person to appear confuted by an elenchus.

It is also sophistical, when a paradox is laid down, to demand that what is apparent should be answered, that being proposed which seemed true from the beginning, and to question things thus, "Whether does it seem so to you?" for it is necessary if the question be of those things from which a syllogism is formed, that there should be either an elenchus or a paradox; if he grants, an elenchus, but if he neither concedes nor says that it seems to him to be true, something contrary to opinion, and if he does not concede, but acknowledges it seems true to him, a form of elenchus.

Moreover, as in rhetorical, so also in elenchtic disputation, we must investigate contrarieties in a similar manner, either (such as are contrary) to what is said by him, or to what he acknowledges well said or done, or to those that seem to be such, or to similars, or to most, or to all. And as also respondents frequently, when they are confuted, assert that what they seem to be confuted in has a two-fold meaning; so questionists must use this mode against objectors, so that if it happens in one way, but not in another, (they say) they admit it only thus, as Cleophon does in his Mandrobulus. It is also necessary, by withdrawing from the argument, to cut off the remaining parts of the attacks, and for the respondent, if he foresees, to anticipate in objection and speaking. Sometimes also, we must attack something different to the assertion, assuming that, if a person has it not in his power to attack the position; which Lycophron did, when the thing proposed was an encomium on the lyre. Against those indeed who require arguments to be advanced against a certain thing, (since it seems necessary to assign a cause, but certain things being mentioned, more caution can be used,) it must be said that it universally happens in elenchi, that we assert contradiction, because we deny what the arguer asserted, but what he denied we assert; but (we must not say that we begin to prove one part of the contradiction); for instance, that there is the same science of contraries, or that there is not the same. But it is not proper to question the conclusion after the manner of a proposition, since some things are not to be questioned, but to be employed as if acknowledged.

 
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From what places then questions are, and how we must make them in contentious exercises, has been shown; but concerning reply, and how it is proper to solve, and what, and for what use such arguments are profitable, must be stated in the next place.

They are useful then to philosophy for two causes; first, indeed, as being for the most part from diction, they enable us to know in a better manner, in how many ways each thing is predicated, and what kind happen similarly, and what differently, both in things and in names. Secondly, (they contribute) to inquiries by oneself, for he who is easily deceived by a paralogism by another, and does not perceive this, may also himself frequently experience the same thing from himself. Thirdly, in the remaining place, (they tend) still more to fame from appearing to be exercised about all things, and not to be unskilful in any thing; for that he who engages in disputation should blame the arguments (of another), without being able to distinguish any thing about their badness, produces a suspicion of apparent indignation, not on account of the truth, but on account of unskilfulness.

How therefore respondents should oppose such arguments is evident, since we have before rightly shown from what, paralogisms arise, and have sufficiently exposed impostures in interrogation. It is not the same thing however assuming an argument to see and to solve its futility, and to be able quickly to oppose an interrogator, for what we know we are often ignorant of, when it is transposed. Moreover, as in other things, the quicker and the slower increase by exercise, so is it also with arguments; hence, if a thing is evident to us, but we have not meditated upon it, we are frequently deficient in it on certain occasions. Sometimes indeed it happens as in diagrams, for having analyzed them, we sometimes are unable to reconstruct them; thus also in elenchi, knowing the cause of the connexion of the argument, we are unable to dissolve the argument.

 
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First then, as we say, we ought sometimes to prefer to syllogize probably, rather than truly, thus also we must solve sometimes rather probably than according to truth, for in short, we must contend with contentious men, not as if they were confuting, but as appearing to do so, since we do not say that they conclude syllogistically, so that we must direct ourselves to their not appearing. For if an elenchus is a contradiction not equivocal, from certain (assumptions), there will be no necessity of distinguishing against things ambiguous and equivocation, for he does not make a syllogism. Still we must make a division, for no other reason than because the conclusion appears to have the form of elenchus. Wherefore we must be cautious not of being confuted, but of seeming to be so, since ambiguous interrogations and those which are from equivocation, and other such deceptions, both obscure the true elenchus, and render it dubious whether a person is confuted by an elenchus or not. For since it is possible at the end, when a conclusion is made (for the respondent) to say that that he has denied, (viz. the interrogator) not what the respondent affirmed, but equivocally, even if he happens especially to tend to the same point, it is doubtful whether he is confuted by an elenchus, for it is dubious whether he now asserts the truth. If on the otber hand, dividing, he questions the equivocal or the ambiguous, the elenchus will not be obscure, and what the contentious less require now than formerly, viz. that the person questioned should answer yes or no, should occur. Nevertheless, now because querists do not question well, it is necessary that the person questioned should add something to his answer, correcting the faultiness of the proposition, since if he, the querist, disanguishes sufficiently, the respondent must necessarily say yes or no.

If, indeed, any one should suppose that to be an elenchus, which is according to equivocation, it will be impossible for the respondent in any way to avoid confutation by an elenchus, for in visible things it is necessary to deny the name which he affirms, and to affirm what he denied. For as some correct there is no benefit, for they say that Coriscus is not musical and unmusical, but that this Coriscus is musical, and that unmusical, since that Coriscus is, will be the same sentence with that this Coriscus is unmusical or musical, which he at one and the same time affirms and denies. Yet perhaps they do not signify the same thing, for neither does the name there, so that there is some difference, if, however, he assigns to the one to mean simply Coriscus, but adds to the other a certain one or this one, it is absurd, for it will not be more in one than in the other, as it is of no consequence to which it is attributed.

Nevertheless, since it is dubious whether he who does not distinguish the ambiguity, is confuted by an elenchus or not, but is allowed in disputations to make a distinction, it is evident that he who does not distinguish, but simply grants the interrogation, errs, wherefore, if not the man himself, yet his argument, resembles a confuted elenchus. It frequently happens, however, that they who see the ambiguity, are unwilling to distinguish from the frequency of those who propose things of this kind, that they may not seem to be morose in every thing, and next, not thinking that the argument depends on this, a person frequently meets with a paradox, wherefore since distinction is allowable, it must not be delayed as we said before.

Unless, indeed, a person makes two interrogations be one, there will not be a paralogism from equivocation and ambiguity, but either an elenchus or not. For what difference is there in asking whether Callias and Themistocles are musicians, or whether to both, being different men, there is one common name? for if that signify more than one, he (who uses it) will ask many things. If, then, it is not right to require that we assume simply, one answer to two questions, it is evidently not becoming to answer simply, any thing equivocal, not even if, as some require, it be true in all; for this is just the same as if it were asked, whether Coriscus and Callias are at home or not? whether both are present or not present? since in both ways the propositions are many. For it does not follow if the assertion is true, that there is on this account our question, since there may be ten thousand different questions asked, to all of which it may be true to answer yes or no, yet nevertheless, one answer must not be given, for disputation would be subverted, and this is the same as if the same name, should be assigned to different things. If, then, it is not right to give one answer to two questions, it is evident that we must not answer yes or no in things equivocal, since neither does he who says this, answer, but speak, (merely,) and this is claimed in a certain respect amongst those who dispute, because the result is concealed.

As, therefore, we said since neither are certain things, elenchi really, which seem to be so, in the same manner also, certain will seem to be solutions which are not, but which we say that sometimes it is necessary to adduce rather than the true, in contentious arguments and in opposition to (a paralogism from) duplicity. Likewise, we must answer things which seem to be (true) by saying, "be it so," for thus, least of all, would there be a parexelenchus, but if a person should be compelled to assert some paradox, there "to seem," must especially be added, for thus, there will appear to be neither an elenchus nor a paradox. Since, however, it is clear how the original proposition is made a postulate, and men think altogether (that it is made so), if it be near (the question) we must subvert and not grant certain things, as if the interrogator made a petitio principii, and when any one requires such a thing to be granted which necessarily, indeed, results from the thesis, but is false or contrary to opinion, it must be said to be the same (as the question), for things consequent from necessity appear to be parts of the thesis itself. Moreover, when universal is assumed not in name but by comparison, it must be said that he (the opponent) assumes it, not as it was given, nor as he proposed it, for from this an elenchus frequently arises.

He however who is excluded from these, must have recourse to (asserting) that the thing is not well demonstrated, objecting according to the definition stated.

In names then, which are properly so called, it is necessary to answer either simply or by distinction. As to, however, those things which we admit, secretly perceiving them, for instance, whatever are not clearly interrogated, but with diminution, from this an elenchus happens, as, for instance, "Is what belongs to the Athenians, the possession of the Athenians?" "Yes." In like manner, as to other things, "Does not man also belong to animals?" "Yes." Man therefore is the possession of animals. For we say that man is of animals, because he is an animal, and Lysander is of the Lacedæmonians, because he is a Lacedaeæmonian; wherefore it is clear that where the proposition is obscure, we must not make a simple concession.

But when of two existents, the one existing, the other also appears of necessity to exist, but this existing, that does not from necessity; he who is asked which of the two (he thinks exists) ought to give that which is less (widely extended), for it is harder to syllogize from many things. Yet if some one should argue that there is something contrary to the one, but not to the other, even if the assertion be true, we must say that the contrary (of the other, is), but that the name of the other, is not laid down.

Nevertheless, since some of the things which the multitude assert, are such that he who does not admit them, they would say, answered falsely, but others are not such; as those of which there are contrary opinions, (for whether the soul of animals, is corruptible or incorruptible, is not determined by the multitude,) in which then it is doubtful how it is usual to enunciate what is proposed, (so that it may be asked) whether (it appears to the respondent) as sentences, for they call both true opinions and universal enunciations sentences, as that the diameter of a square is incommensurate with its side. Besides, of which there is a two-fold opinion as to truth, in these, by transferring the names, a person would especially escape detection, for from its being doubtful in what way the truth subsists, he will not appear sophistically to cavil, and from there, being opinions on both sides, he will not seem to answer falsely, for the transition will render his answer incapable of confutation by an elenchus.

Further, those interrogations which a person foresees, must be previously objected to and declared, for thus especially he will impede the inquirer.

 
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Since however a right solution is the detection of a false syllogism, (showing) by what interrogation the falsity occurs; but a syllogism is called false in two ways, (either if it is falsely concluded, or if not being a syllogism, it seems to be one,) what is now said to be a solution will be a correction of an apparent syllogism, (showing) from what interrogation it is apparent. Hence, it happens that those arguments which conclude by syllogism, are solved by negation, but apparent ones by distinction. Again, since some of the arguments syllogistically concluded are true, but others have a false conclusion; those which are false, according to the conclusion, we may solve in two ways, by taking away some one of the interrogations, and by showing that the conclusion does not thus subsist; but those (which are false), according to the propositions, by taking away some (interrogation) only, for the conclusion is true. So that they who desire to solve an argument, should first consider if it is conclusive or inconclusive; next, whether the conclusion is true or false, that we may solve it either by division or subversion, and subverting it either in this or that way, as was observed before. Still, it makes a great difference whether a person, being interrogated or not, solves the argument, since to foresee is difficult, but to consider at leisure is easy.
 
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Of elenchi which are from equivocation and ambiguity, some have an interrogation signifying many things, but others a conclusion multifariously stated; for instance in the case, that he who is silent speaks, the conclusion is two-fold, but in this, that he who knows, at the same time does not know, one interrogation is ambiguous, and what is two-fold is at one time (true), and at another not, for the two-fold signifies that which is, and that which is not.

In those assertions, therefore, in the conclusion of which there is the multifarious, except (the opponent) assumes contradiction, there is not an elenchus, as in this, that the blind man sees, for without contradiction there was not an elenchus; but in those in the interrogations, of which (there is the multifarious), it is not necessary previously to deny what is two-fold, for the argument does not subsist with reference to this, but on account of this. In the beginning, then, since both the name and the sentence are two-fold, we must answer thus, that it partly is, and partly is not, as that the silent speaks is partly true, and partly not. And that τὰ δέοντα should be done, is true of some things, but not of others, for τὰ δέοντα are predicated multifariously. Still if it be latent, at the end we must correct the interrogation by an addition; "Is it then true, σιγῶντα λέγειν?" "No, but τόνδε σιγῶντα." In those, also, which have the multifarious in the propositions, (we must act) in like manner; "Do they not at the same time then, know what they know?" Yes, but not those who thus know, for it is not the same thing that (those who know), at one and the same time know, and that those who thus know, cannot (at one and the same time know). In short, (the respondent) must contend even if the adversary simply concludes, and (he must assert) that he denied not the thing affirmed by him, but the name, so that it is not an elenchus.

 
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It is evident how these arguments which are from division and composition must be solved, for if a divided and a composite sentence have a different signification, that must be stated which is contrary to the conclusion. Now all such arguments are from composition or division. "Did he strike him with that, with which you saw him striking?" and "with what he struck, with that, did you see him striking?" have something of ambiguous interrogations, but nevertheless it is from composition. For what is assumed from division is not two-fold, because there does not arise the same sentence when divided, unless also ὄροσ, and ὄροσ pronounced with the accent, signify a different thing; but in writings the name is the same, since it is written from the same elements, and after the same manner, and there indeed the marks are the same, but the things pronounced are different. Hence what is assumed from division is not two-fold, and it is likewise clear that not all elenchi are from the two-fold, as some say.

The respondent therefore must make a distinction, for it is not the same thing for a man to say, that he saw some one striking with his eyes, and that with his eyes he saw some one striking, and the argument of Euthydemus (belongs to this). "Have you now, being in Sicily, seen the triremes which are in the Piraeus?" and again, "Can a man being good, be a bad shoemaker?" but some one being a good shoemaker, may be bad, so that there will be a bad shoemaker. (Again,) "Are those exercises worthy, of which the sciences are worthy?" but the exercise of a bad man is worthy; wherefore, what is bad, is a worthy exercise, but what is bad is both an exercise and that which is bad, so that what is bad, is a bad exercise. "Is it true to say now that you are born? you are therefore born now." Or does this (sentence) signify another thing when divided, for it is now true to say that you are born, but not that you are now born. As to the manner in which you are able, and the things which you are able to do, will you do these things, and in this manner? but when not playing on the harp, you have the power of playing, wherefore, you would play when not playing; or may we not say that he has the power of playing on the harp, when he does not play, but when he does not do it, of doing it?

Some indeed solve this (sophism) in another way, for if (the respondent) grants that be is able to do so, they say it does not happen that he who does not play plays, for he does not grant that he does it in whatever way it is possible, nor is it the same thing to say as it is possible, and in whatever way it is possible to do it. Still, it is evident that they do not solve it well, for of arguments from the same (place) there is the same solution, but this will not suit all, nor questions in every way, but is (adapted) to the interrogator, not to the argument.

 
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Arguments indeed are not derived from accent, neither in writings nor sentences pronounced, unless there may be a few, such as this argument, "Is τὸ οὗ καταλύεις a house?" yes! "Is not τὸ οὑ καταλύεις the negation τοῦ καταλύεις? yes! "But you said that τὸ οὗ καταλύεις was a house, therefore a house is a negation." How therefore the solution must be made, is clear, for "ου" does not signify the same thing, when pronounced more acutely, and when more gravely.
 
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Moreover, it is evident how we must oppose arguments derived from things asserted after the same manner, which are not the same, since we have the genera of the categories; for the one indeed grants when interrogated, that it is not any of those things which signify essence, but the other shows that it is one of the number of relatives or quantities, and seems to signify essence on account of the diction, for instance, in this argument. Is it possible to do, and to have done, the same thing at the same time? No. But it is possible to see, and at the same time to have seen, the same thing, and according to the same. Is it possible for any thing which suffers, to act? No. But "it is cut," "it is burned," "it is perceived," are enunciated similarly, and all signify to suffer something; again, "to speak," "to run," "to see" are enunciated similarly with each other, but "to see" is to perceive something, so that it is to suifer, and to act something, at one and the same time. Still, if any one having there granted that it is impossible to do and to have done the same thing at the same time, should say that it is possible to see and to have seen, he is not yet confuted, if he should not say that "to see" is to do something, but to suffer, for there is no need of this interrogation, but he is supposed by the hearer to have granted this, when he granted that "to cut" is to do, and "to cut" is to have done something, and whatever other things are similarly asserted. For the auditor himself supplies the rest as asserted in a similar manner, but this is not similarly asserted, but seems to be so from the diction. The same thing indeed happens, as in equivocations, for in them, he who is ignorant of words, thinks that (the opponent) denies the thing which (the respondent affirms), and not the name (only), though there is still need of an interrogation, whether regarding one thing he asserts the equivocal, for this being granted there will be an elenchus.

The following arguments also are like these: Whether has some one lost that, which once having, he afterwards has not? for he who has lost one die will not have ten dice, or may we not say that he has lost what he has not (now), but which he had before; but that it is not necessary that he who had not so much, or so many things, should have lost so many. Asking then, what he has, in the conclusion he introduces so many, for ten things are so many; if then, it had been asked at first, has he who has not so many things as he formerly had, lost so many, no one would admit it, but either that he had lost so many, or some one of these. Also (the deception is similar), that some one may give what he has not, for he has not one die only, or does he not give that which he has not, but as to the manner in which he had it not, viz. one, for the word "only," does not signify this particular thing, nor such a quality, nor quantity, but how it subsists with relation to something, (i. e.) that it is not with another. It is therefore as if some one asked, can any one give what he has not, and if a person denied it, should ask whether any one can give rapidly, when he does not possess rapidly, and this being agreed to, should conclude that a man may give what he has not. It is also manifest that it is not syllogistically considered, (for to give) rapidly is not to give this thing, but in this way, and a person may give in a manner different from that in which he possesses, for possessing it gladly, he may give it painfully.

Similar also are all the following: Can any one strike with that hand which he has not? or see with the eye which he has not, for he has not one alone. Some indeed solve this by saying, that he has one alone, whether it be an eye or any thing else, who has more than one, but others that he has received what he has, for he gave one die alone, and this man has, they say, one die alone from this man. Others, again, immediately subverting the question, (say) that it is possible to have what he has not received, as if having received sweet wine, when it is corrupted in the receiving of it, a man should have sour wine; still, as we have observed before, all these solve, not with reference to the argument, but to the man. For if this were the solution, he who gave the opposite would not be able to solve it, as in other cases; thus, if the solution is, that it partly is, but partly is not, if it be simply granted, there is a conclusion, but if there is not a conclusion, there cannot be a solution; but in the before-named, all things being granted, we do not admit that there is a syllogism.

Further, of such arguments are the following: Has some one written what is written? But it is written that you now sit, which is a false statement, yet it was true when it was written, wherefore at one and the same time, there was written a false and a true assertion. To declare, however, an assertion or opinion false or true, signifies, not this particular thing, but this quality, for the reasoning also is the same in opinion. Again, as to what a learner learns, is it that which he learns? but some one learns quickly what is slow, therefore he does not say what some one learns, but how he learns. Again, what a person walks through does he tread on? But he walks through the whole day, it is not said that which he walks upon, but when he walks; nor when (we say) he drinks a cup (do we show) what, but from what, he drinks. Also with regard to what a person knows, does he know it by learning or discovery? but of those, one of which he discovers and the other he learns, (with these,) when both are (assumed), neither (accords): or is it that here "every thing" is assumed, but there not "every." Also, (we may add the deception,) that there is a certain third man besides man himself, and individuals, for man and every common thing, is not this particular thing, but signifies a certain "quale" or relative, or in some way, or something of this kind. Likewise, also, in the question, whether Coriscus and Coriscus the musician, are the same or different question, for the former signifies this particular thing, but the other a thing of a certain quality, so that we cannot set out this; nor does the exposition make a third man, but the concession, (that what is common) is that very thing which is this particular thing, for (thus) to be this particular thing, is not that which Callias is, and which man is. Neither will it signify, if some one should say that what is set out, is not what this particular thing is, but what is a thing of a certain quality, for besides the many, there will be one certain thing, for instance man. We must evidently therefore, not grant that what is predicated in common of many, is this particular thing, but that it signifies either quality, or relation, or quantity, or something of the kind.

 
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In short, of disputations from diction, the solution will always be according to the opposite of that from which the argument is derived, thus if the argument is from composition, the solution will be through division, but if from division, it will be through composition. Again, if (the argument) is from acute accent, the grave accent will be the solution, but if from the grave, an acute (will be). If, however, from equivocation, it is possible to solve by adducing the opposite name, thus if it happens that we can say a thing is animated, by denying that it is not animated, we can show that it is animated, but if (the respondent) says it is inanimate, but (the arguer) concludes it is animated, we must say that it is inanimate. In the same way with ambiguity, but if (the argument is derived) from similitude of diction, the opposite will be the solution, as, "Can any one give what he has not?" or not what he has not, but in the way in which he has not; for instance, one die alone. What any one knows, does he know by learning or discovery, and yet not the things which he knows, and does he tread on what he walks through, but not when, and so of the other (deceptions).
 
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With respect to those which are from accident, there is one and the same solution for all of them, for since it is uncertain when an assertion can be made of a thing present from accident, and in some things this appears and is conceded, but in others, men deny that it is necessary, it must be said as being similarly adapted to all, that (the conclusion) is not necessary. Nevertheless, it is necessary to produce something similar. All such arguments however as these are from accident. Do you know what I am about to ask you? Do you know him who approaches, or him who is covered? Is this statue your work; or is the dog your father? Are not a few things, assumed a few times, few? For it is evident in all these, that it is not necessary that what is verified of accident, should also be verified of the thing, for in things alone which according to essence are without difference and one, all things appear to be inherent as the same, since to what is good, it is not the same thing to be good, and to be that which is intended to be asked, neither to him who approaches or who is covered, is it the same thing to be one approaching, and (to be) Coriscus, so that it does not follow, if I know Coriscus, but do not know the person approaching, that I know, and am ignorant of, the same person, neither if this is a work and is mine, is it my work, but either (my) possession, or thing, or something else; the other deceptions also (we must solve) after the same manner.

Some however solve them by distinguishing the question, for they say that it is possible to know, and not to know the same thing, yet not according to the same; therefore not knowing him who approaches, but knowing Coriscus, they say they know indeed, and are ignorant of the same thing, but not according to the same. But in the first place, as we have already said, it is necessary that there should be the same correction of arguments (derived) from the same (place), but this will not be (the solution) if some one does not assume the same axiom from "to know," but from "to be," or "to subsist after a certain manner;" as if this (dog) is a father, and is yours, (therefore it is your father,) for though this is true in certain instances, and it is possible to know, and to be ignorant of, the same thing, yet here what is said, is by no means appropriate. Still there is nothing to prevent the same argument having many faults, yet not the exposition of every fault is a solution, for it is possible that some one may show that to be false, which is syllogistically concluded, but may not show whence it is false; as that argument of Zeno, that nothing can be moved. Wherefore, if some (respondent) should endeavour to lead to the impossible, he errs, though it should be concluded ten thousand times, since this is not a solution, for the solution was the display of a false syllogism, (showing) whence it is false, if then (the opponent) concludes nothing, whether he endeavours to collect the true or the false, the manifestation of that thing is a solution. Perhaps indeed, nothing prevents this occurring in certain cases, except that in these, this cannot appear, for he knows that Coriscus is Coriscus, and that he who approaches is he who approaches. It seems indeed to be possible to know, and not to know the same thing, for instance, to know that a thing is white, but not to know that it is musical, for thus a man knows and does not know the same thing, yet not according to the same, but here he knows what approaches, and Coriscus, and Coriscus (to be) that which approaches, and (to be) Coriscus.

Likewise, also they err, who solve (by stating) that every number is few, as those whom we mentioned, for if nothing being concluded, leaving out this, they say that they have concluded the true, for that every number is both much and few, they err.

Some also solve these syllogisms by duplicity, as that it is your father, or son, or servant; yet it is evident that if the elenchus appears to be assumed from the multifarious, it is necessary that the name or the sentence should properly be of many, but that this person is the son of this man, no one asserts properly, if he is the master of a son, but the composition is from accident. Is this yours? yes! but this is a son, therefore this is your son, because it happens to be both yours and a son, yet not your son.

Also (the solution of the deception by which it is concluded), that something amongst evils is good, since prudence is the science of things evil, for to be of the number of these, (they say) is not predicated multifariously, but (as) possession, or if it should be multifariously, (for we say that man is of the number of animals, yet not their possession, and if any thing is referred to evils, as to be said to be of a certain thing, is it on this account of evils, yet this is not to be of the number of evils;) it seems then (to be assumed) from, "in a certain respect" and "simply." Perhaps, however, it is possible that something good may be of evils in a two-fold respect, yet not in this argument, but rather (in that), "Can there be a good servant of a bad (master)?" But perhaps neither thus, for it does not follow if he is good and pertains to this man, that he is the good of this man at the same time, nor when we say that man is of animals, is this predicated multifariously, since neither when we signify any thing, by removal, is this predicated multifariously, for when we say the half of a verse, we signify, Give me the Iliad, as, for instance, (Give me,) "Sing, Goddess, the anger."

 
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Those which are from this particular thing, being predicated properly, or in a certain respect, or some where, or after a manner, or with a relation to something, and not simply, we must solve by considering the conclusion with reference to contradiction, whether it is possible for any thing of this sort to occur in them. For contraries, and opposites, and affirmation, and negation, simply indeed, cannot possibly be inherent in the same thing, though nothing prevents each of these being inherent in a certain respect, or with relation to something, or after a manner, or one being inherent in a certain respect, but another simply. Wherefore, if one is (predicated) simply, but another in a certain respect, there is not yet an elenchus; but this we must investigate in the conclusion, in reference to contradiction.

Nevertheless, all such arguments are as follow: is it possible, for what is not, to be? But what is not, is something. In like manner being, will not be, for it will not be any one of beings. Is it, then, possible that the same person can at one and the same time take an oath properly, and commit a perjury? Is it possible that the same man, at one and the same time, can believe and not believe, the same person? Or are to be a certain thing, and to be (simply) not the same? But non-being, if it is a certain thing is not simply; neither if a person swears properly this, or in a certain respect, is it necessary that he swears properly; for swearing that he shall be perjured when he swears, he swears this alone in a proper manner, but he does not swear (simply) in a proper manner, nor does he believe who disbelieves, but he believes a certain thing. Similar is the argument about the same person speaking falsely and truly at the same time, but from its not being easy to perceive, whether a person assigns the word simply to the speaking truly or falsely, it (the solution) seems difficult. Still there is nothing to prevent it being false, indeed, simply, but in a certain respect, or of a certain thing, true, also certain things being true and yet not true (simply). Similarly also, in regard to the terms, "with reference to something," and "where" and "when," for all such arguments result from this. Is health or wealth a good thing? but to the foolish and to one who does not use it properly, it is not good, wherefore it is good and not good. Is to be well or to be powerful in a city a good thing? Sometimes this is not better, therefore the same thing is good or not good to the same. Or does nothing prevent what is simply good, not being good to a certain person, or good to this man, but not now, or not good here. Is that which a prudent man would not desire, an evil? But he does not desire to lose good, wherefore good is evil, for it is not the same thing, to say that good is evil, and to lose good. Likewise, also, the argument about the thief, since it does not follow if a thief is a bad thing, that to take him is also bad, therefore he (who wishes to take him) does not desire a bad, but a good thing, for to take a thief is a good thing, and disease is bad, but not to lose disease. Is the just preferable to the unjust, and the justly to the unjustly, yet to die unjustly is preferable. Is it just for every man to have his own property, yet those which some one according to his own opinion adjudges, though it be false, are the property (of that person) by law, therefore the same thing is just and unjust. Also, whether is it necessary to condemn him who speaks justly, or him who speaks unjustly? Yet it is just that the injured should state sufficiently what he has suffered, but these would be unjust things, since it does not follow if to suffer any thing unjustly is eligible, the unjustly is more eligible than the justly, but simply indeed the justly, yet nothing hinders this particular thing, though unjustly (done, being more eligible) than what is justly (done). Also, for every one to have his own is just, but to have another person's, is not just, yet nothing hinders this judgment from being just, e. g. if it be according to the opinion of the judge, since it does not follow if this thing is just or in this way, that it is simply just. Likewise, also, those which are unjust, nothing prevents its being just to relate them, since it does not follow, if it is just to relate them, necessarily that the things are just, as neither if it is beneficial to speak of them, (does it follow) they are beneficial; and the like of just things. Wherefore if things asserted are unjust, it does not follow that he who speaks unjust things prevails, for he says those things which are just to say, but simply, and unjust to bear.

 
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To those which arise from the definition of elenchus, as was before described, we must make a reply by considering the conclusion with reference to contradiction, how it will be the same thing, and according to the same, and with reference to the same, after the same manner, and in the same time. If then, an interrogation be made in the beginning, we must not acknowledge as if it were impossible for the same thing to be double and not double, but we must state that it is not possible so as that an elenchus be acknowledged to be made. All these arguments however are from such a place as this: Does he who knows each particular that it is each particular, know the thing? and the ignorant person in like manner? But some one knowing Coriscus that he is Coriscus, may be ignorant that he is a musician, so that he knows and is ignorant of the same thing. Also, is the size of four cubits greater than that of three cubits? But a size of four cubits in length may be made out of three cubits, and the greater is greater than the less, wherefore the same thing is greater and less than itself.
 
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Those from begging the (original question) and assuming it if it is manifest, must not be granted to the inquirer, not even if it be probable that he speaks the truth; but if it be latent, ignorance, from the fault of such arguments as these, must be retorted on the questionist, as not disputing (well), for an elenchus is without that (which was interrogated) from the beginning. Next, that he granted not that he (the opponent) should use it, but as being about syllogistically to prove the contrary, as in parexelenchi.
 
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Those also which prove from the consequent we must show from the argument itself. Now there is a two-fold consequence of consequents, for it is either as universal to particular, as animal to man, for it is taken for granted, if this is (joined) with that, that also is with this; or according to oppositions, for if this follows that, the opposite also follows the opposite. Hence also the argument of Melissus, for if what was begotten had a beginning, he requires it to be granted that the unbegotten had not (a beginning), wherefore, if the heaven is unbegotten, it is also infinite. Yet this is not so, for the consequence is vice versâ.
 
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In whatever syllogistically conclude from something being added, we must observe whether it being taken away, the impossible, nevertheless, results. Next, we must make this clear, and we must say that it was granted, not as seeming (true), but as adapted to the argument, but he, the arguer, uses what is nothing to the purpose.
 
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Against those which make many interrogations one, we must employ definition immediately in the beginning, for the interrogation is one to which there is one answer, so that neither many things must be affirmed or denied of one thing, nor one of many, but one of one. As indeed in the case of things equivocal, at one time (the attribute) is in both, but at another in neither, so that the interrogation not being simple, it happens that those who answer simply, suffer nothing; in like manner also, in these cases. When then many are present with one, or one with many, nothing repugnant happens to him who simply concedes, and who errs according to this error; but when it is in one, but not in the other, or many are predicated of many, and both are partly present with both, and partly not, this, again, is to be avoided. For instance, in these arguments: If one thing is good, but another evil, it is true to say that these are good and evil, and again, that they are neither good nor evil, since each is not each, wherefore the same thing is good and evil, and is neither good nor evil. Also, Is every thing the same with itself, and different from something else? but since these are not the same with others, but with themselves, and are different from themselves, the same things are different from, and the same with, themselves. Besides, if what is good becomes evil, and what is evil good, there will be two things, and of two, being unequal, each itself will be equal to itself, so that the same things will be equal and unequal to themselves.

Such arguments, then, fall into other solutions, for "both" also, and "all" signify many things, wherefore, except the name, it does not happen that the same thing is affirmed and denied, but this was not an elenchus. Still, it is clear that unless many interrogations are assumed for one, but one thing be affirmed or denied of one, there will not be an impossibility.

 
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With regard to those which lead to frequently saying the same thing, we must evidently not grant that the categories of relatives, separated by themselves, signify any thing; as the double without the double of the half, because it is manifest; for ten is (understood) in (the expression) ten minus one, and "to make" in the (expression) "not to make," in short, affirmation in negation, yet still it does not follow, if a man says that this is not white, that he should say it is white. Perhaps indeed, the double signifies nothing (alone), as neither what is in the half, or if indeed it does signify any thing, yet not the same as when conjoined. Nor does science in species (as if it is medical science) signify what is common, but that was the science of the object of science. Indeed, in those attributes through which (the subjects) are declared, we must say this, that what is signified separately, and what in a sentence are not the same. For the hollow in common, signifies the same thing in a flat nose and a crooked leg, but when added, nothing prevents (its signifying a different thing), but the one signifies (what happens) to the nose, and the other to the leg, for there it signifies a flat nose, but here a crooked leg, and it makes no difference to say a flat nose or a hollow nose. Moreover, we must not grant diction in a direct (case), for it is false, since τὸ σιμὸν is not a hollow nose, but this is an affection, as it were, of the nose, so that there is no absurdity, if a flat nose be a nose having a hollowness of nose.
 
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Concerning solecisms, indeed, whence they appear to happen we have shown before, but how we must solve them will be evident in the arguments themselves. For all these aim at constructing hoc; Is what you say truly this thing truly, but you say that something is a stone, something then is a stone. Or is to say a stone, not to say "quod" but "quem," not "hoc" but "hunc," if then some one should ask; Num quem vere dicis est hunc? he would not seem to speak conformably to the Latin language, as neither if he should say; Num quam dicis esse, est hic? but when he says wood, or whatever signifies neither the feminine nor the masculine, it makes no difference. Wherefore, a solecism does not arise, if what you say is, be "hoc," but you say that wood is, this therefore is wood: a "stone," however, and "hic," have the appellation of the masculine. If, indeed, some one should inquire is he, she? and again, what? (quid)? Is not he Coriscus? and then should say, he therefore is she, he does not syllogistically collect a solecism, not even if Coriscus signify, what she signifies; but the respondent does not grant it, and it is necessary that this should be questioned, besides. If, however, it neither is nor is granted, it is not syllogistically collected, neither in reality nor against him who is questioned, hence in like manner there also, it is necessary that a stone should signify hic, but if this neither is (assumed) nor granted, we must not admit the conclusion, nevertheless it seems to be from the dissimilar case of the noun appearing similar. Is it true to say that hæc is that which you say hanc is? but you say it is a shield, hæc then is a shield. Or is it not necessary if hæc does not signify parmam, but parma, but parmam is hanc. Neither if what you say is hunc be hic, but you say it is Cleon, therefore hic is Cleon, hic is not Cleon, for it was said, quem aio hunc esse, est hic, non hunc; for when the question is thus made it is not according to the rules of grammar. Do you know hoc? but this is a stone, you know then a stone, or does it not signify the same thing in the expression, do you know hoc? and in hoc autem est lapis? but this is a stone? but that in the former it signifies hunc and in the latter hic. Num cujus scientiam habes hoc, scis? Habes autem scientiam lapidis: scis igitur lapidis; is it not that when you say hujus, you say lapidis, but when you say hoc, lapidem? but it is granted cujus scientiam habes, te scire, non hujus, sed hoc; and therefore non lapidis, sed lapidem.

From what is stated then, it is manifest that such arguments as these do not syllogistically collect a solecism, but seem (only) to do so, also why they thus seem, and in what manner they are to be opposed.

 
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Of all arguments we must know that in some it is more easy, and in others more difficult, to perceive from what cause, and in what, they deceive the hearer, since often the one are the same with the other, for we ought to call that the same argument which is derived from the same place, and the same argument may appear to some to be derived from the diction, to others from accident, to others from another (place), because each when it is transferred is not equally evident. As then in (deceptions) from equivocation, which mode of paralogism seems to be the most usual, some are manifest to every one, (for almost all absurd sentences are from diction, for instance, Vir ferebat per scalas δίφρον; a man put δίφρος through a ladder: and ὅπου στέλλεσθε? To the sail-yard: and Utra boum ante pariet? Neutra; sed retro ambæ; again, Estne Boreas καθαρὸς? By no means, for it caused the death of a mendicant and a merchant. Is it Evarchus? No, but Apollonides; and almost all other deceptions in the same manner.) Some seem notwithstanding to escape the most experienced, a proof of which is, that they oftentimes contend about names, as whether the one and being are predicated in the same signification, or in a different one, of all things. For to some indeed, being and the one seem to signify the same thing, but others solve the argument of Zeno and Parmenides, from saying that one and being are predicated multifariously. Likewise, also with regard to those derived from accident and each of the other (places), some arguments will be easy to perceive, but others difficult, and it is not alike easy in all, to perceive in what genus they are contained, and whether it is, or is not an elenchus.

Yet the argument is acute, which reduces a person to the greatest doubt, since this is especially pungent. Now doubt is two-fold, one in arguments concluding syllogistically, with regard to which interrogation is to be subverted, but the other in contentious arguments, as to how some one should speak of the thing proposed, wherefore in the syllogistic, the shrewder arguments cause greater investigation, but a syllogistic argument is most acute, if from things which appear especially probable, a person subverts what is especially probable. For the argument being one, when the contradiction is transposed, will have all the syllogisms alike, for a person will always, from probable assertions, subvert or confirm what is similarly probable, wherefore it will be necessary to doubt. An argument then of this kind is especially acute, which makes a conclusion equal to the questions, but that next, which is from all similar (assumptions), for this in like manner will produce doubt, as to which of the interrogatories is to be subverted; nevertheless, this is difficult, since a subversion is to be made, but what is to be subverted is uncertain. Of contentious arguments, the most acute is that in which at first it is forthwith uncertain whether it is syllogistically concluded or not, and whether the solution is from the false or from division, but the second of the rest is that which evidently must be (solved) through division or removal, but in which it is not clear through the removal or division of what interrogation it must be solved, indeed whether this removal or division is from the conclusion, or from one of the interrogatories.

Sometimes therefore, the argument which is not conclusive is silly, e. g. if the assumptions be very incredible or false, but sometimes it is not to be despised. For when one of such interrogations is deficient, the syllogism about which, and through which, the argument (is employed), and which neither assumes this, nor concludes, is silly, but when (the interrogation is deficient,) which may be externally (assumed), the argument is by no means to be despised, but (here) the argument indeed is good, but the querist has not interrogated well.

Since the solution at one time belongs to the argument, at another to the questionist, and the question, and sometimes to neither of these, in like manner also, it is possible both to question and conclude against the thesis, and against the respondent, and against the time, when the solution requires more time than the present opportunity (allows) to argue against it.

Chapter 34[edit]
From how many, and what kind of particulars then, paralogisms are produced by disputants, also how we shall both prove the false and compel (the opponent) to argue paradoxically; further, from what things a syllogism results, and how we must interrogate, moreover, what is the order of interrogations, for what, too, all such arguments are useful, and concerning both every answer simply, and how arguments and syllogisms must be solved, concerning all these let what we have said suffice. It now remains that recalling our original proposition, we should say something briefly concerning it, and add an end to what has been enunciated.

We designed then to discover a certain syllogistic faculty, about a problem proposed from things in the highest degree probable, for this is the office of the dialectic per se, and also of the peirastic art. Since, however, there is added to this, on account of the affinity of the sophistical art, that a person may not only make trial dialectically, but even as one endowed with knowledge; on this account we not only supposed what was said to be the object of this treatise, viz. to be able to assume an argument, but also that sustaining the argument, we may defend the thesis in a similar manner, through the greatest probabilities. We have besides, assigned the cause of this; since, for this reason also, Socrates questioned, but did not answer, for he confessed that he knew nothing. Moreover, it has been shown in the preceding treatise, with reference to how many, and from what number this will be, and whence we shall be well supplied with these; further, how interrogations must be made, and how every one must be arranged, and likewise, concerning the answers and solutions of things appertaining to syllogisms. Such other particulars besides, have been developed as belong to the same method of arguments, and in addition to these, we have discussed paralogisms, as we stated before, wherefore, it is evident that what we proposed has sufficiently obtained its end. Still we ought not to be ignorant of that which occurs in this treatise; for of all discoveries, some being received formerly from others, elaborated partially afterwards, have been increased by those who received them; but others being discovered from the beginning, are wont to receive, at first, but small increase, becoming much more useful by the increase which they receive from others afterwards. For the beginning of every thing is perhaps, as it is said, the greatest thing, and on this account the most difficult; for that is the hardest to be perceived, which, as it is the most powerful in faculty, is by so much the smallest in size; yet when this is discovered, it is more easy to add and co-increase what mains, which also occurs in rhetorical arguments, and in almost all the other arts. For they who discovered principles, altogether made but little progress; but men who are now celebrated, receiving, as it were, by succession from many who promoted (art) by parts, have thus increased it; Tisias after the tirst (authors), but Thrasymachus after Tisias, Theodorus after him, and many (others) have brought together many particulars, wherefore it is no wonder that the art has a certain multitude (of precepts). Of this subject, however, there has not been a part cultivated, and a part not before, but nothing of it has existed at all, for of those who employed themselves about contentious arguments for gain, there was a certain instruction, similar to the treatise of Gorgias. For some gave rhetorical, others interrogative discourses to learn, into which each thought their conversation with each other would most often fall. Hence the instruction indeed to their disciples was rapid, but without art, since they supposed they should instruct them by delivering not art, but the effects of art, just as if a person professing to deliver the science of keeping feet from injury, should afterwards not teach shoemaking, nor whence such things (as safe-guards for the feet) may be procured, but should exhibit many kinds of shoes of every form; for he would indeed afford assistance as to use, yet not discover the art. And indeed, about rhetoric, many old discourses are extant, but about the art of syllogism we have received nothing at all from the ancients, but we have laboured for a long time by the exercise of investigation. If then, it appear to you, when you have inspected (our writings), that this method derived from such materials as existed originally, when compared with other treatises which have been increased from tradition, has been (handled) sufficiently, it remains for you all, or for those who have heard this work, to excuse the omissions in this method, and to be very grateful for its discoveries.