Fundamental Conceptions in Logic

Aristotle

Enumeration of the Categories.

Of things incomplex enunciated, each signifies either substance, 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 enunciated without any connection, none is either true or false, as "man," "white," "runs," "conquers."

Of Substance

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 the 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"   "of "some certain man," and the definition man of man will be predicated of "some certain man," for "a certain man" [p.346] 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, "color" 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 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 [p.347] 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 "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 [p.348] 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 the individual, but genus in respect both 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 substance 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 [p.349] 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 "color," 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 [p.350] 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. Wherefeore 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.

Of Proposition, Term, Syllogism, and Its Elements

It is first requisite to say what is the subject, concerning which, and why, the present treatise is undertaken, namely, that it is concerning demonstration, and for the sake of demonstrative science; we must afterwards define, what is a proposition, what a term, and what a syllogism, also what kind of syllogism is perfect, and what imperfect; lastly, what it is for a thing to be, or not to be, in a certain whole, and what we say it is to be predicated of every thing, or of nothing (of a class).

A proposition then is a sentence which affirms or denies something of something, and this is universal, or particular, or indefinite; I denominate universal, the being present with all or none; particular, the being present with something, or not with something, or not with every thing; but the indefinite the being present or not being present, without the universal or particular (sign); as for example, that there is the same science of contraries, or that pleasure is not good. But a demonstrative proposition differs from a dialectic in this, that the [p.351] demonstrative is an assumption of one pan of the contradiction, for a demonstrator does not interrogate, but assume, but the dialectic is an interrogation of contradiction. As regards however forming a syllogism from either proposition, there will be no difference between one and the other, since he who demonstrates and he who interrogates syllogize, assuming that something is or is not present with something. Wherefore a syllogistic proposition will be simply an affirmation or negation of something concerning something, after the above-mentioned mode: it is however demonstrative if it be true, and assumed through hypotheses from the beginning, and the dialectic proposition is to him who inquires an interrogation of contradiction, but to him who syllogizes, an assumption of what is seen and probable, as we have shown in the Topics. What therefore a proposition is, and wherein the syllogistic demonstrative and dialectic differ, will be shown accurately in the following treatises, but for our present requirements what has now been determined by us may perhaps suffice. Again, I call that a "term," into which a proposition is resolved, as for instance, the predicate and that of which it is predicated, whether to be or not to be is added or separated. Lastly, a syllogism is a sentence in which certain things being laid down, something else different from the premises necessarily results, in consequence of their existence. I say that, "in consequence of their existence," something results through them, but though something happens through them, there is no need of any external term in order to the existence of the necessary (consequence). Wherefore I call a perfect syllogism that which requires nothing else, beyond (the premises) assumed, for the necessary (consequence) to appear: but an imperfect syllogism, that which requires besides, one or more things, which are necessary, through the supposed terms, but have not been assumed through propositions. But for one thing to be in the whole of another, and for one thing to be predicated of the whole of another, are the same thing, and we say it is predicated of the whole, when nothing can be assumed of the subject, of which the other may not be asserted, and as regards being predicated of nothing, in like manner.