Aristotle · a new plain-English translation from the original language
1| Let this much, then, be said about definitions. H. Whether a thing is the same or different in the strictest of the senses discussed regarding sameness (and it was said that the strictest sense of sameness is what is one in number) should be examined by way of inflections, coordinate terms, and opposites. For if justice is the same as courage, then the just person is the same as the courageous person, and "justly" is the same as "courageously." And likewise with opposites: if these things are the same, then the things opposed to them are also the same, in whatever kind of opposition is meant. For it makes no difference which of the two you take the opposite of, since they are the same. Again, one should look from the point of view of what produces and destroys them, of their comings-to-be and passings-away, and in general of whatever stands in a like relation to each: for things that are the same without qualification also have the same comings-to-be and the same passings-away, and the same things that produce and destroy them. One should also examine those things of which either term is most properly said, to see whether the other of these same terms is also most properly said in the same respect, just as Xenocrates proves that the happy life and the excellent life are the same, since of all lives the excellent is most choiceworthy and so is the happy; for the most choiceworthy and the greatest are one. And likewise in other such cases.
2| But each of the two things called "greatest" or "most choiceworthy" must be one in number. Otherwise it will not have been shown that they are the same; for it is not necessary, if the Peloponnesians and the Spartans are the most courageous of the Greeks, that the Peloponnesians be the same as the Spartans, since neither "Peloponnesian" nor "Spartan" is one in number. Rather, it is necessary that the one be contained by the other, as the Spartans are contained by the Peloponnesians. Otherwise it will follow that each is better than the other, if the ones are not contained by the others. For it would be necessary for the Peloponnesians to be better than the Spartans, if the ones are not contained by the others; for they are better than all the rest. And likewise it would be necessary for the Spartans to be better than the Peloponnesians; for they too are better than all the rest. So they turn out to be better than each other. It is clear, then, that what is called best and greatest must be one in number, if it is to be shown to be the same. That is why Xenocrates does not prove his point: for the happy life and the excellent life are not one in number, so it is not necessary that they be the same because both are most choiceworthy — rather, the one is contained under the other. Again, one should examine whether that with which one of the two is the same, the other is also the same with;
3| for if both are not the same as the same thing, it is clear that they are not the same as each other either. Further, one should examine on the basis of what is accidental to them, and to the things to which they are accidental: for whatever is accidental to the one must also be accidental to the other, and whatever the one of them is accidental to, the other must be accidental to as well. If any of these fails to agree, it is clear that they are not the same. One should also see whether they do not both belong to one genus of predicate, but the one signifies a quality and the other a quantity or a relation. Again, whether the genus of each is not the same, but the one is good and the other bad, or the one is a virtue and the other a knowledge. Or whether, though the genus is the same, the differentiae predicated of each are not the same, but of the one it is said that it is a theoretical knowledge, and of the other that it is a practical one. And likewise in other cases. Further, from the point of view of the more and less: whether the one admits of the more and the other does not, or whether both admit of it but not at the same time — just as the one who is more in love does not more desire intercourse, so that love and the desire for intercourse are not the same. Further, from the point of view of addition: whether each, when added to the same thing, fails to make the whole the same.
4| Or whether, when the same thing is subtracted from each, what remains is different — for instance, if someone said that double a half and multiple of a half are the same. For when the half is subtracted from each, the remainders ought to signify the same thing, but they do not; for "double" and "multiple" do not signify the same thing. One should examine not only whether something impossible already follows from the position as stated, but also whether it would be possible for something impossible to result on a hypothesis, as with those who say that the void and what is full of air are the same. For it is clear that if the air goes out, it will be no less but more void, while it will no longer be full of air. So that, once something is hypothesized, whether false or true (for it makes no difference), the one of them is destroyed and the other is not. So they are not the same. To put it generally: one should examine, from whatever is predicated of each in any way at all, and the things of which these are predicated, whether there is any disagreement anywhere; for whatever is predicated of the one must also be predicated of the other, and whatever the one is predicated of, the other must be predicated of as well. Further, since "the same" is said in many ways, one should examine whether they are the same in some other way as well: for things that are the same in species or genus are not necessarily, or cannot possibly be, the same in number, and we examine whether they are the same in this way or not.
5| Further, whether it is possible for the one to exist without the other; for then they would not be the same. So many, then, are the commonplaces that concern sameness. It is clear from what has been said that all the destructive commonplaces concerning sameness are also useful with regard to definition, as has been said before; for if the name and the account do not signify the same thing, it is clear that the account given could not be the definition. But none of the constructive commonplaces is useful with regard to definition; for it is not enough to show that what falls under the account and the name are the same, in order to establish that it is a definition, but the definition must also have all the other qualities that have been laid down.
6| One must always attempt to demolish a definition in this way and by these means; but if we wish to establish one, first one must know that none, or few, of those who engage in discussion arrive at a definition by syllogism, but all take such a thing as a starting point, as do those concerned with geometry and arithmetic and the other such branches of learning. Next, one must know that it belongs to another study to give a precise account of what a definition is and how one ought to define, while for the present it is enough to say only so much as suffices for our present need — namely, that it is possible for there to be a syllogism of a definition and of the essence. For if a definition is an account that makes clear the essence of a thing, and the things predicated in the definition must be predicated only among the things predicated in the essence of the thing, and the genera and differentiae are what are predicated in the essence, it is evident that if one took only these to be predicated in the essence of the thing, the account containing them would necessarily be a definition; for it is not possible for the definition to be something else, since nothing else is predicated in the essence of the thing. That it is possible, then, for there to be a syllogism of a definition, is evident;
7| but from what premises one must construct it has been determined more precisely elsewhere, while for the present method the same commonplaces are useful. For one must examine the case of contraries and of the other opposites, considering both whole accounts and them part by part; for if the opposite belongs to the opposite, then the stated account must also belong to the thing under discussion. And since there are several combinations of contraries, one must take, of the contraries, whichever contrary definition appears most clearly. So then, whole accounts should be examined as has been said, and part by part as follows. First, whether the genus assigned has been correctly assigned. For if the contrary is in the contrary genus, and the thing under discussion is not in the same genus, it is clear that it would be in the contrary genus, since contraries must be in the same genus or in contrary genera. And we also require that the contrary differentiae be predicated of contraries, as of white and black: for the one is dispersive and the other is contractive of sight. So that if the contrary differentiae are predicated of the contrary, the differentiae assigned would be predicated of the thing under discussion. So that, since both the genus and the differentiae have been correctly assigned, it is clear that the account given would be the definition.
8| Or is it not necessary that contrary things have contrary differentiae predicated of them, unless the contraries are in the same genus? For things whose genera are contrary, nothing prevents the same differentia being predicated of both, as with justice and injustice: the one is a virtue of soul and the other a vice of soul, so that "of soul" is a differentia predicated in both cases, since there is also a virtue and a vice of body. But this much at least is true, that of contraries the differentiae are either contrary or the same. If, then, the contrary of the term in question has the contrary differentia predicated of it, but this term does not have that differentia predicated of it, clearly the differentia we have mentioned would be predicated of it. Speaking generally, since a definition is made up of genus and differentiae, if the definition of the contrary is clear, the definition of the thing before us will also be clear. For since the contrary is either in the same genus or in the contrary genus, and likewise the differentiae predicated of contraries are either contrary or the same, clearly of the thing before us either the very same genus will be predicated as of its contrary, and the differentiae will be contrary, either all of them or some, with the rest the same; or conversely the differentiae will be the same and the genera contrary;
9| or both will be contrary, both the genera and the differentiae. For it is not possible for both to be the same; if they were, the contraries would have the same definition. Further, argue from the inflected forms and from cognate words: for the genera must follow the genera, and the definitions the definitions. For instance, if forgetting is the loss of knowledge, then to forget will be to lose knowledge, and to have forgotten will be to have lost knowledge. So once any one of the terms mentioned has been agreed to, the rest must also be agreed to. Likewise too, if destruction is the dissolution of substance, then to be destroyed is to have substance dissolved, and "destructively" is "dissolutively," and if that which is destructive is dissolutive of substance, then destruction is dissolution of substance. And likewise in other cases too. So that once any one is taken, all the rest are agreed to as well. Argue also from things that stand in a similar relation to one another. For if the healthy is productive of health, then the fitness-producing will be productive of good condition, and the beneficial will be productive of good. For each of the terms mentioned stands in a similar way toward its own proper end, so that if the definition of one of them is "being productive of the end," this would also be the definition of each of the rest.
10| Further, argue from the more and the equally, in as many ways as it is possible to establish the point by comparing two things with two, for instance: if this is more of a definition of this than that is of that, and the latter is a definition, then so is the former, the greater one. And if this is a definition of this in the same way as that is of that, then if the one is a definition of the one, the remaining one is a definition of the remaining one. But when one definition is compared with two things, or two definitions with one thing, the examination from the more is of no use at all; for it is not possible for one term to be the definition of two things, nor for two terms to be the definition of the same thing. The most opportune of the commonplaces are both the ones just mentioned and those from cognate words and from inflected forms. That is why one must above all keep hold of these and have them ready to hand, for they are the most useful for the most cases. And among the rest, the most common ones; for these are the most effective of the others, for instance looking to particular cases, and examining, in the case of the forms (species), whether the account fits, since the form is a synonymous term. Such a procedure is useful against those who posit that there are Forms (Ideas), as has been said before. Further, ask whether he has used the name metaphorically, or has predicated it of itself as though it were something other than itself. And if there is any other commonplace that is common and effective, it must be used.
11| That it is harder to establish a definition than to demolish it will be clear from what will be said next. For it is not easy even to see the point and to obtain from those questioned premises of the following sort: that of the elements given in the account rendered, one is the genus and another the differentia, and that it is in the "what it is" that the genus and the differentiae are predicated. Without these it is impossible for there to be a deduction of a definition; for if certain other things too are predicated of the thing in its "what it is," it is unclear whether the account stated, or some other, is its definition, since a definition is an account that signifies the essence. This is clear also from the following. It is easier to conclude one thing than many. In demolishing, then, it is enough to argue against one point (for once we have demolished any one point whatever, we shall have destroyed the definition), but in establishing it is necessary to bring together the whole case, that everything in the definition belongs. Further, in establishing one must bring a universal deduction; for the definition must be predicated of everything of which the name is predicated, and further, in addition to this, it must convert, if the definition given is to be proper to the thing. In demolishing, on the other hand, it is no longer necessary to show the universal point; it is enough to show that the account is not true of some one of the things that fall under the name.
12| And even if it should be necessary to demolish universally, still even so converting is not necessary for the demolishing; it is enough for one who demolishes universally to show that the account is not predicated of something of which the name is predicated. But the converse is not necessary for showing that the name is predicated of things of which the account is not predicated. Further, even if the account belongs to everything that falls under the name, but not to that alone, the definition is thereby demolished. The same holds likewise for the property and for the genus; in both cases it is easier to demolish than to establish. Concerning the property this is clear from what has been said; for as a rule the property is rendered in a complex form, so that it is possible to demolish it by removing one element, whereas one who establishes it must deduce all the elements together. And nearly all the rest of the points that apply to the definition will fit in being said of the property as well; for one who establishes must show that it belongs to everything that falls under the name, while one who demolishes need only show, in one case, that it does not belong; and if it belongs to everything but not to that alone, it is likewise demolished, just as is said in the case of the definition. Concerning the genus, one must establish it in only one way, by showing that it belongs to everything, but one who demolishes it may do so in two ways;
13| for whether it has been shown not to belong to none, or not to belong to some one thing, the point at issue has been destroyed. Further, in establishing it is not enough to show that it belongs; one must also show why it belongs as a genus. In demolishing, it is enough to show that it does not belong, either to some one thing, or not to all. It seems that, just as in other matters it is easier to destroy than to make, so too in these cases it is easier to demolish than to establish.
14| In the case of the accident, the universal is easier to demolish than to establish; for one who establishes must show that it belongs to everything, while one who demolishes need only show, in one case, that it does not belong. The particular, on the other hand, is conversely easier to establish than to demolish; for one who establishes need only show that it belongs to some one thing, while one who demolishes must show that it belongs to nothing. It is also clear why of all these it is easiest to demolish a definition; for it contains the most given elements, since much has been stated, and a deduction comes about more quickly from more elements, since it is likely that error occurs more in many things than in few. Further, against a definition it is also possible to argue by means of the other topics as well; for whether the account is not proper to the thing, or the genus given is not the genus, or something within the account does not belong, the definition is thereby destroyed. But against the other topics it is not possible to bring to bear either all the arguments drawn from definitions or all the rest; only the arguments directed at the accident are common to all the things mentioned. For each of the things mentioned must belong; but if the genus belongs, though not as a property, the genus has not thereby been destroyed. Likewise, too, the property need not belong as a genus, nor the accident as a genus or property, but only needs to belong.
15| So it is not possible to argue from the other predicables to their counterparts except in the case of definition. It is clear, then, that of all of them a definition is easiest to demolish, but hardest to establish; for one must reason out all of the following (that the things stated do belong, that the genus assigned is the genus, and that the account is peculiar to the thing), and beyond these, that the account shows the essence, and that this has been done correctly. Of the other predicables, the property is most in this position: it is easier to demolish, because it usually rests on many points, but hardest to establish, both because one must fit many things together, and further because it belongs to the thing alone and is counterpredicated of it. Easiest of all to establish is the accident; for with the others one must show not only that the attribute belongs but also that it belongs in this way, whereas with the accident it is enough to show that it belongs at all. But the accident is hardest to overturn, because least is conceded in it; for in stating an accident one does not indicate further how it belongs, so that with the others there are two ways of demolishing it, either by showing that the attribute does not belong or that it does not belong in this way, while with the accident it cannot be demolished except by showing that it does not belong at all.