Chapter IV. How many and what things must be considered in division.

CHAPTER IV. How many and what things must be considered in division. But for proving a term, that is, a definition, through divisions, one must conjecture three things. But I say for proving, both so that the definition may be had as a middle through division, and so that it may be shown that the definition is perfect. First indeed one must conjecture that through division he receives such predicaments, that is, predicates, as are predicated in that which is what it is. The second is, which must be conjectured, that he receive these things, which are predicated in that which is what it is, in order, always placing the proximate act with the proximate potency, and always the less common thing must be ordered after the more common, and he must receive what is first or second, and so concerning the others. And third, that this which is defined must be commensurated to this, and that nothing superfluous and nothing diminished should be present beyond the fact that these are the being of the defined thing. But the first one of these is indeed that the predicate should belong and be predicated in what; for this must be considered, both that it belongs and that it belongs as what. Hence this first thing, as regards belonging, must be searched out through the art which we posited in the Topics, as with respect to an accident's belonging; because there simple belonging is taught, which one must consider and gather through the method of accident, namely that it is and belongs simply. But insofar as it belongs as what, one must gather through the method concerning genus, which is handed down in the fourth book of the Topics, and thus prove that the predicates belong and belong in what. But that which is required for definition is to order as one ought, which was enumerated second among the things to be conjectured, if they receive first, that is, primitively, in division and definition, the most common genus, which inheres as a predicate in all the following things. But all things do not inhere in that as in a subject. For it is necessary that there be some such thing in every coordination, which is the most common of all. But when this has been received in this way, in the second grade of this order one must join to it the first of the other lower things, because in the lower things there is the same mode of receiving, that what is second among things having themselves, that is, among consequent things, is immediately joined to that second. For once it has been removed from division because what is above, that is, supreme, has now been received and posited, which is not received through division but is divided into inferior things, then after this the first of the other inferior things must be received and joined to the supreme. It must be done similarly in all other things. But that all these things gathered together are together, which was the third among the things that must be conjectured, is manifest from the fact that we receive the first according to division, which is genus, since the whole taken together with the first genus is either the defined human being or animal: human being indeed if the most-specific species must be defined, but animal if the subaltern species must be defined. But when this, which has been added to the proximate genus, is the difference of the whole, that is, of the genus, and when it has been gathered together from genus and difference, it differs in nothing by species and form from the whole defined thing which is composed from all the defining things, because definition gathers together all things which are formally in the defined thing. Moreover this is manifest: because in definition no more is added than is in the defined thing. For all things which are from the number of those things which are in that which is what it is are received, which are gathered from such division; nor from the first down to the last of such things does anything at all fail by being left behind. For if something fails, this is surely either genus or difference. The genus indeed does not fail, because this is the first thing which is posited and is received before the others, with the differences received according to division through order joined to it. But all the differences under the genus down to the species which is defined, received continuously through division and gathered, are contained with the genus down to the species of the defined thing. For beyond the defined species there are no further ultimate things which divide the defined species further; for if there were some things further dividing formally that which is defined, then it would follow that the ultimate defined thing, which is the most-specific species, would differ in species, that is, would be predicated of several things differing in species, which is impossible, since it is the most-specific species.