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We must first inquire about definitions reached by the method of
divisions. There is nothing in the definition except the first-named
and the differentiae. The other genera are the first genus and along
with this the differentiae that are taken with it, e.g. the first
may be 'animal', the next 'animal which is two-footed', and again
'animal which is two-footed and featherless', and similarly if the
definition includes more terms. And in general it makes no
difference whether it includes many or few terms,-nor, therefore,
whether it includes few or simply two; and of the two the one is
differentia and the other genus; e.g. in 'two-footed animal'
'animal' is genus, and the other is differentia.
If then the genus absolutely does not exist apart from the
species-of-a-genus, or if it exists but exists as matter (for the
voice is genus and matter, but its differentiae make the species, i.e.
the letters, out of it), clearly the definition is the formula which
comprises the differentiae.
But it is also necessary that the division be by the differentia
of the diferentia; e.g. 'endowed with feet' is a differentia of
'animal'; again the differentia of 'animal endowed with feet' must
be of it qua endowed with feet. Therefore we must not say, if we are
to speak rightly, that of that which is endowed with feet one part has
feathers and one is featherless (if we do this we do it through
incapacity); we must divide it only into cloven-footed and not cloven;
for these are differentiae in the foot; cloven-footedness is a form of
footedness
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