sameness and difference is clear: for when we have discovered a
difference of any kind whatever between the objects before us, we
shall already have shown that they are not the same: while it helps us
in recognizing what a thing is, because we usually distinguish the
expression that is proper to the essence of each particular thing by
means of the differentiae that are proper to it.

  The examination of likeness is useful with a view both to
inductive arguments and to hypothetical reasonings, and also with a
view to the rendering of definitions. It is useful for inductive
arguments, because it is by means of an induction of individuals in
cases that are alike that we claim to bring the universal in evidence:
for it is not easy to do this if we do not know the points of
likeness. It is useful for hypothetical reasonings because it is a
general opinion that among similars what is true of one is true also
of the rest. If, then, with regard to any of them we are well supplied
with matter for a discussion, we shall secure a preliminary
admission that however it is in these cases, so it is also in the case
before us: then when we have shown the former we shall have shown,
on the strength of the hypothesis, the matter before us as well: for
we have first made the hypothesis that however it is in these cases,
so it is also in the case before us, and have then proved the point as
regards these cases. It is useful for the rendering of definitions
because, if we are able to see in one glance what is the same in
each individual case of it, we shall be at no loss into what genus
we ought to put the object before us when we define it: for of the
common predicates that which is most definitely in the category of
essence is likely to be the genus. Likewise, also, in the case of
objects widely divergent, the examination of likeness is useful for
purposes of definition, e.g. the sameness of a calm at sea, and
windlessness in the air (each being a form of rest), and of a point on
a line and the unit in number-each being a starting point. If, then,
we render as the genus what is common to all the cases, we shall get
the credit of defining not inappropriately. Definition-mongers too
nearly always render them in this way: they declare the unit to be the
startingpoint of number, and the point the startingpoint of a line. It
is clear, then, that they place them in that which is common to both
as their genus.

  The means, then, whereby reasonings are effected, are these: the
commonplace rules, for the observance of which the aforesaid means are
useful, are as follows.

                              Book II

                                 1

  Of problems some are universal, others particular. Universal
problems are such as 'Every pleasure is good' and 'No pleasure is
good'; particular problems are such as 'Some pleasure is good' and
'Some pleasure is not good'. The methods of establishing and
overthrowing a view universally are common to both kinds of
problems; for when we have shown that a predicate belongs in every
case, we shall also have shown that it belongs in some cases.
Likewise, also, if we show that it does not belong in any case, we
shall also have shown that it does not belong in every case. First,
then, we must speak of the methods of overthrowing a view universally,
because such are common to both universal and particular problems, and
because people more usually introduce theses asserting a predicate
than denying it, while those who argue with them overthrow it. The
conversion of an appropriate name which is drawn from the element
'accident' is an extremely precarious thing; for in the case of
accidents and in no other it is possible for something to be true
conditionally and not universally. Names drawn from the elements
'definition' and 'property' and 'genus' are bound to be convertible;
e.g. if 'to be an animal that walks on two feet is an attribute of S',
then it will be true by conversion to say that 'S is an animal that
walks on two feet'. Likewise, also, if drawn from the genus; for if
'to be an animal is an attribute of S', then 'S is an animal'. The
same is true also in the case of a property; for if 'to be capable
of learning grammar is an attribute of S', then 'S will be capable
of learning grammar'. For none of these attributes can possibly belong
or not belong in part; they must either belong or not belong
absolutely. In the case of accidents, on the other hand, there is
nothing to prevent an attribute (e.g. whiteness or justice)
belonging in part, so that it is not enough to show that whiteness
or justice is an attribute of a man in order to show that he is
white or just; for it is open to dispute it and say that he is white
or just in part only. Conversion, then, is not a necessary process
in the case of accidents.

  We must also define the errors that occur in problems. They are of
two kinds, caused either by false statement or by transgression of the
established diction. For those who make false statements, and say that
an attribute belongs to thing which does not belong to it, commit
error; and those who call objects by the names of other objects
(e.g. calling a planetree a 'man') transgress the established
terminology.

                                 2

  Now one commonplace rule is to look and see if a man has ascribed as
an accident what belongs in some other way. This mistake is most
commonly made in regard to the genera of things, e.g. if one were to
say that white happens (accidit) to be a colour-for being a colour
does not happen by accident to white, but colour is its genus. The
assertor may of course define it so in so many words, saying (e.g.)
that 'Justice happens (accidit) to be a virtue'; but often even
without such definition it is obvious that he has rendered the genus
as an accident; e.g. suppose that one were to say that whiteness is