The Complete Aristotle (eng.)

rendered, clearly a
mistake has been made.
    See, also, if the opposite of the term has the opposite
definition, whether (e.g.) the definition of ‘half’ is the opposite
of that of ‘double’: for if ‘double’ is ‘that which exceeds another
by an equal amount to that other’, ‘half’ is ‘that which is
exceeded by an amount equal to itself’. In the same way, too, with
contraries. For to the contrary term will apply the definition that
is contrary in some one of the ways in which contraries are
conjoined. Thus (e.g.) if ‘useful’=’productive of good’,
‘injurious’=productive of evil’ or ‘destructive of good’, for one
or the other of thee is bound to be contrary to the term originally
used. Suppose, then, neither of these things to be the contrary of
the term originally used, then clearly neither of the definitions
rendered later could be the definition of the contrary of the term
originally defined: and therefore the definition originally
rendered of the original term has not been rightly rendered either.
Seeing, moreover, that of contraries, the one is sometimes a word
forced to denote the privation of the other, as (e.g.) inequality
is generally held to be the privation of equality (for ‘unequal’
merely describes things that are not equal’), it is therefore clear
that that contrary whose form denotes the privation must of
necessity be defined through the other; whereas the other cannot
then be defined through the one whose form denotes the privation;
for else we should find that each is being interpreted by the
other. We must in the case of contrary terms keep an eye on this
mistake, e.g. supposing any one were to define equality as the
contrary of inequality: for then he is defining it through the term
which denotes privation of it. Moreover, a man who so defines is
bound to use in his definition the very term he is defining; and
this becomes clear, if for the word we substitute its definition.
For to say ‘inequality’ is the same as to say ‘privation of
equality’. Therefore equality so defined will be ‘the contrary of
the privation of equality’, so that he would have used the very
word to be defined. Suppose, however, that neither of the
contraries be so formed as to denote privation, but yet the
definition of it be rendered in a manner like the above, e.g.
suppose ‘good’ to be defined as ‘the contrary of evil’, then, since
it is clear that ‘evil’ too will be ‘the contrary of good’ (for the
definition of things that are contrary in this must be rendered in
a like manner), the result again is that he uses the very term
being defined: for ‘good’ is inherent in the definition of ‘evil’.
If, then, ‘good’ be the contrary of evil, and evil be nothing other
than the ‘contrary of good’, then ‘good’ will be the ‘contrary of
the contrary of good’. Clearly, then, he has used the very word to
be defined.
    Moreover, see if in rendering a term formed to denote privation,
he has failed to render the term of which it is the privation, e.g.
the state, or contrary, or whatever it may be whose privation it
is: also if he has omitted to add either any term at all in which
the privation is naturally formed, or else that in which it is
naturally formed primarily, e.g. whether in defining ‘ignorance’ a
privation he has failed to say that it is the privation of
‘knowledge’; or has failed to add in what it is naturally formed,
or, though he has added this, has failed to render the thing in
which it is primarily formed, placing it (e.g.) in ‘man’ or in ‘the
soul’, and not in the ‘reasoning faculty’: for if in any of these
respects he fails, he has made a mistake. Likewise, also, if he has
failed to say that ‘blindness’ is the ‘privation of sight in an
eye’: for a proper rendering of its essence must state both of what
it is the privation and what it is that is deprived.
    Examine further whether he has defined by the expression ‘a
privation’ a term that is not used to denote a privation: thus a
mistake of this sort also would be generally thought to be incurred
in the case of ‘error’ by any one who is not using it as a merely
negative term. For what is generally thought to be in error is not
that which has no knowledge, but rather that which has been
deceived, and for this reason we do not talk of inanimate things or
of children as ‘erring’. ‘Error’, then, is not used to denote a
mere privation of