Topics   

while if the latter be untrue, so is the former'. Likewise, also, 'If
what is not pleasant be not honourable, then what is honourable is
pleasant'. Clearly, then, the conversion of the sequence formed by
contradiction of the terms of the thesis is a method convertible for
both purposes.
Then look also at the case of the contraries of S and P in the thesis,
and see if the contrary of the one follows upon the contrary of the
other, either directly or conversely, both when you are demolishing
and when you are establishing a view: secure arguments of this kind as
well by means of induction, so far as may be required. Now the
sequence is direct in a case such as that of courage and cowardice:
for upon the one of them virtue follows, and vice upon the other; and
upon the one it follows that it is desirable, while upon the other it
follows that it is objectionable. The sequence, therefore, in the
latter case also is direct; for the desirable is the contrary of the
objectionable. Likewise also in other cases. The sequence is, on the
other hand, converse in such a case as this: Health follows upon
vigour, but disease does not follow upon debility; rather debility
follows upon disease. In this case, then, clearly the sequence is
converse. Converse sequence is, however, rare in the case of
contraries; usually the sequence is direct. If, therefore, the
contrary of the one term does not follow upon the contrary of the
other either directly or conversely, clearly neither does the one term
follow upon the other in the statement made: whereas if the one
followed the other in the case of the contraries, it must of necessity
do so as well in the original statement.
You should look also into cases of the privation or presence of a
state in like manner to the case of contraries. Only, in the case of
such privations the converse sequence does not occur: the sequence is
always bound to be direct: e.g. as sensation follows sight, while
absence of sensation follows blindness. For the opposition of
sensation to absence of sensation is an opposition of the presence to
the privation of a state: for the one of them is a state, and the
other the privation of it.
The case of relative terms should also be studied in like manner to
that of a state and its privation: for the sequence of these as well
is direct; e.g. if 3/1 is a multiple, then 1/3 is a fraction: for 3/1
is relative to 1/3, and so is a multiple to a fraction. Again, if
knowledge be a conceiving, then also the object of knowledge is an
object of conception; and if sight be a sensation, then also the
object of sight is an object of sensation. An objection may be made
that there is no necessity for the sequence to take place, in the case
of relative terms, in the way described: for the object of sensation
is an object of knowledge, whereas sensation is not knowledge. The
objection is, however, not generally received as really true; for many
people deny that there is knowledge of objects of sensation. Moreover,
the principle stated is just as useful for the contrary purpose, e.g.
to show that the object of sensation is not an object of knowledge, on
the ground that neither is sensation knowledge.
Part 9
Again look at the case of the co-ordinates and inflected forms of the
terms in the thesis, both in demolishing and in establishing it. By
co-ordinates' are meant terms such as the following: 'Just deeds' and
the 'just man' are coordinates of 'justice', and 'courageous deeds'
and the 'courageous man' are co-ordinates of courage. Likewise also
things that tend to produce and to preserve anything are called
co-ordinates of that which they tend to produce and to preserve, as
e.g. 'healthy habits' are co-ordinates of 'health' and a 'vigorous
constitutional' of a 'vigorous constitution' and so forth also in
other cases. 'Co-ordinate', then, usually describes cases such as
these, whereas 'inflected forms' are such as the following: 'justly',
'courageously', 'healthily', and such as are formed in this way. It is
usually held that words when used in their inflected forms as well are
co-ordinates, as (e.g.) 'justly' in relation to justice, and