A doubt may be raised whether this account of the negative is really
the true one. The common logicians would say that the 'not-just,'
'not-beautiful,' are not really classes at all, but are merged in one
great class of the infinite or negative. The conception of Plato, in
the days before logic, seems to be more correct than this. For the word
'not' does not altogether annihilate the positive meaning of the word
'just': at least, it does not prevent our looking for the 'not-just'
in or about the same class in which we might expect to find the 'just.'
'Not-just is not-honourable' is neither a false nor an unmeaning
proposition. The reason is that the negative proposition has really
passed into an undefined positive. To say that 'not-just' has no more
meaning than 'not-honourable'--that is to say, that the two cannot in
any degree be distinguished, is clearly repugnant to the common use of
language.
The ordinary logic is also jealous of the explanation of negation as
relation, because seeming to take away the principle of contradiction.
Plato, as far as we know, is the first philosopher who distinctly
enunciated this principle; and though we need not suppose him to have
been always consistent with himself, there is no real inconsistency
between his explanation of the negative and the principle of
contradiction. Neither the Platonic notion of the negative as the
principle of difference, nor the Hegelian identity of Being and
Not-being, at all touch the principle of contradiction. For what is
asserted about Being and Not-Being only relates to our most abstract
notions, and in no way interferes with the principle of contradiction
employed in the concrete. Because Not-being is identified with Other, or
Being with Not-being, this does not make the proposition 'Some have not
eaten' any the less a contradiction of 'All have eaten.'
The explanation of the negative given by Plato in the Sophist is a true
but partial one; for the word 'not,' besides the meaning of 'other,'
may also imply 'opposition.' And difference or opposition may be either
total or partial: the not-beautiful may be other than the beautiful, or
in no relation to the beautiful, or a specific class in various degrees
opposed to the beautiful. And the negative may be a negation of fact
or of thought (ou and me). Lastly, there are certain ideas, such as
'beginning,' 'becoming,' 'the finite,' 'the abstract,' in which
the negative cannot be separated from the positive, and 'Being' and
'Not-being' are inextricably blended.