Negation itself is not a typically
catenical concept, but the concepts of
catenality and noncatenality and the negatory
relationship between them certainly are.
Negation is a
secondary relation but unlike
limitation, opposition and supplementation (in the catenical sense) it is
not
catenary.
In a way, however, all these catenical, secondary relations are more or
less negations.
Limitation is, then, negation on the borderline or fringe of the framework
of the predicate negated itself; opposition is negation within the
framework of the complete
bipolarity (of which the predicate negated
is only a
monopolar part);
catena supplementation is negation within
the framework of the catena
extensionality or the catenality; and,
finally, what we shall call "aspect negation" is negation within the
framework of the aspect concerned, in particular of a form of catenality or
of a form of noncatenality.
Aspect is the name we shall use for the imaginary
collection of all extensional elements and subset-predicates of
one catena and the corresponding noncatenality. Also combinations
of such conceptual sets may be termed "aspects".
Attributes which form part of the aspect of heaviness, or the aspect
weight, for instance, are: heaviness (that is, all proper and
improper heaviness attributes), the neutrality which limits heaviness and
lightness (in
practise the
perineutrality medium heavy),
lightness (all lightness attributes) and non-heaviness-catenality (the
attribute not having any weight, not even 0).
It looks as
tho two aspects could be
distinguished for every two-place relation: one from the standpoint of the
fundament, and one from that of the terminus.
This is misleading altho it depends on the kind of relation how easily the
error can be shown.
For comparative notions it is immediately obvious that
there is actually merely one aspect involved. Consider, for
example, the relation heavier than: if A is heavier than B,
B is lighter than A, and if A is lighter than B, B is
heavier than A. Hence, the aspect comprises in both cases the
same predicates, namely being-heavier, being-lighter and the
corresponding neutrality and noncatenality. But what if A loves
B and B is loved by A, while not being-loved but hating is the
opposite of loving? In this case loving and being-loved are
'isorelative', that is, they concern one and the same relation.
(As the relation is binary it may also be said that being
loved is the 'reverse' of loving. In combinatory logic the term
inversion is used when the order of variables in a two-place
predicate expression is changed.) The intensity of A's love and
of B's being-loved is necessarily the same. There is only one
catena value for this relation regardless of the position from
which it is considered. Yet, this still makes it theoretically
possible to discern two 'related' aspects: that of love, hate
and nonpolarities, and that of being-loved, being-hated and
nonpolarities.
There are many noncomparative predicates which are each other's
isorelative, and which each have an opposite of which they are not an
isorelative.
An example is honor(ing) with the opposite dishonor(ing) and the
isorelative being-honored.
One should bear in mind, however, that predicates which are each
other's isorelative need not be
catenated.
For example, planting and being-planted, being-a-parent and being-a-child
are isorelatives; yet they have no opposites because they are not part of
any catena to start with.
In a way predicates like hate and
being-hated, honor and being-honored, parenthood and childhood
are as inextricably linked as love and hate, and as honor and
dishonor, but there is a significant difference. To love or to
have the predicate of love, is as real as to hate or to have the
predicate of hate, and living beings cannot have both predicates
at precisely the same moment with regard to the same thing. (To
understand this one must not forget that a whole and one of its
parts, or two different parts of the same whole, are not the
same thing.)
On the other hand, to be loved is not 'as real as' to love: ontologically
someone or something that is loved does not have any proper predicate
whatsoever on the basis of its being loved.
It may certainly change or be changed or influenced because of its being
loved, but all the proper predicates it may have for that reason are
ontologically contingent -- at the most the
relation of loving-and-being-loved and those predicates are related as
cause and effect.
Thus it is quite feasible, and
common, to like or dislike someone and to be liked or disliked
by that person at exactly the same moment. Yet, the state of
being liked or loved, or disliked or hated, by the other does
not correspond to any logically necessary, proper predicate in
the person liked or disliked. One person may take someone else's
hate or love to heart, whereas another person may just make
little or nothing of it. All passive isorelatives such as
being-liked, being-disliked, being-planted, being-a-child (in
contradistinction to being-a-parent) are linguistically contrived
pseudo-predicates.
And as the argument is not relevantly different with respect to three- or
more-place relations, this implies that a multiplicity of relational
positions (fundament, terminus, and so on) has no bearing on aspectual
diversity.
