2.1.2 |
THE CONCATENATE PREDICATES OF A CATENA |
If a material thing is bound to be light, medium heavy
(or 'medium light') or heavy, it is bound to have one of the
properties of a certain set of properties which are inseparably
connected with each other. And if it is bound to be lighter
than, as heavy as or heavier than another material thing, it is
bound to have one of the relations of a certain set of relations
which are inseparably connected with each other.
The set of properties is not a
primary, simplex thing, for an object
cannot be light (have the property of lightness) and medium heavy or heavy
(have the property of heaviness) at the same time: it is the
extensionality of a
secondary thing.
The properties in the first set are therefore to be conceived of as
secondary things themselves, that is, as simplex things in the second
domain of discourse.
The relations in the second set can only be things in
the second domain of discourse, but also the set of these
relations is a mere extensionality belonging to a complex,
secondary thing. Neither the set of connected properties nor
the set of connected relations is purely conceptual, because then
we would be faced again with the 'logical' predicament in which
heavier than could turn out to be formally combined not only
with as heavy as but also with as slow as or some other
equivalence relation.
The 'intensionally' connected series of lighter than, as heavy
as and heavier than must distinguish itself from a mere set
(such as that of heavier than and as slow as), because it is
an existing whole with its own
secondary predicates.
The relationships between its constituent parts are now not merely
conceptual or accidental any more: the
primary predicates which constitute one
and the same whole in the second domain of discourse are linked together or
'concatenate'.
The connected series of related primary predicates itself we shall call "a
catena", "a catena of attributes or relations".
A predicate catena comprises all the, and only those, primary
predicates that are inseparably linked together. Hence, the
relations heavier than and as slow as do not constitute a
catena, because talk of both relations presupposes the existence of
other catenas before we can even speak of "heavier than" and "as
slow as". But the relations heavier than and as heavy as
do not constitute a catena either, since the relation lighter than
is needed to complete its extensionality. (As light as may mean
the same as as heavy as, lighter than certainly does not
mean the same as heavier than.) The attributes light and
heavy do not make up a catena, because they are inseparably
connected with an attribute lying between lightness and heaviness:
neither light nor heavy (but having a weight nevertheless)
(if thinking of a borderline) or medium heavy (if thinking
of a transitional zone). The terms light and heavy
are so-called 'vague' predicate expressions in that it is not
always evident when light becomes heavy, or conversely.
It is therefore preferable to first illustrate the new concept of the
catena by means of some other, clearer examples.
The predicates of electropositivity, electroneutrality and
electronegativity cannot exist without each other and make up the
extensionality of —what we shall name after its positivity—
the 'electropositivity catena' (of which secondary predicates form the
attributive predicament).
The attributes of happiness, of the state of indifference between happiness
and unhappiness and of unhappiness form extensionally the happiness
catena. Increase, decrease and the concatenate neither increasing
nor decreasing are together the component parts of an
increase catena. (There is not one increase catena but there are
many of them.) Rest, or being-at-rest, is itself a borderline
predicate between motion in positive and motion in negative
direction, and therefore rest and motion together constitute a
motion catena without any third predicate or set of predicates.
Just as increase catena is the common denominator of all
increase catenas, so motion is the common denominator of all
positive or negative velocities or degrees of motion, happiness
the common denominator of all degrees of happiness; and so
are unhappiness, electropositivity, and so on.
What is special about heavier than and as heavy as is
that they belong to the same catena of relations (together with
lighter than). There is a real relationship of having between
this one catena and the relation heavier than and also between
this catena and the relation as heavy as. The so-called
'relationship' of catenation, that is, of belonging-to-the-same-catena,
between heavier than and as heavy as themselves is
therefore not ontic. Nevertheless it refers to the existence of
a real, but abstract, whole with real, but abstract, components.
What deserves our attention in particular is that this conceptual
relation of catenation between primary relations is not at
all different from the one between attributes as heaviness and
lightness or, for that matter, happiness and unhappiness.
That is why it would be a rather fragmentary approach to recognize a formal
property such as connectedness (our 'concatenatedness') solely with regard
to relations and not with regard to attributes, especially when the
existence or recognition of the 'qualitative' attribute catena precedes or
is presupposed by the existence or recognition of the comparative relation
catena.
