CATENALITY AND NONCATENALITY
catena is a totality of all
atomic positivities, one
atomic neutrality and all atomic negativities which are inseparably
linked together. Having a positive predicate of catena
C is the complete positivity of catena C, having a negative
predicate of catena C the complete negativity of that catena.
Loosely, we call having a positive or negative
predicate "predicates" too.
They are, then, improper predicates.
Altho improper, we
classify them as
catenated predicates with the
atomic, proper predicates to which they refer. Typical, improper,
catenated predicates we have thus distinguished are, besides
monopolarity (positivity or negativity),
Now, there is also a limiting case we have not yet discussed.
It is the predicate having a predicate of catena C, not just
perineutral or bipolar one.
The catena 'subset' corresponding to this predicate is the improper
'subset' of the
extensionality of the catena concerned,
that is, the entire extensionality itself.
A primary thing which has a predicate of a catena is a
'catenal', and the predicate of having-a-predicate-of-a-catena
(These semi-neologisms are introduced here because of the importance of the
distinction between catenality and noncatenality, and --as we will see-- also
between noncatenality and neutrality.)
If not further qualified, catenality is a derelativized relation, since a
primary thing may be catenal with respect to one catena or system of
catenas and not catenal with respect to another catena or system of catenas.
When catenality is interpreted in its most general sense, that is,
with respect to any catena, it is questionable whether there is
any primary thing that is not catenal. At least all objects are
Catenality is not what all positively catenal (for example, happy),
neutrally catenal and negatively catenal (unhappy) persons, objects or
things have in common (and what they do not have in common with other
So far as this aspect is concerned, positively, neutrally and negatively
catenal things have nothing
factual in common.
They may have the possibility of being positively, neutrally or
negatively catenal in common, but that is a
modal, not a factual, condition.
Catenality is not what all positivities, the neutrality and all
negativities have in common either, because what they may have in common
secondary predicates, and as a
predicate of primary things catenality is a
primary predicate (albeit improper
and, strictly speaking, not existing on our construction).
The differences between catenality, noncatenality and neutrality
or neutral catenality can easily be demonstrated by
means of the motion- and happiness-catenals. 'Motion catenality'
is having a predicate of the motion catena, that is, having the
predicate of being-in-motion or of being-at-rest. It is concrete
things which have such predicates. Since abstract things are
neither in motion nor at rest (certainly not the predicates of
the motion catena themselves), they are noncatenal with respect
to the motion catena. 'Happiness catenality' is having a
predicate of the happiness catena. It is sentient beings which
have such a predicate. Noncatenal with respect to the happiness
catena are insentient, concrete beings like stones, plants and
artifacts, and all abstract entities. They are not happy, not
neutrally neither happy nor unhappy, and not unhappy; they are
noncatenally neither happy nor unhappy. (The question of which
beings are exactly happiness-catenal, and when, is a scientific
one, and the answer to this question need not concern us here.)
Neutrality with respect to the motion catena, or
motion-catenated neutrality, is
This is something entirely different from being-abstract, that is,
being noncatenal with respect to the motion catena.
A thing which is at rest is not less 'concrete' (in the sense of
motion-catenal) than a thing which moves.
Happiness-catenated neutrality is the predicate
a sentient being has when it is responsive to (real or
imaginary, oneiric or nononeiric) impressions, and when it is
neither (made) happy nor (made) unhappy. This state of being is
wholly different, again, from that of a being (even if an
object) which is not responsive to impressions at all and which
cannot even be brought into a certain
(at least not at the moment concerned). So when people say
"neither happy nor unhappy", they may refer to two basically
different states of being. Not happy could even refer to one
of three different conditions: (1) unhappy, the opposite of
being-happy; (2) unhappy or neutrally neither happy nor
unhappy, the catena supplement of being-happy; or (3)
insentient, that is, noncatenality with respect to the
While catenality is a limiting case of an improper, catenated
predicate, it does not seem appropriate to classify it as a
catenated predicate itself, simply because there is no extensional
catena element left to which it is catenated. Conceptually, it may
be inseparably connected to noncatenality but that 'predicate' is
not a catena element either. (Noncatenality would even be a
privative pseudopredicate, if catenality had been a
proper predicate.) Moreover, every predicate is 'linked' to its
negation denoted by non-, of whatever order or type.
We have now distinguished three
catenical, main categories of predicates:
- catenated (primary) predicates
- catenary (secondary) predicates
- two (sorts of) noncatenated, primary predicates, namely catenality
As primary things can only have primary determinative attributes,
and secondary things only secondary determinative attributes,
the different catenical concepts and the corresponding terms
should not be mixed up. Thus primary predicates (concepts, numbers
or secondary things) may be positive as secondary things,
but objects and other primary things can only be positively catenal.
(If they are called "positive", "neutral" or "negative"
nevertheless, these words may be used in a different sense,
often in a sense specifically related to one or a few catenas
Objects may be good, bad or something else, but goodness itself is
absolutely not good (or bad) -- it may be
goodness-predicative and goodness-catenary (or badness-catenary),
that is, part of a goodness- (or badness-)catena.
Only objects or other nonbasic, primary things are catenal (for
example, happiness-catenal) -- other things can
only be catenary (for example, happiness-catenary).
And everything that is catenary is always noncatenal.