QUASI-HEXADUADS AND QUASI-MONADS
The set of the physical predicates deep, neither deep
nor shallow and shallow seems to be the
extensionality of an
explicit triad, and similarly, the set of high,
neither high nor low and low in a purely physical sense too.
Yet, in point of fact, solely the values of and below the zero level of the
value collection of the original catena --let us
call it "the altitude catena"-- occur in the
value collection of the former and solely those of and above that zero
level in the value collection of the latter.
Therefore, the values corresponding to the physical predicates from
deep to shallow represent only one half of a catenary system
and those of the physical predicates from low to high the
It is the combination of all six predicates of the two triads together
which is a
catenary collection, and it is the whole of
which such a combination is the extensionality which we shall call "a
Granting that normality is the positivity of a derivative
normality catena and slowness of a derivative slowness catena,
consistence requires that the positivity of a quasi-hexaduad be
that combination of predicates which also corresponds to the
perineutrality of the original catena.
For the above-mentioned predicates related to the altitude catena this is
the set of all shallowness and lowness predicates, which we shall refer to
Hence, the quasi-hexaduad concerned is the shallow-or-lowness catena.
Proximity may also be a common denominator for shallow-or-lowness
but this term does not only apply to altitude; it equally applies
to what would be 'latitude' and 'longitude' in a three- or
more-dimensional, spatial system.
As quasi-hexaduads and explicit triads are both named after the positivity
of the catena, the term positivity catena itself can be used
for both of them.
Catenas with respect to which there is an atomic expression in ordinary
language for the improper subset of its extensionality, that is, for the
catenality, are 'quasi-monads'.
The predicate itself, which serves as common denominator of all the
catenated predicates in question, is a
All quasi-monadic predicates are catenalities but, conversely,
catenalities need not be quasi-monadic.
There may be important catenalities no-one has ever thought of,
let alone assigned a name to in the language spoken.
The concreteness catena is a quasi-monad identical to the
quasi-duad of the motion catena as long as we define
concrete directly or indirectly as motion-catenal.
Concreteness itself is in this case a quasi-monadic attribute.
Length, width, height, speed, and so on, are all quasi-monadic
attributes or relations, at least if we do not read
"length" as "longness", "width" as "wideness", and so forth. As
noted before, terms like long and wide are unmarked, and
when someone wants to know the width of a road,
'e does not necessarily assume that
it is wide. What is its width? means what is its (degree of)
wideness catenality? (or narrowness catenality if
narrowness is positive). Thus, the quasi-monad of
the width catena is at the same time an explicit triad, namely
of narrowness, the neutral or perineutral neither narrow nor
wide and wideness. The quasi-monad of the speed catena is
nothing else than the motion catena in one sense and the
slowness catena in another.
By calling a predicative whole "a quasi-monad" we force ourselves to
ultimately distinguish three types of extensional elements of that whole;
by calling a predicative whole "a quasi-duad" we force ourselves to
recognize the bipartite structure of one of its two extensional subsets
(in the case of
bipolarity catenas), or we force ourselves
to look upon the first subset as part of the second, and the second subset
itself as of a tripartite nature (in the case of
extremity catenas); by calling a
predicative whole "an explicit triad", we force ourselves not to forget the
third predicate or predicative subset in addition to the two
This classification of catenas on the
basis of the existing vocabulary of the ordinary, nontechnical
variant of the language employed does, strictly speaking, not
tell us anything about catenas themselves; it merely tells us
something about linguistic usage. Yet, this grouping together on
the basis of language spoken is very useful as it will make it
easier to switch from the ordinary or traditional way of
thinking in that language to catenical thought. It will be
practically impossible now to ignore that there are really three
primordial kinds of catenated predicates involved where formerly
only one or two, or more than three, were believed to exist or
to be primordial.