2.4.4 |
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 other half. 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
quasi-hexaduad".
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 as
"shallow-or-lowness". 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 'quasi-monadic predicate'.
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 monopolar ones. 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.
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