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MODEL OF NEUTRAL-INCLUSIVITY
BOOK OF INSTRUMENTS
CATENAS OF ATTRIBUTES AND RELATIONS
WAYS OF CLASSIFYING CATENAS

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.


©MVVM, 41-57 ASWW
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Model of Neutral-Inclusivity
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