A catena of which the extensionality is implicitly subdivided into two subsets in ordinary language, assuming that no subset is disregarded, is a 'quasi-duad'. (Quasi-, because every catena is to be interpreted as a triad in the end.) If the predicative units distinguished are the complete or non-perineutral bipolarity and the neutrality or perineutrality (disregarded or not), this quasi-duad is called after its bipolarity: "a bipolarity catena". If one unit is an extremity and the other the catena supplement limited by it, we shall speak of "extremity catena". Every extremity catena is called after the extremity explicitly recognized in the language concerned.

There are no separate expressions for the monopolarities of a bipolarity catena. They have to be described by means of circumlocutions; for example, motion in positive direction and motion in negative direction, positive abnormality and negative abnormality, positively charged and negatively charged.

If we assume that a predicate like normality is solely catenated to abnormality (and that there is no neutral predicate neither normal nor abnormal), then the catena of both predicates is a quasi-duad. (It is something else of course to assume that there is no such catena at all.) This quasi-duad of normality and abnormality can only be conceived of as a bipolarity catena of which normality is the neutrality or perineutrality; abnormality is, then, not neutral, or at least not perineutral. To look upon normality as a neutrality between positive abnormality (what is too much) and negative abnormality (too little) would imply that no variation is possible within the range of the normal. This would probably be incompatible with ordinary usage where within the limits of the 'normal' some variation seems still to be possible, altho the extent to which deviation is tolerated may diverge considerably (not in the least when abnormal is predominantly a doxastic, normative notion). The fact that normality is probably to be interpreted as moderateness in ordinary usage has much to do with the fact that the catena of which abnormality is the bipolarity is a catena of special scope without a point which is clearly neutral. (What special scope means in this context will be discussed in the division on the scope of catenization.)

As terms for the predicates of an abnormality catena normal and abnormal are understood in a purely statistical sense, as designations from the perspective of the mean or most frequent value in a frequency distribution. They are, then, not used in some normative or evaluative sense like according to a rule or standard. If abnormality is taken to be the opposite (in the catenical sense) of normality, limited by a neutral attribute neither normal nor abnormal or the corresponding perineutral predicate, the catena of these attributes is an explicit triad: the normality catena. The direct reason to regard normality here as the positivity of a positivity catena is not that it tends to be evaluated positive in ordinary language, because this is probably due to the series of misassociations from affirmation to affirmity to positivity to goodness, and vice versa. The direct reason is merely that normal is the base-word from which abnormal has been derived. But indirectly the above associations appear to be the very reason for the direction the derivation has taken in ordinary language.

If there is a link between the abnormality and the normality catenas, then the perineutrality of the former catena is the positivity of the latter one. In this case it can also be defended from a (nonlinguistic) systematic point of view that the abnormality predicate of the explicit triad must be designated a negativity, because the values of this predicate deviate more from the mean value or the 'mode' than the value of the concatenate predicate neither normal nor abnormal. 'More abnormal' is, then, less like what is related to the statistical mean or mode.

The relationship between the motion and the slowness catenas is of a similar nature: slowness is the perineutrality of the quasi-duad of motion and rest, and at the same time the positivity of the explicit triad of slowness, fastness and the neutral predicate neither slow nor fast. The neutrality of the motion catena, rest, is in a way an extreme form of slowness and the positivity of the slowness catena comprises in terms of the motion catena slow motion in a positive direction, rest and slow motion in a negative direction. It will turn out that the slowness catena is the same sort of derivative catena as the normality catena, and that the motion and abnormality catenas are both original quasi-duads, that is, 'original' with respect to the derivative explicit triads; they are not necessarily basic with respect to a whole derivation system. (Theoretically it is not only possible to derive positivity catenas from bipolarity catenas but also the other way around -- something we will not attempt to do here.)

A catenary quasi-duad which undergoes transmutation to become an explicit triad has to be strictly distinguished from a quasi-duad which is simultaneously an explicit triad. Being both a quasi-duad and an explicit triad has nothing to do with derivations, but is a question of wealth of words. A catena which is both a quasi-duad and an explicit triad has atomic expressions for both the bipolarity and the two monopolarities. For example, change (in the sense of change of value or change of degree), increase and decrease all belong to the same catena: the quasi-duad of the change catena, which is identical to the explicit triad of the increase catena.

©MVVM, 41-57 ASWW

Model of Neutral-Inclusivity
Book of Instruments
Catenas of Attributes and Relations
Ways of Classifying Catenas