It depends on the context what one calls "small", "medium large" or "large" and, furthermore, on the size of the things one is familiar with in such contexts. This familiar is, then, a psychological notion: to be able to call some things "small" and other things "large" it is not necessary to see all these things together at one and the same moment. It certainly is the easiest and most accurate way of comparison, but it is not a prerequisite for the meaningful use of terms like small and large, for we do have a memory which does not only make us remember physical sounds or sound combinations like small, medium and large, but also objects of a small, of a medium and of a large size. In both cases the things remembered are of the same physical or perceptional nature, especially when taking loud, medium loud and soft as examples of catenated predicate expressions.

The confrontation with new things in the same context may change someone's idea of what is 'small' or 'large', 'short' or 'tall', and so on. Thus, if someone has always lived among adult people whose average height used to be 160 cm, and then moves to an area where the average height of adult people is 200 cm, 'e will eventually start calling people "short", whom 'e used to call "tall" or "medium (tall)" before. On the other hand, if someone had never been confronted with anybody else, and only knew 'er own (body's) height in terms of centimeters, 'e would have no idea whether 'e were 'short', 'tall' or something in between; at least, 'e would have no reason to consider 'imself unneutrally catenal, that is, short or tall.

The fact that the use of predicate expressions like small, short and close is context-dependent implies that we do not compare a catenal with all other things in the universe that are catenal with respect to the same catena, but only with catenals in a particular proper subset of this universal set. And the fact that we may describe two things with the same physical dimension in different catenical terms means that the context or special subset also determines where we draw the line or fuzzy border between smallness and largeness, between shortness and tallness, between closeness and farness, and so forth. Hence, the transformation from empirical to catenical value is related to a special collection of catenals, not to the universal collection of all catenals. That is why we will say that the scope of catenization is 'special', rather than 'universal' in these instances.

To compare a catenal with a number of other catenals from a catenary angle is in the first place to compare it with their mean value. Unlike their minimum and maximum value, and unlike their statistical mode, this is a truly general value of such a collection of catenals. If it is the mean of all the things that are catenal with respect to the same catena, it is a universal value. A catenization in which this universal, mean, empirical value is taken as a neutral catenical value is therefore a catenization of universal scope. Whether this mean is an average or an arithmetic mean, however, depends on the type of catenization function. In general: a mean value is the value m for which

 k(m) = SIGMA k(vi) / n.

If  ûi  [vi with a caret over the v, the symbol for the catena value] or k(vi ) = A*vi + B, then m is indeed the arithmetic mean; but, for example, if k(vi ) = A*log vi + B, m is a geometric mean; and if k(vi ) = A*1/vi + B, m is a harmonic mean.

The mean value can also be taken as a neutral value if the catenization is special. It is, then, simply not the mean over the class of all the catenals but over a proper subclass thereof. It depends on the relevancy of the distinction drawn between the class of catenals taken into consideration and all the other catenals whether this can be justified. But in a closed system the mean can be based (or 'must' be based) on the mean of this particular system itself. This can have no repercussions on communication, because where there is communication the persons communicating cannot belong to different closed systems themselves, even if vehemently disagreeing. If someone belongs to a tribe, for instance, which never had any contact with other tribes, it does not matter that 'e bases 'er closeness- and smallness-catenization entirely and solely upon the distances and sizes of catenals in 'er own environment. It is not until 'e comes into contact with persons belonging to other tribes with different catenizations, that 'e cannot treat 'er own special collection of catenals as a closed system anymore (and neither can those other people). The referential collection of catenals compared with has now to be extended, but in practise it cannot be extended so far that it would comprise all the things in the universe that are catenal with respect to the same catena.

©MVVM, 41-57 ASWW

Model of Neutral-Inclusivity
Book of Instruments
Catenas of Attributes and Relations
The Scope of Catenization