As regards the original catena of the energy increase catena no neutrality is given, since energy in this sense is always nonnegative. Taking the mean energy of all objects in the closed system mentioned above, this mean would, then, only determine the amount of energy under which an object does have little, and above which an object has much energy, at least if no perineutrality were to be distinguished. Unlike the increase-catenary mean, which is always 0, this mean is variable in physical terms. It changes as the number of objects changes (because of fusion and fission, for instance).

If someone did not have the slightest idea of what a short or tall, adult person would be, and 'e were confronted with (the body of) an adult person of a height of 150 cm, 'e might call that person "short" if 'e is shorter than 'imself and "tall" if 'e is taller than 'imself (that is, so much shorter or taller that it is noticeable). The average height in this imaginary, closed system would be a height between that of 'er own and that of the other person's body. If a third person turned up of exactly this average height, 'e would be called "neither short nor tall" or "of middling height" (assuming that the catenization would be linear).

Yet, this picture is not a realistic one, because in practise everyone who knows how to use the words short and tall has already compared heights many times, and will also have an idea already whether 'e is short, medium or tall 'imself. Moreover, 'e will always use the expressions in such a manner that short, medium short or medium tall and tall cannot denote one and the same person or thing at a time. Such a person who knows how to use the expressions has already formed some mental frame of reference before facing a person 150 cm tall 'e is able to call "short". Even if 'e merely compares the other person's height with 'er own height, 'e has still to know whether 'e is short or tall or of middling height 'imself. Knowing this, 'e knows roughly what height is that of adult people who are neither short nor tall. Thus when the other person thereupon starts growing many mm consecutively (as in the imaginary sorites example), 'e only has to compare that other person's height with 'er own height and with what is the normal (neutral) or moderate (perineutral) height in 'er frame of reference. This means nothing else than that 'e sticks to the procedure 'e started out with, when 'e called the other person "short" the first time.

The hypothesis of mean-neutrality implies that an adult person who has the mean height of all the adult persons belonging to a real or imaginary group on which the shortness catenization is based is neither short nor tall. Like in the case of the amount of energy objects have, this mean is variable in a physical sense. It is particularly variable because the limits of the special collection of catenals are very vague themselves -- there usually is no completely closed system in this respect. That is why it is not sensible from a pragmatic point of view to emphasize the mean value of one special collection of catenals at one particular moment. And we are usually not able to measure this mean either; we would just have to estimate it. Thus even granted that the mean, theoretically speaking, exactly determines the neutral value of the catena for the special collection concerned, it still does not make the boundary between positivity and negativity sharp in practise. Moreover, it should not go unnoticed that by the very addition to the collection of catenals of one object to be judged, the mean and neutral value itself moves in the direction of the value of the object to be judged.

As there is no sharp boundary between positivity and negativity in practise when the neutral value is not clearly given, neither nor does usually not refer to neutrality here, but to perineutrality, together with medium, middling and moderately. Since the position of the neutral value is hard to establish, the perineutralities of such catenas remain recognized as such in common parlance. Where the boundary between positivity and negativity is sharp, and where the neutral value can easily be assessed, perineutralities tend to disappear and to reemerge as the positivity of a neutrality-moreness catena (as in the case of slowness). It is because of the practical impossibility to calculate the universal mean value that the scope of catenization must always be special when the derivation is factitious and the position of the neutrality not sufficiently clear.

©MVVM, 41-57 ASWW

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