The neutral predicate of any difference catena is a predicate of equality. If the difference catena is monovariant (and bicatenal), every predicate of the original catena corresponds to one predicate of the difference catena. Given that a catenal has a certain predicate of the original catena, it must then have a certain other predicate of the difference catena. Given that it has a certain predicate of the difference catena, it must have one particular original predicate (if an extremity-difference catena) or one of two original predicates (if a neutrality-difference catena). It does therefore not make sense to consider the normative value of a predicate of a monovariant difference catena. The superiority or inferiority of such a predicate is the superiority or inferiority of the one or more predicates of the original catena to which it corresponds, since we hold that an original catena takes precedence over a derived one. Hence, the value of the equality of a monovariant difference catena would simply be the value of the original predicate or predicates corresponding to it.

Bivariant equality can be either monocatenal or bicatenal. Monocatenal equality is equality between component parts of one and the same whole, whereas bicatenal equality is equality between different wholes. The form of catenated equality which is the limit-element of the monocatenal bivariant positivity-difference catena stands for being-neutrally-nondirectional. (The positivity of this catena stands for having-a-positive-direction or being-positivity-directed.) The form of catenated equality which is the limit-element of the monocatenal bivariant neutrality-difference catena is well-known as symmetry. A catenal is of course neutrally nondirectional and symmetrical, regardless of the value it assumes with respect to the original catena. All other things being equal, being neutrally nondirectional and symmetrical are thus states of being which are normatively superior to being directional and asymmetrical. (Those who would like to narrowly confine the notion of normative superiority to ethical matters, should realize that our position is ontologically not different here from that of people claiming that beauty is an ultimate or perfective value, that is, normatively superior to ugliness.)

Some may associate being-nondirectional or a 'lack of direction' with indirection or aimlessness. But if aimlessness, that is, a 'lack of aim or purpose', is wrong, it is either wrong, because processes do take place and people do act without any aim or purpose or because processes do not take place and people do not act, where this would further a good end. Since the principle of neutrality makes neutrality the ultimate aim or purpose of everything and everyone, it does not justify the former kinds of aimless processes or actions, while the relevantistic interpretation of this principle can justify a process or action which is neutral-directed and thus 'directional'. In such a case, however, the ceteris paribus clause does not hold. Therefore, the catenary superiority of being-neutrally-non-directional does not warrant the kind of indirection or aimlessness which is wrong. (Note that being-non-directional denotes both the neutral 'being-nan-directional' and the noncatenality of the same aspect.)

The difference between mono- and bi-catenal, bivariant equality is not that the one notion of equality is comparative and the other not. Both are comparative in that we compare different catenals, but the catenals concerned belong to a whole which is catenal itself in the former case and do not belong to such a catenal whole in the latter case. Yet, when people speak of "equality" or even of "comparative equality" in traditional terms, they tend --translated into catenical parlance-- to think of the neutralities of bicatenal bivariant difference catenas only. Furthermore, they seem to have always taken it for granted that these difference catenas were positivity-difference catenas. (Extremity-difference catenas amounts to the same here.) One question we will have to ask ourselves later in this division is therefore why equality, even bicatenal bivariant difference-catenary equality, should solely be associated with an extremity- and not with a neutrality-difference catena. Evidently we must then also examine whether it matters whether the one aspectual value is taken for the difference catena or the other.

Nature itself provides us with weighty examples of bicatenal bivariant nonextremity catenas namely those derived from the spatial basic catenas. But many people would not notice that the neutrality of this kind of catena is a form of equality. It is the predicate of having-the-same-location. Part of the reason is, perhaps, that different material primary things can never have exactly the same location, however great a role the nanaic force of gravity and the nanaic nuclear force play to bring this about. A more important part of the reason is probably that people cannot select the principles of nature and that people are not physical bodies. They can be ignorant of certain principles, they can adopt principles by hypothesis and they can call structurelessness "chaos", but this is not the kind of freedom which alters the natural ground-world itself. Whether they like locational equality or not, gravitation is here to stay.

Bicatenal bivariant equality did become important for many people when they started thinking of it as a principle in interpersonal, social or distributive affairs. It is especially in this context that we should take a closer look at the temporal aspect of equality. For saying that two catenals are equal in a certain respect is not necessarily saying that these two catenals are different individuals which are equal at the same moment. And if they are, it is only their equality in the future we could bring about (for example, by giving each of them one orange). But we can also bring future equality between two individuals about at different moments in the future (for example, by giving one a banana the one day, and the other a banana the next day). In these two instances in which the equality is a relation in the future, a consequentialist scheme will tell us what to do, provided that the good to bring about is here equality (or bicatenal bivariant equality in interpersonal, distributive affairs). It is a limit-case when one of the catenals is considered at the present moment, while the other is considered at a moment in the future. Can it be called "a consequence of one's action that B will receive the same amount of a certain good as A receives right now"? It will certainly become counterintuitive to speak of "consequences" and of "a consequentialistic scheme", when the equality between one catenal in the past and one in the future is considered. To give an example: striving for equality between A and B, we may decide to give an apple to B tomorrow, because A did already get one yesterday. (Here it does not matter from whom or in what way.)

The norm of neutrality is 'temporally neutral' in that the normative superiority of neutrality does not depend on the moment or period of neutrality. Hence, equality as a neutral predicate may be equality in the future, in the present, in the past and between the future and the present, between the future and the past and between the present and the past. It is only because of the asymmetry of time, or for reasons of causality, that the good of equality cannot be produced in the past. But this is a modal condition and not something that follows from the ananorm, for the ananorm itself is future-, present- and past-regarding. The neutralistic doctrine may be labeled "consequentialistic" insofar as it is future-regarding and dealing with causal effects; it is 'antecedentialistic' insofar as it is past-regarding ; and --who knows-- dependent on the definition also 'deontological' insofar as it is present-regarding. What is certain is that it is a past-, present-, and future-regarding teleological doctrine in which nothing else than catenated neutrality in general and catenated equality in particular ought to be chosen as a goal of one's action. The form of bicatenal bivariant equality to be taken into account is, then, not only equality in future relations but also equality in temporal relations which extend from the past to the present or future.

When temporal equality concerns one and the same individual we do not speak of "a bicatenal bivariant difference catena" but of "a differentiation" and of "a time-differential catena". Neutralness is then sameness or constancy and, when there is a capacity to restore a disturbed equilibrium, stability. This sameness, constancy or stability is normatively superior to change and disturbance. But when differentiation and time-differential neutrality merely serve a status quo of inequality, or merely perpetuate polarity in terms of the original catena, such neutralness is not ananormatively superior and positive, neutral-directed action can then be warranted. Likewise, even where there is bicatenal bivariant equality, we must not lose sight of the original predicate catena. That catena, too, has a neutrality which is ananormatively superior. The main objection against traditional egalitarianism is that it would prefer an equal division of unhappiness or poverty to an unequal division of happiness or wealth. The same ideologues and philosophers who have rejected utilitarianism for neglecting distributive justice, egalitarian or not, have rejected egalitarianism for neglecting well-being, utilitarian or not.