Each catena is a totality of all atomic positivities, one atomic neutrality and all atomic negativities which are inseparably linked together. Having a positive predicate of catena C is the complete positivity of catena C, having a negative predicate of catena C the complete negativity of that catena. Loosely, we call having a positive or negative predicate "predicates" too. They are, then, improper predicates. Altho improper, we classify them as catenated predicates with the atomic, proper predicates to which they refer. Typical, improper, catenated predicates we have thus distinguished are, besides monopolarity (positivity or negativity), moderateness and bipolarity. Now, there is also a limiting case we have not yet discussed. It is the predicate having a predicate of catena C, not just a monopolar, perineutral or bipolar one. The catena 'subset' corresponding to this predicate is the improper 'subset' of the extensionality of the catena concerned, that is, the entire extensionality itself.

A primary thing which has a predicate of a catena is a 'catenal', and the predicate of having-a-predicate-of-a-catena is 'catenality'. (These semi-neologisms are introduced here because of the importance of the distinction between catenality and noncatenality, and --as we will see-- also between noncatenality and neutrality.) If not further qualified, catenality is a derelativized relation since a primary thing may be catenal with respect to one catena or system of catenas and not catenal with respect to another catena or system of catenas. When catenality is interpreted in its most general sense, that is, with respect to any catena, it is questionable whether there is any primary thing that is not catenal. At least all objects are catenal.

Catenality is not what all positively catenal (for example, happy), neutrally catenal and negatively catenal (unhappy) persons, objects or things have in common (and what they do not have in common with other things). So far as this aspect is concerned, positively, neutrally and negatively catenal things have nothing factual in common. They may have the possibility of being positively, neutrally or negatively catenal in common, but that is a modal, not a factual, condition. Catenality is not what all positivities, the neutrality and all negativities have in common either, because what they may have in common are secondary predicates, and as a predicate of primary things catenality is a primary predicate (albeit improper and, strictly speaking, not existing on our construction).

The differences between catenality, noncatenality and neutrality or neutral catenality can easily be demonstrated by means of the motion- and happiness-catenals. 'Motion catenality' is having a predicate of the motion catena, that is, having the predicate of being-in-motion or of being-at-rest. It is concrete things which have such predicates. Since abstract things are neither in motion nor at rest (certainly not the predicates of the motion catena themselves), they are noncatenal with respect to the motion catena. 'Happiness catenality' is having a predicate of the happiness catena. It is sentient beings which have such a predicate. Noncatenal with respect to the happiness catena are insentient, concrete beings like stones, plants and artifacts, and all abstract entities. They are not happy, not neutrally neither happy nor unhappy, and not unhappy; they are noncatenally neither happy nor unhappy. (The question of which beings are exactly happiness-catenal, and when, is a scientific one, and the answer to this question need not concern us here.)

Neutrality with respect to the motion catena, or motion-catenated neutrality, is being-at-rest. This is something entirely different from being-abstract, that is, being noncatenal with respect to the motion catena. A thing which is at rest is not less 'concrete' (in the sense of motion-catenal) than a thing which moves. Happiness-catenated neutrality is the predicate a sentient being has when it is responsive to (real or imaginary, oneiric or nononeiric) impressions, and when it is neither (made) happy nor (made) unhappy. This state of being is wholly different, again, from that of a being (even if an object) which is not responsive to impressions at all and which cannot even be brought into a certain happiness-catenary state (at least not at the moment concerned). So when people say "neither happy nor unhappy", they may refer to two basically different states of being. Not happy could even refer to one of three different conditions: (1) unhappy, the opposite of being-happy; (2) unhappy or neutrally neither happy nor unhappy, the catena supplement of being-happy; or (3) insentient, that is, noncatenality with respect to the happiness catena.

While catenality is a limiting case of an improper, catenated predicate, it does not seem appropriate to classify it as a catenated predicate itself, simply because there is no extensional catena element left to which it is catenated. Conceptually it may be inseparably connected to noncatenality but that is not a catena element either. (Noncatenality would even be a privative pseudopredicate, if catenality had been a proper predicate.) Moreover, every predicate is 'linked' to its negation denoted by non-, of whatever order or type.

We have now distinguished three catenical, main categories of predicates: (1) catenated (primary) predicates; (2) catenary (secondary) predicates; and (3) two (sorts of) noncatenated, primary predicates, namely catenality and noncatenality. As primary things can only have primary determinative attributes, and secondary things only secondary determinative attributes, the different catenical concepts and the corresponding terms should not be mixed up. Thus primary predicates (concepts, numbers or secondary things) may be positive as secondary things, but objects and other primary things can only be positively catenal. (If they are called "positive", "neutral" or "negative" nevertheless, these words may be used in a different sense, often in a sense specifically related to one or a few catenas only.) Objects may be good, bad or something else, but goodness itself is absolutely not good (or bad) -- it might be goodness-predicative and goodness-catenary (or badness-catenary), that is, part of a goodness- (or badness-)catena. Only objects or other nonbasic, primary things are catenal (for example, happiness-catenal) -- other things can only be catenary (for example, happiness-catenary). And everything that is catenary is always noncatenal.