An attribute or relation is a kind of secondary entity (if not of a higher order) which a primary entity, like a person, has (or had or will have), can have or should have; or which it does not, cannot or should not have. If it has it, this having of the predicate in question is a (specific) fact, that is, a factual condition; if it can have it, a modal condition; if it should or ought to have it, a normative condition. As explained in section 3.1.3, the concept fact must be defined in terms of a nonmodal, nonnormative is or has, and the concept norm or normative condition in terms of a nonfactual, nonmodal should (be/have). A 'normative condition' is, then, a specific situation in which a universal or general 'norm' applies. Neither norms nor normative conditions, or, for that matter, modal or factual conditions, are entities in the first- or second- or any higher-order domain of discourse. Thus, on our ontology a normative condition does in no way resemble an attribute or relation as existing in the second- or a higher-order predicative domain. That is also why it is preferable to speak of "auxiliary series" rather than of "catenas of factual values" (that is, degrees of realization), "modal values" (probabilities) and "normative values", each corresponding to their own attribute or relation.

If something has a high value on the normative auxiliary it may be called "normatively superior" or "good", and if something produces a high or higher value, "right". It is obvious that such a value, or 'goodness' or 'rightness', is not a quality like tallness or any other primary attribute. If 'goodness' is applied to a person or other primary thing, it does at least play the same role as a primary attribute, but if it is applied to attributes, relations or situations even that is not the case.

Value (in the normative sense), goodness and rightness have to be defined in terms of normative superiority, or of a normative auxiliary. The connection is that something that should be, should be had or should be done is itself normatively superior or promotes what is normatively superior. One may also reverse the definitions and define (normative) superiority or should in terms of (normative) value or goodness. Whichever way is preferred on this level of reasoning, there is some conception involved which is incapable of definition. In the factual sphere it is fact, (factual) value, degree of realization or (factual) being which is equally incapable of definition. This has been argued before, but with the use of the wrong analogies.

We must start with noting that, while they belong to the same auxiliary series, goodness and badness correspond to different 'values'. (Now using value in a general, auxiliary sense.) When goodness is then compared with, for example, factual tallness, this tallness corresponds to particular values of the collection of a particular predicate catena. If the normative auxiliary series has negative, neutral and positive values like a catena, and if goodness corresponds to (a) positive value(s), then goodness is normative positivity, and then its analog in the factual sphere is factual positivity. Perhaps tallness is a form of factual positivity, but it is not factual positivity itself. The analog of factual tallness is not goodness but normative tallness, that is, the normative condition (or 'fact' in a loose sense) that something should be tall. Even if both goodness and tallness were incapable of definition, it would not be because they have the same status.

A major objection against goodness being indefinable like redness or some other 'absolutely simple quality' is that people do not all agree that certain objects are good in the way they all agree that certain objects are red --and tall?--. There is no test for value, it is said, like there is a test for fact. The correct analogy, however, is not between tallness or redness and goodness, but between the question whether a certain object is tall or red, and the question whether it should be tall or red. But, for the sake of argument let us agree that there is a test for the former, and not for the latter. The kind of test referred to is, then, one which makes use of 'absolutely simple' observations, at least so far as a factual condition like that of redness is concerned. Yet, even without these kinds of test, people usually do have theoretical, ethical standards by which they judge whether something should or should not be the case in a moral sense. To arrive at such judgments it suffices to have one or a limited number of general normative premises, but it is indeed never possible to observe in a direct sense whether something should or should not be the case, like it is sometimes possible to directly perceive whether something is or is not the case.

Ethical intuitionists would not agree with what is averred here: they claim that what makes something good is a direct sense or feeling on a person's part that it is so, or --reformulated in terms of the triadic sphericity of reality-- what makes something as it should be is a feeling on a person's part that it is as it should be. However, this sort of reasoning which confuses the world with thoughts or feelings about the world we must repudiate as we did several times before. Also our position towards intuitionism is instrumentalistic tho: we can live with the diehards of intuitionism who are not willing to give up their belief. All we demand is that they intuit the same as what we arrive at by thinking about it, and that they accept that what we arrive at by reasoning is the same as what we would have apprehended by intuition. Should they intuit something different, while wanting to convince us nevertheless, they will have to turn to reasoning as well, whether they like it or not. (And since even mathematicians have given up the belief in a priori concepts and self-evident truths, they had better be prepared.)