Until now we have only looked at one domain of discourse in isolation, namely that of objects, or of objects and attributes of objects. We have confined attention to the attributes and relations of these objects, and we have compared the capacities of the objectual and the attributive interpretations of formal systems to deal with the possession of these attributes and the existence of these relations. We have not yet considered the attributes and relations of these predicates themselves. Doing this will open up a new field, or even a second domain of discourse.

In the predicate calculus predicates of predicates are called "second-order". In principle this hierarchy of orders of predicate expressions is unlimited. An example of a predicate expression which is taken to be second-order is < (-- is a) color > 'because green is a color' and green [<green>] itself is a first-order predicate expression, 'because grass is green' and grass is chosen as an entity (or collection of entities) in the domain. An expression like unhealthy may be treated as a compound second-order predicate term which results when a productive process is applied to the second-order predicate term healthy, like in exercises are healthy. Unhealthy is then analyzed as if it would mean not healthy. The first flaw in this approach is that the prefix un- in unhealthy, like in unhappy or unwise , does not simply mean not. For example, something that or someone who is unhappy is not happy, but something that is not happy is not necessarily unhappy at all. As we will see later (in 2.3.2) no fewer than three possibilities' of not being happy must be distinguished instead of one.'

There are other objections that can be made against the above approach, such as treating the same term both as a first- and as a second-order expression, even tho it looks like this is done in everyday discourse. While words like healthy are also applied to attributive expressions, no-one could understand their meaning if one did not first understand what a healthy living being or person is. And in the latter usage healthy is not of the second but of the first order. That exercising is healthy should therefore be read as there is a causal relationship between somebody's exercising and somebody's being healthy/becoming healthier. In this way we still speak of a relation between attributes of the first order which is second-order itself. The difference is that causality is, then, always a second-order relation and health(iness) always a first-order attribute. In a hierarchy of orders it is important that expressions or entities of a different order have different names (something that does not apply to entities without order such as having-as-an-element or being-an-element-of and existing).

If we look upon grass as a basic object, then grass is green (assuming that this is true), grass is colored and grass has a color. This means that, if color is an attribute, it is just a first-order attribute but an indefinite one. Color is certainly not an ontic property beside being green, being red, and so on. It is rather a conceptually produced property: if something is green or red or .., then it is (said to be) colored, and then it has a color. Hence, being-green or greenness, being-red or redness, and so on, is having-a-color. Now, green is also said to be a color, but then green is considered a basic object in a domain of discourse, not a first-order attribute in such a domain. Treating color simply as a second-order predicate expression therefore passes by the tendency in everyday language to treat phenomena of perception, or objects of experience, as basic entities of the or a domain of discourse. Thus we speak of colors, sounds, feelings, smells and flavors as particulars and not as intensions of first- or second-order predicate expressions or something of that nature. In this respect everyday discourse seems to be phenomenalistic (and realistic) instead of physicalistic. The objectual interpretation of formal systems is just not very well suited to handle such an ontology in which both physical things like grass and phenomenal things like greenness or the color green are recognized as real entities.

The objectual and the attributive views are, strictly speaking, not dissimilar logical views. Yet, it is not impossible that the development of certain logical theories only makes sense in an objectualist frame of mind or, for that matter, in an attributivist frame of mind. Nevertheless, everything that can be formulated in attributivist terms can be formulated in objectualist terms, and vice versa, at least so far as the essentials of our conceptual framework are concerned. Given our ontological presuppositions, and in view of the constructional, normative doctrine to be expounded in due course, the attributivist instrument is much more adequate, however. Hence, we will use this tool from now on and look how it works in more detail.