To exist, a whole of things must have at least one real attribute in addition to its parts. (See 1.3.2.) Not only should such an attribute not be a pseudo-attribute, it should also be an attribute of the whole itself rather than of one or more (or even all) of its component parts. (It may be a derelativized relation tho.) So far as such a whole-attribute is a prerequsite for the existence of the whole, it must be logically independent of the part-attributes. In other words, a whole is a gestalt, that is, a unit with attributes in addition to and not derivable from its parts in summation. It is in this literal sense that a whole is 'greater' than the sum of its parts.

If whole-attributes could be derived from part-attributes, every set or 'sum' of concrete individuals could pop up as an entity, since one can always conceive of a physical attribute which would correspond to the 'sum' of the part-attributes. Thus, the volume of the whole, which is the total of the volumes of its parts, would be a characteristic of the whole, however far separated from one another its parts. Another such 'improper' whole-attribute would be the one relating to the average value of its component parts.

The difference between attributes of a (whole) thing and attributes of its parts is often crucial and has but too often been blurred, for example, in discussions on individuation and identity thru time. Somebody who has brown hair first and gray hair later in life does not have any different property at all later on. Instead, such a person('s body) has a component part or parts (the person's hair) which were brown first and gray later on. It is this part or these parts which change properties. Strictly speaking, a whole consisting of several phenomenal parts actually never has any color of its own. If it is said to be parti-colored or to have one or more colors, these colors are the qualia, qualities or attributes of its parts. Only if all parts have, or seem to have, the same color, may this color, for the sake of convenience, be attributed to the whole consisting of these parts.

Now, some predicate expressions precisely refer to the having of parts with certain characteristics or of a certain kind. In the above example one might come up with having brown hair (or <-- has brown hair>) and having gray hair as predicate terms designating a property of somebody considered as a whole. Such predicate expressions have to be devised in an objectualist ontology which cannot handle the part-whole relation very well. On the attributivist construction, however, it is evident that such constructions are completely artificial and do not denote any real attribute of the whole itself. Particularly notorious expressions of this ilk are being cordate and being renate, because they happen to have the same extension, so far as known. Cordateness is having a heart; renateness is having kidneys. As hearts and kidneys are organs or parts of the animal beings which have them, to say that an animal being is 'cordate' or 'renate' is nothing else than to say that it has parts of a certain type. Such expressions could be constructed for any type of having parts, for example, for a table which would be 'legged' or 'four-legged'. But of course, this would in no way force us to accept as real attributes like 'leggedness', 'four-leggedness' or, for that matter, quadrupedality.

Cordateness is having a heart, not the property of having a particular part which is a heart or which has the property of being a heart (provided there is such a unitary factual attribute). If it were a question of having one particular thing which is a heart, there would be as many cordateness properties as there are hearts and mammals. Each such property would, then, be a haecceity predicate of the mammal concerned, that is, a predicate which no other thing has or can have as well. To avoid this consequence the predicate being a heart must be brought in, or a combination of predicates necessary to keep the same total meaning of (being a) heart. Cordateness is then the property of having something as a part that is a heart. 'Cordateness' and also 'renateness' are therefore pseudo-attributes. It is easy to understand why they are not synonyms altho cordate and renate are true of the same things: being a heart is just not the same as being a kidney, even tho one might have thought that having a heart would amount to the same as having a kidney. The ontological heartiness of logicians with kidneys has allowed some theoreticians to array their body of thought with the most fancy of predicate terms, also where the structure of wholes and parts is concerned. From a constructional point of view, however, it remains important that attributes of parts (such as being a heart) can be clearly and distinctly told apart from attributes of the whole (other than pseudo-predicates such as being cordate or having a heart). It is on this distinction that the existence of wholes or gestalts depends. Without the recognition of this distinction one will never gain a full insight into the configuration of these wholes.