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MODEL OF NEUTRAL-INCLUSIVITY
BOOK OF INSTRUMENTS
HAVING AND THINGNESS
ATTRIBUTES AS ULTIMATE CONSTITUENTS

1.4.3 

CONCRETE AND ABSTRACT


If we compared the ultimate factors of a system to physical atoms, then concretums could be compared to molecules. And --as has been argued too-- as no fragment of a molecule of water is water, so no fragment of a simplicial concretum is concrete. Moreover, since a glassful of water is water, but not a molecule of water, it has been suggested that individuals of which a concretum is a proper part be called "concrete", altho they are not concretums themselves. Concrete would, then, mean that the individual's extensionality were exhaustively divisible into concretums. Thus, because human beings and their parts are concretums, humankind would be 'concrete' in the terminology of such a constructional system. We will not adopt this terminology. Instead of it we will later define concreteness in such a way that a concrete thing must be either in motion or at rest. (Abstract things are neither in motion nor at rest.) Furthermore, one concrete thing must in this view have one velocity with respect to a certain frame of reference. Hence, a glassful of water may be considered to be a concrete individual in this sense but humankind is not, since it is not part of the meaning of the term humankind that all humans always have the same velocity. (The simile was therefore not valid.) Humankind is either the whole of all human beings with its own attributes, or it is the collection of all human beings, the extension of being human. In the first case humankind would exist as an abstract entity, assuming that its predicament contains attributes which characterize it in a way logically independent of (the predicates of) its components. (The number of humans or some human average will therefore not do as a characteristic.) In the second case 'humankind' is a conceptual construct denoting the set of all things that have a certain characteristic combination of properties in common. In neither case humankind is concrete itself in our manner of speaking, but it or its extensionality is exhaustively divisible into concretums nevertheless.

For each spatial dimension concrete things have a negative velocity ('the' property of moving in a negative direction), a neutral velocity (the property of being at rest) or a positive velocity ('the' property of moving in a positive direction). We will use the word object only for those things which have one of these properties. (To be more precise, they are derelativized relations: something 'is at rest', if it does not change place with respect to a particular, other object or frame of reference.) The properties of motion and rest or motionlessness are primary attributes which belong to concretums but the negativity and positivity of certain kinds of motion and the neutrality of motionlessness are secondary attributes. The attributes of primary attributes are never primary and therefore the properties of velocity (of motion and motionlessness) do not have a velocity themselves. Negative, neutral and positive velocity are abstract entities tho they are things in the first domain of discourse. (We thus employ abstract in the sense of not having any neutral or unneutral velocity, which is roughly synonymous to immaterial or intangible.)

Altho objects are solely found in the primary domain, it follows that it would be a serious mistake to believe that all things in the primary domain were objects, that is, concrete. Whereas some primary things, like properties, are abstract entities which do not even have a concrete component, other primary things, like humankind (if existing as a whole), are abstract entities which do have components which are concrete. Secondary things and things of a higher order, however, are always abstract. If they are wholes consisting of one or more component parts, they are abstract wholes of abstract entities.


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Model of Neutral-Inclusivity
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