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 would be 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 are 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.
