1.4.2 |
ABSTRACTION AND CONCRETION |
As the ultimate constituents of our universe of discourse
are attributes, we are formally faced with a problem of
concretion. (See
1.2.2) But, actually, we have started the
other way around, namely with the assumption that complex,
concrete things have both component parts and attributes, and
those parts in turn also parts and attributes. We have thus
considered complex things and their parts to be of the same
ontological category, since they all have parts and attributes as
their elements. Yet, whereas complex things have attributes,
attributes never have things of that same category: a table may
have a weight, but (a) weight cannot have a table. (It may
belong to one at the most.) In subdividing complex things into
smaller things (parts of a lower type) we have first formed a
picture of abstraction which looks like the one in figure
I.1.4.2.1.
The crucial theoretical question is now whether we do arrive
in this way at components which are mere sets of attributes
(but which have relations as well). Without such an end to the
abstraction process one might object against the 'categorical'
discrepancy between things as parts and attributes and maintain
that this discrepancy remains, however far down the components
are subdivided into their elements. But then, one should bear in
mind that the question whether the difference is categorical
from any ontological point of view is the very matter at issue
here.
If parts and attributes can never be taken as ultimate elements of one and
the same thing, the aversion of this sort of combination may be the very
reason to postulate that there is an end to the abstraction ladder so
that all parts, that is, all things, ultimately only have attributes,
tho certainly not as
their elements or components.
A second point to take into consideration is that in the
beginning the things of our domain were phenomenal or material
things such as pens and fingers, but if there is an end to
materiality when subdividing these things, there should be
borderline cases. And indeed, there are such borderline cases:
elementary particles do not have 'material', that is, constituent
parts, and fail to count as bodies in this respect. They are
not material in that they are not decomposable into matter, and
yet they are material in that they are components of matter. It
is here where we have arrived at a level where we can merely
speak of an object's purely physical attributes and relations.
And it is here where mass and energy become one and the same,
where the material world transubstantiates to become immaterial.
At this level objects are purely 'intensional', precisely like
attributes, in that they have no extensional elements anymore.
If this is not correct for particles such as neutrinos, one may
assume that it still applies to 'truly' elementary particles,
unless one is absolutely unwilling to ever accept the existence
of such simplex objects.
By choosing attributes as the ultimate constituents of the
first and all other domains of discourse we have implicitly
postulated that there is an end to the abstraction ladder. That
there is, then, a beginning of a concretion ladder amounts to
the same: to approach the problem of concretion we are faced
with we reverse the picture of abstraction.
In general, every realistic constructional system needs at least one
primitive relation which will make it possible to differentiate
systematically between those abstract qualities (such as attributes)
which form concrete things and those which do not.
As the basic concreting relation one might choose togetherness,
in our case among attributes, which obtains between any two attributes
belonging to some one concretum or thing in general. (Choosing
having as primitive does not make a difference: two qualities
are 'together', if they are 'had' or possessed by the same
thing.) If the relation of togetherness did not hold between
any two attributes of a set (that is, if they did not belong to
one and the same thing), the set in question would simply not be
ontic, that is, (trivially) would not exist as a thing. The
notion of togetherness can subsequently be extended to obtain
not only between distinct, atomic qualities, qualia or elements
but between every two discrete elements of a concretum or other
thing. The elements may be component parts or attributes of the
whole.
In our constructional system a concretum may be conceived of as a
single physical body with all its parts and its
(whole-)attributes.
All the elements of such things 'are together', that is, bear the relation
of togetherness to each other, but the whole itself is not a part of
another thing in which it bears the same relation of togetherness to other
things.
In a biological or physical sense human beings, for instance, are
concretums but humankind is not a concretum.
An old metaphysical issue is that of the distinction and
relation between instance and quality. But as the 'atoms' of our
constructional system are attributes we have no problem since
they are 'fully repeatable, universal individuals'. The
instance/quality distinction is in our case an instance/element
distinction.
Whether we regard a whole as an instance or as an element (component)
simply depends upon whether we are concerned with its relationship to
its attributes (those belonging to its
predicament) or to a whole of which it is
itself a component part.
In our system instances of a property or attribute are
never entirely separate. They may be discrete in space-time and
in every other respect, yet they still have at least one common
element: the common attribute itself. As has already been
rightly argued before, attributes are not metaphysical sums of
various particles which would occur in several instances. When
concrete individuals which are believed to stand wholly by
themselves 'participate in' a single property, their similarity
is due to identity between at least one of their predicative
elements. This could be shown diagrammatically by having the
predicaments of the things in question overlap, by drawing the
identity relation between one or more predicative elements of
these things or by giving identical and unique names to
identical and unique elements.
