ESKO MARJOMAA
DIFFERENCE BETWEEN CONCRETE AND ABSTRACT
ENTITIES
ASPECTS OF RELEVANCE IN INFORMATION MODELLING,
PP. 90-96
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Introduction
The difference between concrete and abstract
entities can be expressed with the following
two characterizations
C1 A concrete entity is an actually sensed
particular occupant of a spatio-temporal
location; and
C2 An abstract entity is an entity, which
is not concrete.
There are, of course, also many other ways
to state the abstract/concrete distinction.
For example, Hale (1988: 86-87) has gathered
the following characterizations which are
not equivalent to each other (nor with C1
and C2, above):
(1) Abstract entities are not in spacetime
whereas concrete entities are;
(2) Abstract entities cannot participate
in causal networks but concrete entities
can;
(3) Abstract entities have only relational
properties while concrete entities have some
intrinsic properties;
(4) Abstract entities are universals and
concrete entities are particulars;
(5) Abstract entities are sets and concrete
entities are individuals;
(6) Abstract entities are never indiscernible
from one another whereas concrete entities
(sometimes) are;
(7) Abstract entities are human constructions
or creations, whereas concrete entities exist
independently of human minds or language;
(8) Abstract entities are types and concrete
entities are tokens;
(9) Negative terms apply, but positive ones
do not, to abstract entities;
(10) Concrete entities are known by observation
whereas abstract entities are known in some
other way, e. g., by abstraction, by intuition,
a priori;
(11) Concrete entities "can be pinned
down by pointing" but abstract entities
cannot be ostended;
(12) An individual is concrete if and only
if it is exhaustively divisible into concreta,
i. e. into fully determinate parts, and an
individual is abstract if and only if it
contains no concretum.
We can add here also the following one:
(13) All concrete entities have in common
the characteristic "existend",
but it is quite questionable whether there
is any characteristic which all abstracts
have in common.
Strictly speaking, all these "definitions"
are imperfect (including C1 and C2 above,
but perhaps not (13)) in the sense that being
a concrete (or abstract) entity always involves
an agent: An entity can be concrete for an
agent A only if it is actually sensed by
A.
Hale (1988: 85) gives us three conditions
for the legitimate epistemological use of
the abstract/concrete distinction: 1) Clarity
Condition: it can be clearly drawn; 2) Ontological
Significance Condition: it can be shown to
divide our ontology into two fundamentally
different kinds; and 3) Epistemological Significance
Condition: it can be shown to have some epistemological
significance.
These conditions are not very easy to fulfil,
but I think that on the basis of C1 and C2
this difficulty would vanish. This, however,
requires that we are able to define "abstractness"
using positive terms. And one way to solve
this latter "definitional" problem
is first to try to define the degree of abstractness.
But this is not any easy task, because of
two main reasons:
(1) There are many different characteristics
of abstract entities - such as connectivity,
bootstrapness, epistemological depth, relationality,
relativity, ontological rank, complexity,
generality, degree of quantification (i.
e. the logical type of the entity), etc.
- in respect to how they differ from concrete
objects and maybe also from each other.
(2) There are many different ways to give
weights to different characteristics of abstract
entities.
We can also characterize the difference between
concrete and (highly) abstract entities by
saying that the extension of an (highly)
abstract term is not very easy to determine,
while the extension of a concrete term is
generally easier to determine. Strictly speaking,
it is not correct to use the expressions
"abstract term" and "concrete
term", because the terms do not usually
differ in degree of abstractness, but the
extensions of the concepts connoted by the
terms. So, it is better to speak about "concrete"
and "abstract extensions" of the
concepts connoted by "singular"
and "general terms", respectively.
However, for the sake of familiarity, we
shall use the short expressions, viz., "abstract
terms", "abstract names",
etc.
According to Quine (1963b: 75), "the
ostensions which introduce a general term
differ from those which introduce a singular
term in that the former do not impute identity
of indicated object between occasions of
pointing." And, he continues, "the
general term does not, or need not, purport
to be a name in turn of a separate entity
of any sort, whereas the singular term does."
In other words, "a singular term names
or purports to name just one object, though
as complex or diffuse an object as you please,
while a general term is true of each, severally,
of any number of objects".
According to Griffin (1977:22-23), it is
necessary to be able to mark general nouns
as distinct from the predicates in which
they occur. It is also necessary to be able
to distinguish sortal general nouns (e. g.
"dog", "car", "unicorn",
"cup") from mass terms (e. g. "water",
"sugar", "bread", "phlogiston").
So, Griffin (1977: 23) draws a distinction
between two kinds of general terms, +count
and -count general terms:
A general term "T" is +count if
"There are n Ts..." makes sense,
where "n" is a variable taking
numerals
as values; otherwise "T" is -count.
while all +count general terms are general
nouns some -count general terms are also
general nouns. Intuitively (see Griffin 1977:25),
-count nouns seem to fall into at least three
distinct groups. (1) Names of materials (e.
g. "gold", "water", "iron")
and terms that behave in exactly the same
way (e. g. "meat", "wheat",
"garbage"). (2) Similarly behaving
abstract terms (e. g. "music",
"cricket", "mathematics",
"information", "entertainment",
"redness"). (3) Characterizing
terms (e. g. "intelligence", "chastity",
"indigence", "quality",
"viscosity", "efficiency"
- typically abstract names of qualities).
Because general terms refer to abstract entities
(at least in the sense of C1 and C2, above),
it is important to have a look at the problem
whether it is possible to define the degree
of abstractness (hereafter the DoA) of a
selected entity.
Quine (1960: 90-1). See also Griffin (1977:
22).
That it is a selected entity we are here
talking about is essential, because it seems
very plausible that the entity in question
should not be any arbitrary given entity,
the characteristics of which may be entirely
unknown.
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