=Paper=
{{Paper
|id=Vol-2050/foust-paper6
|storemode=property
|title=On Qualitatively Unstable Objects
|pdfUrl=https://ceur-ws.org/Vol-2050/FOUST_paper_6.pdf
|volume=Vol-2050
|authors=Pawel Garbacz
|dblpUrl=https://dblp.org/rec/conf/jowo/Garbacz17
}}
==On Qualitatively Unstable Objects
==
https://ceur-ws.org/Vol-2050/FOUST_paper_6.pdf
On Qualitatively Unstable Objects
Pawel GARBACZ
Department of Philosophy
The John Paul II Catholic University of Lublin
Poland
Abstract. I present in this paper a certain classification of objects with re-
spect to their qualitative stability, i.e., with respect whether they change
their qualities. The resulting classification is a flat typology of objects
with two facets and three types in each facet. Assuming this classifica-
tion the paper is then focused on one of these types: very weakly unsta-
ble objects. In particular, I discuss the problem of their persistence and
attempt to sketch identity criteria over time.
Keywords. quality, change, persistence, identity
1. Introduction
Suppose that developing a computer system you designed a relational database
whose one table looks like table 1 below. That is to say, you ended up with a set
of tables and one of them is a table (relation) with just one column (attribute)
whose values look as if they were meant to identify certain objects.
Although your table is allowed by most (if not all) database languages and
although it does not breach any usual design principle 1 , there is something wrong
with it: the values in the column do not seem to provide any information, so the
table is void of any content although it contains some data.
Identifiers
1
2
...
Table 1. Table
Is there a reasonable scenario when such situation may occur? Well, suppose
that the system in question is a historic-geographical system or more specifically
that it is designed to gather information about histories of (human) settlements.
The design requirements specify that we need to trace the location, name, and
the type of such settlements. You know from the SMEs that each settlement may
change its location, name, and type in time, so that a settlement may have at
time t1 different location and name, and type than it has at time t2 , i.e., all
1 In fact, it satisfies the third normal form of E. Codd, because it has only one attribute.
these attributes may change from t1 to t2 (cf. [11]). So you need another table
for settlement states (or manifestations) at different times – e.g., similar to table
2 below. Now since attribute SettlementIds in this table looks like a foreign key,
Ids SettlementIds Locations Names Types Starts Ends
1 1 N52◦ 99.210 E18◦ 59.160 Podgorz Village 1555 1611
2 1 N52◦ 99.210 E18◦ 59.160 Podgorz City 1612 1833
3 1 N52◦ 99.210 E18◦ 59.160 Podgorz Village 1834 1924
4 1 N52◦ 99.210 E18◦ 59.160 Podgorz City 1925 1938
5 1 N52◦ 99.210 E18◦ 59.160 Podgorz Suburb 1939 2017
... ... ... ... ... ... ...
Table 2. Settlement States Table
you think you need a table where this attribute constitutes a primary key, so you
end up with a table whose schema is identical to that of table 1.
Brushing aside the database design issues I claim that the aforementioned
scenario concerns objects of an unusual ontological kind. Namely, they exist and
change in time, but, given the scope of the presupposed conceptualisation of the
domain, neither of these objects is bound to keep any of its characteristics in
time, i.e., an object of this kind may change all its properties or qualities in time
while maintaining its identity. In this sense they are qualitatively unstable.
2. Types Of Qualitative (Un-)Stability
Now the kind of objects described in the previous section can be defined as a
component of the formal framework below. The typology I outline in this section
classifies objects with respect to their qualitative stability, i.e., to that how stable
their qualities remain in the course of time.
The framework in question is in fact a thin first-order theory of objects or
rather of things with qualities.2 It assumes a multi-sorted language defined as
below:
1. four (disjoint) sorts: Sobject , Squality , Svalue , Stime ;
2. and their sorted individual variables:
(a) x, x1 , x2 , · · · : Sobject
(b) q, q1 , q2 , · · · : Squality
(c) v, v1 , v2 , · · · : Svalue
(d) t, t1 , t2 · · · : Stime .
The framework takes off with two primitive predicates: Q(x, q, v, t) and
Exist(x, t), whose informal readings are given in table 3.
The theory in question is philosophically “thin”, i.e., it assumes a few basic
ontological features of objects, which are described by the following four axioms:
2 It is not, thus, a theory of qualities in the sense of [5].
Formula Informal Reading
Q(x, q, v, t) object x has quality q that has value v at time t
Exist(x, t) object x exists at time t
Table 3. Primitive Predicates
∃tExist(x, t) (1)
Exist(x, t) → ∃q, vQ(x, q, v, t) (2)
Q(x, q, v, t) → Exist(x, t) (3)
Q(x, q, v1 , t) ∧ Q(x, q, v2 , t) → v1 = v2 (4)
The theory’s scope is limited to things with qualities that exist in time, so axiom 1
has it that all objects, and not necessarily the qualities themselves, exist in time.3
The term “quality” is taken here in a fairly broad sense: qualities are those entities
that can be predicated of things or attributed to them because things bear, possess
or exemplify them ([8]). Then the main, although modest, ontological assumption
is the “quadruple” distinction between objects, their qualities, quality values,
and times. In particular, a quality (of a certain object) may have different values
at different times at which this object exists, although by axiom 4 no quality
(of a given object) can have more than one value at a time. Axiom 2 excludes
from this consideration “bare objects”, i.e., objects without qualities. Axiom 3
excludes qualities of non-existing objects. All other philosophical controversies
about qualities are left open. In particular, I do not make any assumption in this
section on the individuation of qualities, their extensionality, etc.
Now within this framework one can define two types of relations between
objects and their qualities: weak and strong stability.4 By definition 6 a quality is
weakly stable for an object if this object has this quality throughout its lifetime
although at different moments in this lifetime its values may differ. By definition
7 a quality is strongly stable for an object if this object has this quality all the
time (when it exists) and the quality has the same value all the time. An example
of an object with a quality that is not even weakly stable might be a lump of
bronze that undergoes a phase transition change, say, melting. When in the solid
state the lump has the a certain ductility, i.e., it has the ductility quality with a
certain value, but this quality is lost when it is in the liquid state since ductility
is a property of solid bodies only. The population size of a city may exemplify
weakly stable qualities. Finally, the charge of an electron seems to be a strongly
stable quality thereof.
3 That is to say, if there exist atemporal things with qualities, they are not within the scope
of this paper.
4 For the sake of simplicity, no formal definition provided in this paper has any explicit modal-
ity. If the reader finds this lack disturbing, he or she may prefix the definienda of the respective
definition with the necessity operator.
Formula Informal Reading
Span(q, x) quality q belongs to the quality span of object x
SS(q, x) quality q is a strongly stable quality of object x
WS(q, x) quality q is a weakly stable quality of object x
Table 4. Auxiliary Predicates
Formula Informal Reading
FullySS(x) object x is fully strongly stable
FullyWS(x) object x is fully weakly stable
PartiallySS(x) object x is partially strongly stable
PartiallyWS(x) object x is partially weakly stable
FullyWunS(x) object x is fully weakly unstable
FullySunS(x) object x is fully strongly unstable
PartiallyWunS(x) object x is partially weakly unstable
PartiallySunS(x) object x is partially strongly unstable
Table 5. Types of Qualitative (Un-)Stability
Span(q, x) , ∃t, vQ(x, q, v, t) (5)
WS(q, x) , ∀t[Exist(x, t) → ∃vQ(x, q, v, t)] (6)
SS(q, x) , ∃v∀t[Exist(x, t) → Q(x, q, v, t)] (7)
Now this distinction may be used to classify all objects with respect to the
following eight (basic) types.
FullySS(x) , ∀q[Span(q, x) → SS(q, x)] (8)
FullyWS(x) , ∀q[Span(q, x) → WS(q, x)] (9)
PartiallySS(x) , ¬FullySS(x) ∧ ∃qSS(q, x) (10)
PartiallyWS(x) , ¬FullyWS(x) ∧ ∃qWS(q, x) (11)
FullySunS(x) , ∀q[Span(q, x) → ¬WS(q, x)] (12)
FullyWunS(x) , ∀q[Span(q, x) → ¬SS(q, x)] (13)
PartiallySunS(x) , ¬FullySunS(x) ∧ ∃q[Span(q, x) ∧ ¬WS(q, x)] (14)
PartiallyWunS(x) , ¬FullyWunS(x) ∧ ∃q[Span(q, x) ∧ ¬SS(q, x)] (15)
The corollaries below show the basic set-theoretical relationships between these
types:
FullySS(x) → FullyWS(x) (16)
PartiallySS(x) → PartiallyWS(x) (17)
PartiallySS(x) ≡ PartiallyWunS(x) (18)
PartiallyWS(x) ≡ PartiallySunS(x) (19)
PartiallySunS(x) → PartiallyWunS(x) (20)
FullySunS(x) → FullyWunS(x) (21)
FullySS(x) ∨ PartiallySS(x) ∨ FullyWunS(x) (22)
FullyWS(x) ∨ PartiallyWS(x) ∨ FullySunS(x) (23)
The resulting typology of objects has thus two overlapping facets, which are de-
termined by two types of quality stability: 6 and 7. Each facet contains, effectively,
three types:
1. strong stability facet: FullySS PartiallySS, and FullyWunS;
2. weak stability facet: FullyWS, PartiallyWS and FullySunS.
Combining the types from the two facets, we can get six new types, which are the
intersections of the original ones. These intersections are shown in cells of table 6,
where the column and row headings are the intersecting types. These “combined”
types are pairwise disjoint and collectively exhaustive.
FullySS PartiallySS FullyWunS
FullyWS Strongly Stable Weakly Stable Very Weakly Unstable
PartiallyWS ∅ Partially (Un-)Stable Weakly Unstable
FullySunS ∅ ∅ Strongly Unstable
Table 6. Combined Types of Qualitative (Un-)Stability
Now let me say a few words about the resulting typology. First, it is obvious
that whether a certain object belongs to a certain type depends, among other
things, on a scope of qualities under consideration. So two different sets of qualities
may give rise to two different classifications of the same object. For this reason
the above framework should be taken as relative to or parameterised with a set
of qualities.5 This relativisation may pose a problem for philosophy where some
search for the ultimate conceptualisation, but in the engineering context of applied
ontology it is more acceptable, perhaps even justifiable, if one is ready to embrace
such meta-principles as perspectivalism ([1, p. 44-45]).
Secondly, let me risk providing some instances of the “combined” types.
Strongly stable objects are fairly exceptional as they are objects that exist in time,
but do not change in time. So the least controversial cases thereof are instanta-
neous objects, i.e., objects that exists only at one time, e.g., events. Weakly stable
objects are more frequent – in fact such ontologies as Dolce [6] seem to postulate
that all objects are fully weakly stable, so probably some kinds of animals, e.g.,
5 Formally, we could add an additional axiom schema like “Q (q)”, whose semantic interpre-
i
tations may express this parametrisation.
birds, may by weakly stable. An example of a partially (un-)stable object might
our lump of bronze (with the melting temperature point as a stable property). If
the case described in the introduction is accurate, than human settlements may
constitute a class of very weakly unstable objects provided that they do not gain
or lose any quality during their existence. The type of weakly unstable objects
is tricky as it contains those things whose all qualities change in time and in
addition which may gain or lose some qualities. The question whether this cat-
egory is empty or not is left open here. Strongly unstable objects are relatively
rare either. In fact one can argue that this class is empty if we assume that each
object that exists in time has at every time it exists a certain location and that
this location is among its qualities. Then all objects will be (at least) partially
weakly stable. On the other hand if you think that certain temporal objects have
no spatial location, e.g., events, then weird mereological fusions of such objects
and other, spatially determined, objects may fall into this category. For instance,
the mereological fusion of the Big Bang event and the village of Podgorz may be
a strongly unstable object.
Finally, the above framework implies that all these types are rigid, i.e., that
whether an object belongs to a certain type or not is not accidental. So any
object begins its existence, persists, and ceases to exist belonging to the same
type. In this sense they are ontological types, although I envisage that their
application may be more valuable on the meta-ontological level where we may
mark up ontological categories with these types respective to the types of objects
falling under these categories.
3. On Very Weakly Unstable Objects
Let me restate that an object is very weakly unstable if all its qualities may
change their values during its lifetime but it cannot gain or lose any of these
qualities. As such very weakly unstable objects present a particular challenge for
ontological engineering as their identity does not seem to be grounded, at least not
intrinsically. That is to say, these objects persist in time, but they lack grounds
for this persistence because their qualities are in constant flux. The rationale for
this claim is the intuition that if the ground for its persistence was internal to an
object, e.g., it was grounded in its mereological structure, then this fact would
entail that some of its qualities would be strongly stable. Obviously, not every
strongly stable quality of an object has to do with its identity, but if the object
persists in time its identity cannot be grounded in qualities that are not strongly
stable.
So if there is a ground for the fact that a certain very weakly unstable object
maintains its identity, then this ground must be external to the object, i.e., it
might be a certain relation that this object keeps to some other entity during
the lifetime of the former. Again, it must be an external relation, i.e., it must
not depend on the qualities of the object. But then the object turns out to be
ontologically volatile since its identity is grounded in something else than itself.
And there are ontological viewpoints which would explicitly disqualify such entity
because its putative existence would violate the so-called ’The Only X and Y’
principle [7]: whether x is identical to y can depend only on facts about x and y
and the relationships between them.
This is not to say that all aspects of very weakly unstable objects are acciden-
tal to them. Consider the category of human settlements and one of its members,
say, the (contemporary) suburb of Podgorz. Now it is possible that Podgorz will
become a city (or even a capitol) or a village in the future (in fact it was a village
and a city in the past – see table 2), but it is unlikely that it will become a river
or a car. So it seems that the category of settlements is rigid (in the sense of [4])
and that its members are necessarily settlements, i.e., metaphorically speaking,
they are born and they die as settlements. So weakly stable objects may have
some necessary or essential aspects although these aspects do not individuate
them sufficiently enough to ground their identity over time.6
This theoretical problem is accompanied by more practical issues. Let us go
back to the database mentioned in Introduction. Suppose that you finalised the
design of the table for settlement states and started filling it up with the data.
After some time its content looks like in table 7. Now the question arises whether
Ids SettlementIds Locations Names Types Starts Ends
1 1 Loc1 Name1 Type1 t1 t2
2 2 Loc1 Name1 Type1 t1 t2
3 2 Loc1 Name2 Type1 t2 t3
... ... ... ... ... ... ...
999 2 Loc2 Name2 Type2 t999 t1000
Table 7. Settlement Identity Issues
this body of data is correct or even consistent. In the first interval, i.e., from time
t1 to t2, the table has it that there are two settlements with the same location,
name, and type. Is it possible that there are two different settlements located at
same time in the same place, having then the same names and types? Comparing
the second and the first interval, one can ask whether it is possible that a single
settlement may change its name? Finally, records id=3 and id=999 imply there
is a settlement that changed its location and type in a long period of time. Is this
possible?
Needless to say, to provide non-arbitrary answers to such questions one needs
some theoretical principles that have to do with the nature of settlements, their
persistence, etc. One possibility is to establish settlement identity criteria – in
both versions: synchronic and diachronic (cf. [3]). As the reader may expect very
weakly unstable objects pose a special challenge for those who search for the
former. It is not an obvious matter under what conditions (very weakly unstable)
object x1 is identical to (very weakly unstable) object x2 when x1 exists at time
t1 and x2 exists at time t2 (t1 6= t2 ).
The problems with identity criteria are notorious ([2]) and the fact that we
deal with very weakly unstable objects does not help. Nonetheless I will attempt
to sketch a certain theoretical proposal on how to arrive at such criteria. The
6 One could probably say that such objects have general, but not individual, essences in the
sense of [9].
proposal below was coined to fit the case of settlements, but it aspires to provide
a general solution for all very weakly unstable objects. Since very weakly unstable
objects are rather irregular types of entities, the proposal has largely stipulative
nature. Let me summarise it before a more detailed exposition is provided. First,
I assume that there exists such synchronic criterion of identity for (a certain kind
of) very weakly unstable objects that entails that there is a set of qualities such
that objects indiscernible with respect to these qualities are identical. Secondly, I
claim that a very weakly unstable object maintains its identity throughout certain
changes such that each change affects no more than one of such qualities.
So suppose that we deal with a class (type) X of very weakly unstable objects,
e.g., let X be the class of settlements. The proposal in question presupposes that
we are able to formulate a synchronic criterion of identity for X that is equivalent
or entails the following principle:
X(x) ∧ X(y) ∧
[Q(x, q1 , v1 , t) ∧ Q(y, q1 , v1 , t)] ∧ · · · ∧ [Q(x, qn , vn , t) ∧ Q(y, qn , vn , t)] →
x = y. (24)
That is to say, I take it for granted that there are qualities q1 , q2 , . . . , qn such
that no two X-objects can have the same values of these qualities at any time.For
instance, if X is the category of settlements, [11] has it that this set includes
names, locations, and types.7
Secondly, let me define the notion of qualitative transformation for very
weakly unstable objects. Suppose that x and y are very weakly unstable objects
(possibly x = y). Let then p be a process that starts at time t1 and terminates at
time t2 . Object y will be called a p-transformant of object x at time t with respect
to quality q from set of qualities Q = {q, q1 , q2 , . . . , qn } if all below conditions are
met:
1. t1 < t ≤ t2 ;
2. x participates at t1 in p and its qualities q, q1 , q2 , . . . , qn have at that time
values v, v1 , v2 , . . . , vn ;
3. y participates at t in p and its qualities q, q1 , q2 , . . . , qn have at that time
values v 0 , v1 , v2 , . . . , vn (possibly v 0 = v);
4. there is no other (than x and y) object z such that z participates at t in p
and its qualities q, q1 , q2 , . . . , qn have at that time values v 00 , v1 , v2 , . . . , vn ,
where v 00 6= v.8
7 Interestingly enough, some studies suggest that there are very rare cases of settlements that
at some point in their existence share the name, location, and type, so the list in the main text
may be too short. For instance, [10, p. 34] gives three examples of such “duplicated” villages:
there were two villages of Mikuszowice, two villages of Biertoltowice, and two of Komorowice
at the same location in the end of the XVI century. The quality (if this is a quality) that made
them different is their different administrative affiliation: one village of Mikuszowice belonged
to the Kingdom of Poland and the other belonged to the Kingdom of Silesia. If this finding is
accurate, the list given in the main text needs to be extended or modified.
8 For the sake of simplicity, some parts of the phrases of the form “p-transformant of object x
at time t with respect to quality q from set of qualities Q = {q, q1 , q2 , . . . , qn }” will be dropped
in what follows provided that the context where these phrases occur make it obvious what
exactly was dropped.
Moreover, if the value of q at t is the same as it was at t1 , I will also speak about
y as a p-idempotent transformant of x at t; otherwise, it will be called a p-proper
transformant. Note that no object can have more than one transformant with re-
spect to any quality, process, or time in a given context. If y is the p-transformant
of x at t with respect to q, then process p will be called a q−transformation of x
at t into y.
Suppose now that some x from X start its existence at time t0 . Since x is a
very weakly unstable object, it has at this and all other times when it exists all
qualities from a set Q = {q1 , q2 , . . . , qn }. Suppose also that these qualities have
at t0 certain values, say, respectively: v1t0 , v2t0 , . . . , vnt0 . Let us consider set P0 of all
processes in which x starts to participate at t0 or, if this set is empty, the set of
all processes at a later time when x starts to participate in any process. If there
are two processes in P0 such that one is a proper part of another, we remove the
latter from P0 . Let “t1 ” denote the time at which the first member of such P0
ceases to exist, i.e., if p ∈ P0 dies at time t, then t1 ≤ t. There are four pairwise
disjoint and collectively exhaustive possibilities now:
1. P0 has no qi -transformation of x at t1 in the context of Q (1 ≤ i ≤ n);
2. P0 has such transformations, but all of them are idempotent;
3. P0 has such transformations, but all of them that are proper are also qi -
transformations for some single quality qi ;
4. P0 has (at least) two proper transformations: qi -transformation and qj -
transformation and qi 6= qj .
If either case 1 or 4 holds, then I claim that x ceases to exist at some time between
t0 and t1 , so x is not identical to any object that exists at t1 (or at any later
time). Otherwise, I claim that x keeps its identity within the [t0 , t1 ] interval and
is identical with all its p-transformants (where p ∈ P0 ).
Consequently, qualitative transformations provide a kind of local criterion of
identity for weakly stable objects, i.e., the above procedure establishes a principle
that allows us to answer identity questions at the boundaries of the [t0 , t1 ] interval.
Naturally, the question of identity within this interval remains open.
If you want to get a less local criterion, then if x survived the changes from
P0 , you need to repeat the above procedure starting from t1 instead of t0 , i.e.,
now you find out that qualities from Q have at time t1 values, say, respectively:
v1t1 , v2t1 , . . . , vnt1 . And you consider set P1 of all processes in which x participates
at t1 . Etc. Assuming that x terminates its existence at some point in time, the
procedure I just described will give us a sequence of local criteria of identity.
Combining them sequentially will result in a (global), but restricted, criterion
of identity for very weakly unstable objects. Namely, we will arrive at a set of
times {t0 , t1 , . . . , tk } such that we can say under which conditions a (very weakly
unstable) object x1 is identical to a (very weakly unstable) object x2 even if x1
exists at time ti and x2 exists at time tj (0 ≤ i, j ≤ k).
4. Conclusions
In my view the main contribution of this paper is a certain perspective on objects
that change their qualities over time. Despite the fact that the prospective was
defined outside the usual research agenda of applied ontology, but it may throw
new light on some existing problems there. It provides a new typology of such
objects and brings to the reader’s attention the category of very weakly unstable
objects as entities of a peculiar ontological kind. The perspective I sketched here
definitely needs further elaboration – in particular my discussion of identity of
such objects lacks both formal outlook and some deeper philosophical insight
– but may be mature enough to revive discussion on such issues as criteria of
identity for less usual ontological kinds. For example, I find the type of weakly
unstable objects worth further investigation in this respect.
Still even now one can envisage some applications of this theoretical research.
One obvious case that comes to mind is a (meta-)classification of ontological
categories (from some given applied ontology) by means of the types described
above. This may help in better understanding of the nature of these categories and
in ontology alignment, when we try to match categories that belong to different
ontologies. I envisage that this application may be more valuable in the case of
comparing domain ontologies than in the case of upper-level ontologies whose
categories usually include objects from various such types described in this paper.
5. Acknowledgements
The research presented in this paper was supported by the Ontological Foun-
dations for Building Historical Geoinformation Systems (2bH 15 0216 83) grant
funded by National Programme for the Development of Humanities.
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