GFO Part I Basic Principles
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7.4 Material Persistants and Object-Process Integration

Material persistants are particular universals whose instances are material structures; they are related to those entities that are sometimes called continuants or objects, as apples, cars or houses. Material persistants represent the phenomenon of persistance through time of a material object. A material persistant $P$ satisfies a number of neccessary conditions. For every material persistant $P$, there exists a process $\GProc(P)$ such that the set of instances of $P$ coincides with the set of process-boundaries of $\GProc(P)$. This implies the existence of a chronoid $\GChron(C)$, such that for every time-point $t$ of $\GChron(C)$, there exists exactly one instance of $P$ at time point $t$. Persistants exhibit a particular kind of categorial abstraction over a collection of presentials that are boundaries of processes. The construction of persistants seems to be connected to the cognitive abilities of agents, human beings or animals. 1314

The complete specfication of a material structure, say an ordinary object, integrates three aspects into one system: the object as a presential, as a process, and as a persistant. We explain and demonstrate this interrelation and integration using an ontological analysis. Consider an everyday name like ``John''. What does John refer to in an ontologically precise sense? There are, obviously, three possibilities, i.e., three entities of different categories:

  • John denotes a presential $\GPres(John,t)$ at some point $t$ in time,
  • John refers to a persistant $\GPerst(John)$, or
  • the name is given to a process $\GProc(John)$.
The following connections between these three entities can be stated. Starting with an act of perception of John, we assume that a presential is recognized, call it $\GPres(John,t)$. If one has seen John several times, with probably varying properties, but still being able to identify him, this forms the basis for a persistant, say $\GPerst(John)$. Now one may consider the extension of this persistant (which is a universal), i.e., the class $\GExt(\GPerst(John)= \{ J \vert J \Ginst \GPerst(John) \}$. Obviously, the entity $\GPres(John,t)$ referred to above is a member of this class. Also, one can say that any two members of that class represent ``the same John''.

In the third interpretation, the name John denotes a process $\GProc(John)$ of a special kind. We postulate the existence of a process $\GProc(John)$ whose set of projections to its time-boundaries equals the class of instances of $\GPerst(John)$. Such processes are called persistant-processes, and they exhibit an integration of an object (a continuant, a persistant) with a process. Furthermore, we see that the presentials associated to John can be derived from a process by taking the projections of this process to time-boundaries. On the other hand, the persistant $\GPerst(John)$ cannot be directly derived from a process because a categorial abstraction must be taken into consideration. Hence, the system $(\GPerst(John), \GProc(John))$ represents the complete information about the entity whose name is ``John''. The categorial abstraction over the presentialist Johns captures an important aspect of John's personal identity.15

Finally, we show that a complete understanding and decription of concrete individuals needs all three aspects specified in our integrative system. If one of these aspects is missing we will face problems. If, for example, we consider John as a persistant only, then this John cannot engage in any temporal action, for example, the activity of eating. John's actions and activities are realized on the process level. If we consider John as the set of all presentialist Johns, then we have the same problem; since any action takes time a presentialist John cannot carry out any action. If John is a process only, then the problem becomes identifying the boundaries of the process because any natural process may be prolonged both into the future and into the past. Furthermore, we perceive John as a presential, which is missing in a pure processual understanding. We face similar problems pertaining to a full understanding of concrete entities, if we combine only two of the above aspects.16

Robert Hoehndorf 2006-10-18


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