GFO Part I Basic Principles
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6.1 Endurants, Presentials, and Persistants

In our approach, we make a more precise distinction between presentials and processes, because the philosophical notion of endurant combines two contradictory aspects. Persistence is accounted for by two distinct categories: presentials and persistants. A presential exists wholly at a time-boundary. We introduce the relation $\Gat(x,y)$ with the meaning the presential x exists at time-boundary y. We pursue an approach which accounts for persistence using a suitable universal whose instances are presentials. Such universals are called persistants. These do not change, and they can be used to explain how presentials that have different properties at different times can, nevertheless, be the same.

Endurants exhibit two aspects that contradict each other. If, for example, an endurant $x$ is wholly present at two different time-points $t$ and $s$, then there are two different entities ``$x$ at $t$'' and ``$x$ at $s$'', denoted by $x(t)$ and $x(s)$, respectively. Now let us assume that $x$ persists from $x(t)$ to $x(s)$. For example, newborn Caesar exists at time $t$, $\GCaesar(t)$, while Caesar at age of 50 at $s$, $\GCaesar(s)$; both entities $\GCaesar(s)$ and $\GCaesar(t)$ are wholly present at these time-points, and they are obviously different. What would it mean to say that both are identical? Our solution to this problem is to separate endurants into wholly present presentials and persisting persistants. That means, $x(t)$ and $x(s)$ are not identical, but they are equivalent, because both are instances of the persistant.

If we assume that only those things exist that exist at present (presence understood as a time-point without any extension), then presentials should be wholly present at the present time-point. Persistants are not arbitrary universals. They satisfy a number of conditions, among them the following: (a) every instance of a persistant is a presential; (b) for every time-boundary there is at most one instance which exists at this time-boundary; and (c) there is a chronoid $c$ such that for every time-boundary of $c$ the persistant has an instance at this time-boundary. Further conditions should concern the relation of ontical connectedness and the relation of persistants to processes.

Robert Hoehndorf 2006-10-18


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