In an appendix to Person and Object, Roderick Chisholm argues that the 4Der, one who maintains that persisting entities perdure (i.e. exists at different times in virtue of having temporal parts that exist at those times), must presume that something endures (i.e. is "wholly present" at any time it exists), if she is to give an account of why some sums of temporal stages are ordinary physical objects, e.g. rivers, and others are not.
To make the argument more concrete, Chisholm asks the 4Der, "Under what conditions are three river stages, a, b, and c (existing at different times), stages of the same river?" (Henceforth, I will call this question, and any questions of this form, "Chisholm's question.") Chisholm says that five answers suggest themselves. The first and last of these answers are clearly circular in nature. Answer (1) is that a, b, and c are stages of the same river if and only if there is a river such that a, b, and c, are stages of it. Answer (5) is that a, b, and c are stages of the same river if and only if a, b, and c are "co-fluvial."
Chisholm's second suggested answer lets us see clearly the problem that faces the 4Der. Chisholm suggests the following as an acceptable (i.e. non-circular) answer. Stages a, b, and c are stages of the same river if and only if a, b, and c are all to be found in the same river bed, or between the same river banks. But as Chisholm points out, this presupposes the persistence of river beds or river banks: these must either endure or perdure. The 4Der must say that river beds and river banks perdure, and Chisholm's question can then be repeated for river beds or river banks: "What makes three river bed stages, a, b, and c, stages of the same river bed?"
But of course the 4Der need not answer the question by appealing to other physical objects. Chisholm suggests the following answer: a, b, and c, are stages of the same river if and only if a, b, and c, are "accessible to observation" for some person or persons. (This assumes that persons are not physical objects.) But since a, b, and c, exist at different times, the person or persons to whom a, b, and c, are observationally accessible must exist at different times. And Chisholm's question can then be repeated for persons: "What makes three-person stages, a, b, and c, stages of the same person?" (This is probably a more difficult question than the original one.)
Chisholm's fourth suggested answer is the most plausible one, both for rivers and for other ordinary physical objects: a, b, and c are stages of the same river if and only if a, b, and c occupy the same place. More generally, we might say that two F-stages are stages of an F-thing if and only if the stages are spatio-temporally continuous. But as Chisholm points out, to say that two stages occupy the same place presupposes an account of persisting places, as does the common analysis of spatio-temporal continuity. If places persist, they must either perdure or endure. If the 4Der says that places perdure, an account of this perdurance (an answer to Chisholm's question for places) must be given. On the other hand, the 4Der may wish to say that places endure, and thus put an end to the cycle of analysis, if she is willing to adopt a substantival theory of space. For spaces presumably do not undergo changes in their intrinsic one-place properties, and the temporary intrinsic two-place relations that they stand in, such as the relation of occupation, may be accounted for by the perdurance of the physical objects they stand in these relations to.
On the other hand, if the 4Der is unwilling to adopt a substantival theory of space and say that spaces endure, the 4Der must give an analysis of spatio-temporal continuity which does not appeal to an unanalyzed relation of being the same place as.
The problem Chisholm poses for the 4Der arises because when we trace the careers of persisting objects, we generally do so in terms of their relations to other things, generally to places, not in virtue of their intrinsic properties. These other things must either perdure or endure. If they perdure, we need an account of their persistence conditions (i.e. an answer to Chisholm's question), which will either be in terms of their intrinsic one-place properties or in terms of their relations to other things. If the account can be given in terms of intrinsic one-place properties, the cycle of analysis ends there, otherwise Chisholm's question may be posed again. Note that it is impossible for a general account of the perdurance of places to be given in terms of intrinsic one-place properties, for congruent regions of space do not differ in their intrinsic one-place properties.
Three options are open to the 4Der. (1) She may admit that some things, probably places, endure, and answer Chisholm's question in terms of the relations of physical objects to these things. (2) She may find some things, perhaps the persons of Chisholm's third suggested answer, which have their stages united in virtue of intrinsic one-place properties of those stages, and analyze the persistence of ordinary physical objects in terms of their relations to these things. (3) She may give an account of spatio-temporal continuity which does not appeal to an unanalyzed relation of being the same place as.
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