[The Concept of Nature by Alfred North Whitehead]@TWC D-Link bookThe Concept of Nature CHAPTER III 25/54
This is one instance of the indeterminateness of sense-awareness.
Exactness is an ideal of thought, and is only realised in experience by the selection of a route of approximation. The absence of maximum and minimum durations does not exhaust the properties of nature which make up its continuity.
The passage of nature involves the existence of a family of durations.
When two durations belong to the same family either one contains the other, or they overlap each other in a subordinate duration without either containing the other; or they are completely separate.
The excluded case is that of durations overlapping in finite events but not containing a third duration as a common part. It is evident that the relation of extension is transitive; namely as applied to durations, if duration A is part of duration B, and duration B is part of duration C, then A is part of C.Thus the first two cases may be combined into one and we can say that two durations which belong to the same family _either_ are such that there are durations which are parts of both _or_ are completely separate. Furthermore the converse of this proposition holds; namely, if two durations have other durations which are parts of both _or_ if the two durations are completely separate, then they belong to the same family. The further characteristics of the continuity of nature--so far as durations are concerned--which has not yet been formulated arises in connexion with a family of durations.
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