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Updated: June 5, 2025
Let the satisfaction of the condition σ by an abstractive set mean that the two given event-particles and the event-particles lying between them on the rect all lie in every event belonging to the abstractive set. The group of σ-primes, where σ has this meaning, form an abstractive element. Such abstractive elements are rectilinear routes.
Its particular property of being closed prevents it from being definable as an abstractive element. When a moment intersects an event, it also intersects the boundary of that event. This locus, which is the portion of the boundary contained in the moment, is the bounding surface of the corresponding volume of that event contained in the moment. It is a two-dimensional locus.
The intrinsic character of a σ-prime has a certain minimum of fullness among those abstractive sets which are subject to the condition of satisfying σ; whereas the intrinsic character of a σ-antiprime has a corresponding maximum of fullness, and includes all it can in the circumstances.
We may term these connexions of the component durations the 'extrinsic' properties of a moment; the 'intrinsic' properties of the moment are the properties of nature arrived at as a limit as we proceed along any one of its abstractive sets. These are the properties of nature 'at that moment, or 'at that instant.
Between that which Balzac tabulated as the "abstractive" type of human evolvement and that which is fully cosmic in consciousness, there are many and diverse degrees of the higher faculties; but the poet always expresses some one of these degrees of the higher consciousness; indeed some poets are of that versatile nature that they run the entire gamut of the emotional nature, now descending to the ordinary normal consciousness which takes account only of the personal self; again ascending to the heights of the impersonal fearlessness and unassailable confidence that is the heritage of those who have reached the full stature of the "man-god whom we await" the cosmic conscious race that is to be.
Let us first consider what help the notion of antiprimes could give us in the definition of moments which we gave in the last lecture. Let the condition σ be the property of being a class whose members are all durations. An abstractive set which satisfies this condition is thus an abstractive set composed wholly of durations.
Let the condition named σ stand for the fact that each of the events of any abstractive set satisfying it has all the event-particles of some particular solid lying in it. Then the group of all the σ-primes is the abstractive element which is associated with the given solid.
There are durations of the same family as the given duration which overlap it but are not contained in it. Consider an abstractive set of such durations. Such a set defines a moment which is just as much without the duration as within it. Such a moment is a boundary moment of the duration.
The abstractive elements which lie in the instantaneous space of a given moment M are differentiated from each other by the various other moments which intersect M so as to contain various selections of these abstractive elements. It is this differentiation of the elements which constitutes their differentiation of position.
I state this difficulty at some length because its existence guides the development of our line of argument. We have got to annex some condition to the root property of being covered by any abstractive set which it covers.
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