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Updated: May 5, 2025
It will be remembered that an abstractive element is a certain group of abstractive sets, and that each abstractive set is a set of events. This definition defines the location of an element in any type of abstractive element. In this sense we can talk of the existence of an object at an instant, meaning thereby its location in some definite moment.
An abstractive element which belongs to a punct has the simplest type of position in M, an abstractive element which belongs to a rect but not to a punct has a more complex quality of position, an abstractive element which belongs to a level and not to a rect has a still more complex quality of position, and finally the most complex quality of position belongs to an abstractive element which belongs to a volume and not to a level.
I call the limiting character of natural relations which is indicated by an abstractive set, the 'intrinsic character' of the set; also the properties, connected with the relation of whole and part as concerning its members, by which an abstractive set is defined together form what I call its 'extrinsic character. The fact that the extrinsic character of an abstractive set determines a definite intrinsic character is the reason of the importance of the precise concepts of space and time.
Accordingly an event-particle could cover no other abstractive element. This is the definition which I originally proposed at a congress in Paris in 1914 . There is however a difficulty involved in this definition if adopted without some further addition, and I am now not satisfied with the way in which I attempted to get over that difficulty in the paper referred to.
In other words you cannot get any abstractive set satisfying the condition σ which exhibits intrinsic character more simple than that of a σ-prime. There are also the correlative abstractive sets which I call the sets of σ-antiprimes. In other words you cannot get any abstractive set satisfying the condition σ which exhibits an intrinsic character more complex than that of a σ-antiprime.
When this is the case I shall call the two sets 'equal in abstractive force. When there is no danger of misunderstanding I shall shorten this phrase by simply saying that the two abstractive sets are 'equal. The possibility of this equality of abstractive sets arises from the fact that both sets, p and q, are infinite series towards their small ends.
If an abstractive set p covers an abstractive set q, then any abstractive set belonging to the abstractive element of which p is a member will cover any abstractive set belonging to the element of which q is a member. Accordingly it is useful to stretch the meaning of the term 'covering, and to speak of one abstractive element 'covering' another abstractive element.
The abstractive elements form the fundamental elements of space and time, and we now turn to the consideration of the properties involved in the formation of special classes of such elements. In my last lecture I have already investigated one class of abstractive elements, namely moments.
My limited and abstractive art is to be found under every hedge and in every lane, and therefore nobody thinks it worth while picking up. My art flatters nobody by imitation: it courts nobody by smoothness: it tickles nobody by politeness: it is without either fol-de-rol or fiddle-de-dee. How can I hope to be popular?" Ruskin's attack on Whistler is another case in point.
To observe too who these are whose opinions and voices give reputation; what death is, and the fact that, if a man looks at it in itself, and by the abstractive power of reflection resolves into their parts all the things which present themselves to the imagination in it, he will then consider it to be nothing else than an operation of nature; and if any one is afraid of an operation of nature, he is a child.
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