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A definite event-particle is defined in reference to a definite punct in the following manner: Let the condition σ mean the property of covering all the abstractive elements which are members of that punct; so that an abstractive set which satisfies the condition σ is an abstractive set which covers every abstractive element belonging to the punct.
Also if P be any moment, either every abstractive element belonging to a given punct lies in P, or no abstractive element of that punct lies in P. Position is the quality which an abstractive element possesses in virtue of the moments in which it lies.
Accordingly an event-particle as thus defined is an abstractive element, namely it is the group of those abstractive sets which are each equal to some given abstractive set. An event-particle has position by reason of its association with a punct, and conversely the punct gains its derived character as a route of approximation from its association with the event-particle.
Accordingly an instantaneous plane in the instantaneous space of a moment will be called a 'level, an instantaneous straight line will be called a 'rect, and an instantaneous point will be called a 'punct. Thus a punct is the assemblage of abstractive elements which lie in each of four moments whose families have no special relations to each other.
"No, you're so infernally punct so delicate-minded, my love," said the Captain, pulling himself up suddenly, for the second time. "Forgive me if I was impatient just now. You look at these things from a higher point of view than that of a battered old man of the world like me. But if you should see anything remarkable in Mr.
The peculiar simplicity of an instantaneous point has a twofold origin, one connected with position, that is to say with its character as a punct, and the other connected with its character as an event-particle. The simplicity of the punct arises from its indivisibility by a moment. The simplicity of an event-particle arises from the indivisibility of its intrinsic character.
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.
Then the definition of the event-particle associated with the punct is that it is the group of all the σ-primes, where σ has this particular meaning. It is evident that with this meaning of σ every abstractive set equal to a σ-prime is itself a σ-prime.
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