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Meanwhile we will ignore them. Also I will always speak of 'event-particles' in preference to 'puncts, the latter being an artificial word for which I have no great affection. Parallelism among rects and levels is now explicable. Consider the instantaneous space belonging to a moment A, and let A belong to the temporal series of moments which I will call α.
These two characters of simplicity enjoyed respectively by event-particles and puncts define a meaning for Euclid's phrase, 'without parts and without magnitude. It is obviously convenient to sweep away out of our thoughts all these stray abstractive sets which are covered by event-particles without themselves being members of them. They give us nothing new in the way of intrinsic character.
A volume however has not yet been defined. This definition will be given in the next lecture. Evidently levels, rects, and puncts in their capacity as infinite aggregates cannot be the termini of sense-awareness, nor can they be limits which are approximated to in sense-awareness.
Any rect in M which intersects all these levels in its set of puncts, thereby receives for its puncts an order of position on it. So spatial order is derivative from temporal order. Furthermore there are alternative time-systems, but there is only one definite spatial order in each instantaneous space.
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