An enquiry concerning the principles of natural knowledgeWhitehead, Alfred North
Philosophy
An enquiry concerning the principles of natural knowledge
Whitehead, Alfred North
Knowledge, Theory of; Science -- Philosophy; Space and time
41.3 Each event-particle in a duration is covered by one and only
one station in that duration; and any event-particle covered by a
station can be taken as the 'assigned event-particle' of the formative
condition, inherent in every event which is a member of the station.
Every station is a route; and also every station in a duration
intersects every moment of that duration [i.e. inherent in it] in one
and only one event-particle, and intersects no other moments of that
time-system. It will be noted that a station is associated with a
definite time-system, namely the time-system corresponding to its
duration.
41.4 A station of one time-system either does not intersect a
station of another time-system or intersects it in one event-particle
only. Thus stations belong to the type of routes which have been
denominated 'kinematic routes.' Each station exhibits an unchanging
meaning of 'here' throughout the duration in which it is a station;
namely, every event-particle in a station is 'here' in the duration in
the same sense of 'here' as for every other event-particle in that
station.
42. Point-Tracks and Points. 42.1
Consider all the durations belonging to one time-system. Of these
durations some intersect each other, and some are parts of others. Thus
any event-particle is covered by many durations of this
time-system, and lies in stations corresponding to these durations. We
have now to consider the relations to each other of these various
stations, each containing . The fundamental theorem is as follows:
If and ′ be durations of the same time-system, and
extends over ′, and if be an event-particle inhering in
′ and and ′ be the stations of in and ′
respectively, then covers ′. In other words used in less
technical senses, If ′ be part of , then ′ is part of
.
42.2 Any given station in a duration can thus be
indefinitely prolonged throughout the time-system to which
belongs. For let be any other duration of the same time-system
which intersects in the duration ′ and also extends beyond
. Then the part of which is included in ′, namely ′
(say), is a station in ′. Also there is one and only one station in
, (say), which covers ′; and no other station in
covers any event-particle of ′. In this way the station
is prolonged in the time-system by the addition of the station
, and so on indefinitely. The complete locus of event-particles
thus defined by the indefinite prolongation of a station throughout its
associated time-system is called a 'point-track.'
A point-track intersects any moment of any time-system in one and only
one event-particle.
42.3 Each point-track has a unique association with the
time-system in which the routes lying on it are stations. A point-track
is called a 'point' in the 'space of its associated time-system.' This
space of a time-system is called 'time-less' because its points have no
special relation to any one moment of its associated time-system.
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