The Concept of Nature: The Tarner Lectures Delivered in Trinity College, November 1919Whitehead, Alfred North
Philosophy
The Concept of Nature: The Tarner Lectures Delivered in Trinity College, November 1919
Whitehead, Alfred North
Knowledge, Theory of; Nature; Science -- Philosophy
Let P be any event-particle lying in a given duration d. Consider
the aggregate of events in which P lies and which are also cogredient
with d. Each of these events occupies its own aggregate of
event-particles. These aggregates will have a common portion, namely the
class of event-particle lying in all of them. This class of
event-particles is what I call the 'station' of the event-particle P
in the duration d. This is the station in the character of a locus. A
station can also be defined in the character of an abstractive element.
Let the property σ be the name of the property which an abstractive set
possesses when (i) each of its events is cogredient with the duration
d and (ii) the event-particle P lies in each of its events. Then the
group of σ-primes, where σ has this meaning, is an abstractive element
and is the station of P in d as an abstractive element. The locus of
event-particles covered by the station of P in d as an abstractive
element is the station of P in d as a locus. A station has
accordingly the usual three characters, namely, its character of
position, its extrinsic character as an abstractive element, and its
intrinsic character.
It follows from the peculiar properties of rest that two stations
belonging to the same duration cannot intersect. Accordingly every
event-particle on a station of a duration has that station as its
station in the duration. Also every duration which is part of a given
duration intersects the stations of the given duration in loci which are
its own stations. By means of these properties we can utilise the
overlappings of the durations of one family--that is, of one
time-system--to prolong stations indefinitely backwards and forwards.
Such a prolonged station will be called a point-track. A point-track is
a locus of event-particles. It is defined by reference to one
particular time-system, α say. Corresponding to any other time-system
these will be a different group of point-tracks. Every event-particle
will lie on one and only one point-track of the group belonging to any
one time-system. The group of point-tracks of the time-system α is the
group of points of the timeless space of α. Each such point indicates a
certain quality of absolute position in reference to the durations of
the family associated with α, and thence in reference to the successive
instantaneous spaces lying in the successive moments of α. Each moment
of α will intersect a point-track in one and only one event-particle.
This property of the unique intersection of a moment and a point-track
is not confined to the case when the moment and the point-track belong
to the same time-system. Any two event-particles on a point-track are
sequential, so that they cannot lie in the same moment. Accordingly no
moment can intersect a point-track more than once, and every moment
intersects a point-track in one event-particle.
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