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
56.2 If be a material object of a certain sort and
be a volume in which is located and be a portion
of , then the material object of the same sort as
which is located in is called an 'extensive component'
of .
56.3 It is by means of the properties of material objects that
the atomic properties of objects are combined in mathematical
calculations with the extensive continuity of events. Apart from
material objects mathematical physics as at present developed would be
impossible. For example where the physicist sees the electron as an
atomic whole, the mathematician sees a distribution of electricity
continuous in time and in space and capable of division into component
objects which are also analogous distributions.
57. Stationary Events. 57.1 In order
to understand the theory of the motion of material objects, it is first
necessary to define the concept of a 'stationary' event.
Consider some given time-system , and let denote
a volume lying in a certain moment of this time-system.
Let be a duration of bounded by moments and ,
and inhered in by ; so that , ,
are three parallel moments of the time-system , and
lies between and . The volume is the locus
of a set of event-particles and each of these event-particles
lies in one and only one station of the duration .
Also each station of either does not intersect or
intersects it in one event-particle only. The assemblage
of event-particles lying on stations of d which intersect
[namely, each event-particle lying on one of these
stations] is the complete set of event-particles analysing[8]
an event. Such an event is called stationary in the time-system
and stretches throughout the duration . It
can also be called 'stationary in ,' since defines the
time-system . Every event-particle within the event
lies on a station of ; and a station of either has all
its event-particles lying within the event or none of
them. The volume is the section of the event by the
moment . Furthermore if ′ be any other moment
of the time-system it lying between and , it
intersects the event in a volume ′ which is a geometrical
replica of the volume . The moments
and which bound the duration are the terminal
moments of any event which is stationary in . The
stations of lying in the event intersect and in
terminal volumes and which are geometrical
replicas of and ′. A volume, such as ', in which
a moment of intersects an event stationary in is
called a 'normal cross-section' of the event. A moment
of another time-system which intersects the stationary
event in a volume , but does not intersect either of the
terminal volumes, is said to intersect it in an 'oblique cross-section.'
All the oblique cross-sections of a stationary event which are made by
moments of the same time-system are geometrical replicas of each other.
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