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
If an abstractive class be an absolute antiprime, it is evident that the
formative condition of 'covering it' is regular for antiprimes. Thus the
set of events which are members of the absolute antiprimes which cover
some one assigned absolute antiprime constitutes an abstractive element.
Such an element will be called a 'moment.' Thus a moment is an
abstractive element deduced from the condition of covering an absolute
antiprime.
Only events of a certain type can be members of an absolute antiprime,
namely events which in Part II have been called
'durations.' Only durations can extend over durations, and accordingly
all the members of a moment are durations.
33.3 We may conceive of a duration as a sort of temporal thickness
(or, slab) of nature[6].
In an absolute antiprime we have a series of temporal thicknesses
successively packed one inside the other and converging towards the
ideal of no thickness. An absolute antiprime indicates the ideal of an
extensionless moment of time.
[6]The slab of nature forming a duration is limited in its temporal
dimension and unlimited in its spatial dimensions. Thus it represents
a finite time and infinite space.
Fig. 7.
For example let the horizontal
line represent the time; and assume nature to be spatially one-dimensional,
so that an unlimited vertical line in the diagram represents space at
an instant.
Fig. 8.
Then the area between the unlimited parallel lines and
represents a duration. Also the area between and
represents another duration which is extended over by the duration
bounded by and . But in fig. 7 we
have assumed only one time-system, which is the Newtonian hypothesis.
Suppose there are many time-systems and consider two such systems
and . These are represented by two lines inclined to
each other. A duration of time-system is represented by the
area between and , and a duration of time-system
is represented by the area between and . Two such durations
necessarily intersect and also can neither completely extend over the
other.
These diagrams are crude illustrations of some properties of durations
and are in many respects misleading as the sequel will show.
The set of moments which inhere in a duration are completely
characteristic of that duration, and vice versa. A moment is to be
conceived as an abstract of all nature at an instant. No abstractive
element can cover a moment except that moment itself. A moment is a
route of approximation to all nature which has lost its (essential)
temporal extension; thus it is nature under the aspect of a
three-dimensional instantaneous space. This is the ideal to which we
endeavour to approximate in our exact observations.
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