An enquiry concerning the principles of natural knowledge — John Shaqi
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
8.2 An event-particle occupies instantaneously a certain point in
the space of and a certain point in the space of .
Thus instantaneously there is a certain correlation between the points
of the space of and the points of the space of .
Also if the particle has the character of material at rest at the point
in the space of , this material-particle has a certain
velocity in the space of ; and if it be material at rest at the
point in the space of , the material-particle has a certain
velocity in the space of . The direction in -space of
the velocity due to rest in the correlated -point is said to
be opposite to the direction in -space of the velocity due to
rest in the correlated -point. Also with congruent units of
space and of time, the measures of the velocities are numerically equal.
The consequences of these fundamental facts are investigated in
Part III. The relation of the -space to the
-space which is expressed by the velocities at points in
-space due to rest in the points of -space and by the
opposite velocities in -space due to rest in the points of
-space is called the 'kinematic relation' between the two
consentient sets, or between the two spaces.
8.3 The simplest form of this kinematic relation between a pair
of consentient sets is when the motion of either set in the space of the
other is a uniform translation without acceleration and without
rotation. Such a kinematic relation will be called 'simple.' If a
consentient group has a simple kinematic relation to each of
two consentient sets, and , then
and have a simple kinematic relation to each other. In technical
logical language a simple kinematic relation is symmetrical and
transitive.
The whole group of consentient sets with simple kinematic relations to
any one consentient set, including that set itself, is called a 'simple'
group of consentient sets.
The kinematic relation is called 'translatory' when the relative motion
does not involve rotation; namely, it is a translation but not
necessarily uniform.
8.4 The fact that the relational theory of space involves that
each consentient set has its own space with its own peculiar points is
ignored in the traditional presentation of physical science. The reason
is that the absolute theory of space is not really abandoned, and the
relative motion, which is all that can be observed, is treated as the
differential effect of two absolute motions.
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