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
35. Levels, Rects, and Puncts.
35.1 The electromagnetic theory of relativity is obviously the
more general of the two. It has also the merit of providing definitions
of flatness, of straightness, of punctual position, of parallelism, of
time-order and spatial order as interconnected phenomena, and (with the
help of cogredience) of perpendicularity and of congruence. The theory
of extension has also provided the definition of a duration. It is a
remarkable fact that the characteristic concepts of time and of geometry
should thus be exhibited as arising out of the nature of things as
expressed by the two fundamental relations of extension and cogredience.
It has already been explained that a moment is the route of
approximation towards an instantaneous three-dimensional whole of
nature. The set of abstractive elements and abstractive classes covered
by both of two non-parallel moments is the locus which is their common
intersection. Such a locus will be called a 'level' in either moment. A
level is in fact an instantaneous plane in the instantaneous space of
any moment in which it lies. But we reserve the conventional spatial
terms, such as 'plane,' for the time-less spaces to be defined later.
Accordingly the word 'level' is used here.
35.2 An indefinite number of non-parallel moments will intersect
each other in the same level, forming their complete intersection;
and one level will never be merely a (logical) part of another
level. Let three mutually intersecting moments
(, say)
intersect in the levels . Then
three cases can arise: either (i) the levels are all identical
[this will happen if any two are identical], or (ii) no pair of
the levels intersect, or (iii) a pair of the levels, say
and , intersect. In case (i) the three moments are
called 'co-level.' In case (ii) there are special relations of
parallelism of levels, to be considered later. In case (iii) the locus
of abstractive elements and abstractive classes which forms the
intersection of and will be called a 'rect'; let
this rect be named . Then is also the complete
intersection of and , and of and , and of
the three moments . When three moments have a
rect as their complete intersection they are called 'co-rect.' A rect is
an instantaneous straight line in the instantaneous three-dimensional
space of any moment in which it lies. But, as before, the conventional
space-nomenclature is avoided in connection with instantaneous spaces.
35.3 For four distinct moments there are four possible cases in
respect to their intersection. In case (i) there is no common
intersection: in case (ii) there is a common intersection which is a
level: in case (iii) there is a common intersection which is a rect: in
case (iv) there is a common intersection which is neither a rect nor a
level; in this case the common intersection will be called a 'punct.'
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