The organisation of thought, educational and scientificWhitehead, Alfred North
Philosophy
The organisation of thought, educational and scientific
Whitehead, Alfred North
Education
We note again that the relational theory of space from another point
of view brings us back to the idea of the fundamental space-entities
as being logical constructs from the relations between things. The
difference is, that this paragraph is written from a more developed
point of view, as it implicitly assumes the things in space, and
conceives space as an expression of certain of their relations.
Combining this paragraph with what has gone before, we see that the
suggested procedure is first to define "things" in terms of the data of
experience, and then to define space in terms of the relations between
things.
This procedure is explicitly assumed in the next short paragraph: "In
this connection ... from the events."
The gist of the remaining paragraphs of this section is contained in
the paragraph at the bottom of p. 196: "The point in time ... new
importance."
The sentence, "We live in durations, and not in points," can be
amplified by the addition, "We live in space-extensions and not in
space-points."
It must be noted that "whole and part" as applied to extensions in
space or time must be different from the "all and some" of logic,
unless we admit points to be the fundamental entities. For "spatial
whole and spatial part" can only mean "all and some" if they really
mean "all the points and some of the points." But if extensions and
their relations are more fundamental than points, this interpretation
is precluded. I suggest that "spatial whole and spatial part" is
intimately connected with the fundamental relation between things from
which our space ideas spring.
The relation of space whole to space part has many formal properties
which are identical with the properties of "all and some." Also when
points have been defined, we can replace it by the conception of "all
the points and some of the points." But the confusion between the two
relations is fatal to sound views on the subject.
_Diverse Euclidean Measure Systems_
The next section deals with the measure systems applicable to space.
Public-domain text, read in full here on John Shaqi.
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