stratifications of nature bears on the
formulation of the laws of nature. It has been laid down that these laws
are to be expressed in differential equations which, as expressed in any
general system of measurement, should bear no reference to any other
particular measure-system. This requirement is purely arbitrary. For a
measure-system measures something inherent in nature; otherwise it has
no connexion with nature at all. And that something which is measured
by a particular measure-system may have a special relation to the
phenomenon whose law is being formulated. For example the gravitational
field due to a material object at rest in a certain time-system may be
expected to exhibit in its formulation particular reference to spatial
and temporal quantities of that time-system. The field can of course be
expressed in any measure-systems, but the particular reference will
remain as the simple physical explanation.

NOTE: ON THE GREEK CONCEPT OF A POINT

The preceding pages had been passed for press before I had the pleasure
of seeing Sir T. L. Heath's _Euclid in Greek_[14]. In the original
Euclid's first definition is

semeion estin, ou meros outhen.

I have quoted it on p. 86 in the expanded form taught to me in
childhood, 'without parts and without magnitude.' I should have
consulted Heath's English edition--a classic from the moment of its
issue--before committing myself to a statement about Euclid. This is
however a trivial correction not affecting sense and not worth a note. I
wish here to draw attention to Heath's own note to this definition in
his _Euclid in Greek_. He summarises Greek thought on the nature of a
point, from the Pythagoreans, through Plato and Aristotle, to Euclid. My
analysis of the requisite character of a point on pp. 89 and 90 is in
complete agreement with the outcome of the Greek discussion.

[14] Camb. Univ. Press, 1920.

NOTE: ON SIGNIFICANCE AND INFINITE EVENTS

The theory of significance has been expanded and made more definite in
the present volume. It had already been introduced in the _Principles of
Natural Knowledge_ (cf. subarticles 3.3 to 3.8 and 16.1, 16.2, 19.4, and
articles 20, 21). In reading over the proofs of the present volume, I
come to the conclusion that in the light of this development my
limitation of infinite events to durations is untenable. This limitation
is stated in article 33 of the _Principles_ and at the beginning of
Chapter IV (p. 74) of this