Page:The Concept of Nature.djvu/210

 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.

The preceding pages had been passed for press before I had the pleasure of seeing Sir T. L. Heath’s Euclid in Greek. In the original Euclid’s first definition is

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.

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