Another illustration, more purely logical, may be useful. It seems natural to say that any given shade of colour is a quality, i.e. that when we say "this is red," we are saying that "this" has a characteristic which we cannot express otherwise than by a predicate—assuming, for the moment, that "red" stands for just one shade of colour. But although this may be the right view, there is no logical necessity for supposing that it is. We might define one shade of colour as "all the coloured surfaces which have exact colour-similarity to a given surface." Thus "this has the colour " is replaced by "this is one of the class of entities that have exact colour-similarity with "; and " is a colour" will be replaced by " is the class of all entities having exact colour-similarity with a given entity." In this case, no facts can be conceived which would give reason for preferring one form of statement to the other, since any ascertainable fact can be interpreted equally well on either theory. We have, in fact, something more or less analogous to the arbitrariness of co-ordinates in the general theory of relativity. Provided our symbols have the same interpretation when they apply to percepts, their interpretation elsewhere is arbitrary, since, so long as the formulæ remain the same, the structure[Pg 289] asserted is the same whatever interpretation we give. Structure, and nothing else, is just what is asserted by formulæ in which the meaning of the terms is unknown, but the purely, logical symbols have definite meanings (see Chapter XVII.). Even the purely logical symbols are arbitrary to a certain limited extent, as we saw in the above example of colours. But often, when facts from different regions have to be brought into connection, one interpretation is much simpler than another. Often, also, one interpretation involves less inference than another, and is therefore less likely to be wrong. These are the main motives governing any suggested interpretation of the symbols which occur in mathematical physics. FOOTNOTES: [58] Dr C. D. Broad, in The Mind and its Place in Nature, lays stress upon what he calls "emergent" properties of complexes—i.e. such as cannot be inferred from the properties and relations of the parts. I believe that "emergent" properties represent merely scientific incompleteness, which would not exist in the ideal physics. It is difficult to advance any conclusive argument on either side as to the ultimate character of apparently "emergent" properties, but I think my view is supported by such examples as the explanation of chemistry in terms of physics by means of the Rutherford-Bohr theory of atomic structure. [Pg 290] CHAPTER XXVIII THE CONSTRUCTION OF POINTS[59]