12.2 It may be objected that whenever the footrules are brought together, or when stuffs measured by them are brought together, the coincidences will be observed; and that this is all we need for the importance of measurement.
But the coincidences will not be observed unless the circumstances of the various experiments are sufficiently uniform. The stuffs must be under the same tension or at the same temperatures as on previous occasions. Sooner or later and somehow or other a judgment of constancy, that is, of the preservation of property, is required. Ultimately this judgment reposes upon direct common sense; namely, obviously the footrule is of good stiff material and has not perceptibly changed amid slight differences of circumstance. The coincidences which can easily be obtained between lengths of elastic thread inspire no such beliefs, because evidently the thread has been stretched.
12.3 Again, in Einstein's own example, there is the direct judgment of the uniformity of conditions for the uniform transmission of light. Thus any ordinary event among the fixed stars does not affect this uniformity for the transmission from the sun to the earth. Apart from such presuppositions, so obvious that they do not enter into consciousness, the whole theory collapses.
12.4 These judgments of constancy are based on an immediate comparison of circumstances at different times and at different places. Such judgments are not infallible and are capable of being tested under certain circumstances. For example it may be judged that two footrules would coincide if they were brought together; and this experiment can be made, and the judgment tested.
The rejection of an immediate judgment of constancy is no paradox. There are differences between any distinct sets of circumstances, and it is always possible that these differences cut deeper than we have perceived so as to produce unsuspected divergences of properties.
But a judgment of constancy is recognition, and recognition is the source of all our natural knowledge. Accordingly though isolated judgments may be rejected, it is essential that a rational consideration of nature should assume the truth of the greater part of such judgments and should issue in theories which embody them.
12.5 This recognition of congruity between distinct circumstances has no especial connection with coincidence and extends far beyond the mere judgments of time and space. Thus judgments of the matching of colours can be made without coincidence by most people to some slight extent, and by some people with surprising accuracy. It may be urged that only in the case of judgments of spatial and temporal coincidence can great accuracy be obtained. This may be true; but complete accuracy is never obtained, and the ideal of accuracy shows that the meaning is not derived from the measurement. Our recognitions are the ultimate facts of nature for science, and the whole scientific theory is nothing else than an attempt to systematise our knowledge of the circumstances in which such recognitions will occur. The theory of congruence is one branch of the more general theory of recognitions. Another branch is the theory of objects which is considered in the next part of this enquiry.
[PART II]
THE DATA OF SCIENCE
[CHAPTER V]
THE NATURAL ELEMENTS
[13. The Diversification of Nature]. 13.1 Our perceptual knowledge of nature consists in the breaking up of a whole which is the subject matter of perceptual experience, or is the given presentation which is experience—or however else we prefer to describe the ultimate experienced fact. This whole is discriminated as being a complex of related entities, each entity having determinate qualities and relations and being a subject concerning which our perceptions, either directly of indirectly, afford definite information. This process of breaking up the subject matter of experience into a complex of entities will be called the 'diversification of nature.'