Different sorts of relations between concepts are conceivable in the transition zone where the number changes. We may find that other examples are like that of temperature, which is simply a statistical effect of a great many phenomena which may be described individually in terms of the ordinary concepts of mechanics, so that in this case the number of concepts changes merely by temperature dropping out, leaving the others more or less unaffected. Or all the concepts may be more closely interwoven, so that when the total number of concepts changes it may not be possible to separate out a group of concepts whose defining operations are unchanged. In such a case we must say that the original concepts are not applicable on the new level. The most immediate application of this idea has been already mentioned, namely, to the concepts of space and time. If the operations by which space and time are measured on the ordinary scale of magnitude cannot be carried down as a whole into the region of quantum phenomena, then we must say that the ordinary concepts of space and time are not applicable to these phenomena. Closely connected with the sharper analysis of the operational structure of our concepts, we may expect in the future also a closer analysis of our inventions. This will take the form of a search for new physical facts which shall give to our inventions the character of physical reality. In case prolonged search fails to disclose such phenomena (as is probably now the case with the field concept of electrodynamics), we must then find some way of embodying explicitly in our thinking the fact that we are dealing with pure inventions and not realities. INDEX Absolute, 26 Absolute time, 4 Action at a distance, 46 Analysis of large into small, 51, 220 Arithmetic, 35 Atom, 59 Bell, 84 Birkhoff, 72 Black body, 112 Bohr, 190, 192 Born, 222 Boscovitch, 46 Bothe and Geiger, 116 Bridgman, 201 Brownian movement, 107, 129, 143 Bush, 142 Caloric fluid, 59 Campbell, 117 Carnot engine, 125 Causality, 80 ff Causal train of events, 85 Clifford, 28 Clock, 70 ff, 176 Compton, 116, 188 Continuity, 94 Conservation of charge, 135, 136 Conservative functions, 113 Constructs, 53 Correlation, 37 Cosmic units, 182 Cross word puzzle, 202 Descriptive background, 64 Determinism, 114, 209 ff Discontinuous space, 191 Döppler effect, 166 ds, 72 Eddington, 93 Einstein, vii, 1, 2, 3, 4, 7, 8, 9, 12, 13, 14, 64, 100, 155, 162, 163, 164, 167, 169, 170, 171, 172, 173, 175, 176, 177, 206 Electrical concepts, 131 ff Electrical explanation of universe, 50 Electrical mass, 139 Electric field, 56, 133 Empiricism, 3 Energy, 108 ff, 126 ff Euclidean space, 14, 15, 16, 18, 23, 52, 61, 67 Event, 95, 167 Explanation, 37 Explanatory crisis, 41 Extended time, 77