These considerations also give us a means of appraising the oft-repeated statement that in contradistinction to the physical laws the mathematical laws are absolutely accurate. The mathematical laws do not refer to real things, but to imaginary ideal limit cases. Consequently they cannot be tested by experience at all, and the demands science makes on them lie in quite a different sphere. Their nature must be such that _experience should approximate them infinitely_, if certain definite well-known postulates are to be more and more fulfilled, and that the various abstractions and idealizations should be so chosen as not to contradict one another. Such contradictions have by no means always been avoided. But we must not regard them as inherent in the inner organization of our mind, as Kant did. These contradictions spring from careless handling of the concept technique, by which postulates elsewhere rejected are treated as valid. We have already come across an instance of such relations in the application of the concept of equality to unlimited groups (p. 84). We must be guided by the same rules of precaution in answering the question whether the things felt as continuous--for example, space and time--are "truly" continuous, or whether in the last analysis they must not be conceived of as discontinuous. The various sense organs, and still more, the various physical apparatus with which we examine given states, are of very varying degrees of "sensibility," that is, the threshold for distinguishing the differences may be of very different magnitudes. Therefore, a thing which is discontinuous for a sensitive apparatus will behave as if it were continuous with a less sensitive apparatus. Accordingly, we shall find so many the more things continuous the less sharply developed our ability is to differentiate. While this circumstance makes it possible that we should regard discontinuous things as continuous, time relations in certain circumstances produce the opposite effect. Even if in a process the change is continuous but very rapid, and the new state remains unchanged for a certain time, we easily conceive of this sequence as discontinuous. We cannot resist this view of the process when the change occurs in a shorter time than the threshold time of our mind for each step in the process. But since this threshold changes with our general condition, one and the same process can appear to us both continuous and discontinuous according to circumstances. Here, therefore, we have a cause through the operation of which, with advancing knowledge, more and more things will become recognized as _continuous_.