of transformations, beginning in A, ending (so far) in B, and leaving invariant the characters I.”
Now all that we mean by the laws governing a system of facts is that within this system certain series of observed or of validly conceived “transformations” can be defined, such that throughout the whole series of transformations some definable characters of the objects that are undergoing the transformation do not vary. Wherever I can say that, in passing from A to B, through a series of stages which I have a right to view as real facts in the world, I observe, or validly conceive, that all the stages have certain uniform or “invariant” characters, I then have discovered a law which, in this way of interpreting the world, I conceive as expressing the nature and structure of the facts that I acknowledge as real.
Thus, moving a body from one part of space to another leaves, of itself, the shape of the body unchanged. Whoever discovers that, discovers the property of space defined by the so-called “axiom” or law of “free mobility.” All physical and chemical changes, so far as known, leave the mass of matter unaltered. This is another example of law. All the transformations which a gravitating system of bodies undergoes are such as to leave invariant the precise system of relationships which that law defines. And so one could continue indefinitely. What laws our discriminating intelligence and our discovery of the serial linkages shall lead us to define, this view of our world leaves us unable to predict. But that some laws will come to be acknowledged, this is as certain as that the serial method of interpreting the
