But we are not obliged to have our fundamental cube one inch in size. We can take it as small as we like, and build up the block, using a greater number of such cubes. We can take it the twenty-seventh of the twenty-seventh of an inch cube; or, in fact, as small as ever we like. And if we take a very small cube as the fundamental one with which we build up the Block III., then, using this same fundamental cube to build up Block IV., we should find a disadjustment, although this disadjustment would only come in when we come down to the very minute cube, and studied its relationship to the whole Block IV.
Thus, apparently, the Block IV. could never be built up consistently, using as its fundamental cube the fundamental cube out of Block III. But in saying this we have really made an assumption.
It is obvious that Cubes V. and VI., just like Cubes III. and IV., considered as shapes made up of matter, are very different, and could not be shifted one on to the other.
But all our laws and feelings about movements and possibilities are founded on the observation of objects having a certain degree of magnitude.
But the fundamental cube, which we must assume, may be supposed to be of a degree of magnitude less than any known degree.
In cubes of a certain size V. and VI. are different, and cannot be made to coincide.
But we are absolutely unable to say anything about cubes beyond a certain degree of smallness. With cubes of a certain degree of minuteness, V. and VI. might be able to be made coincide.
Thus, for instance, we feel as if we could divide a piece of matter on and on for ever. But chemists tell us that, after a certain number of divisions, the next division would split it up into two different kinds of matter. Since all our reasoning is founded on the behaviour of objects of known size, we can tell nothing at all by inference about the behaviour of very small objects.
It is obvious that, from our customary experience, we can assert absolutely nothing at all about the extremely minute or the extremely large. All reasoning which is founded on the likeness between the extremely small and the ordinary objects of our observation is absolutely valueless as telling us any truth.
Of course, by saying this we have not got rid of the argument for the difference of III. and IV. But we have put the thing from the observation of which that argument is drawn out of the region of known things. We have put it into the hazy land of the extremely minute. Its argument is good, but it depends on its being of a certain size. We suppose it less than that size, and we can consider the subject without regard to its argument.