Finally; the Logician, intent upon perfecting the certitudes of his methods rather than upon expressing the confusing subtleties of truth, has done little to help thinking men in the perpetual difficulty that arises from the fact that the universe can be seen in many different fashions and expressed by many different systems of terms, each expression within its limits true and yet incommensurable with expression upon a differing system.  There is a sort of stratification in human ideas.  I have it very much in mind that various terms in our reasoning lie, as it were, at different levels and in different planes, and that we accomplish a large amount of error and confusion by reasoning terms together that do not lie or nearly lie in the same plane.

Let me endeavour to make myself a little less obscure by a flagrant instance from physical things.  Suppose some one began to talk seriously of a man seeing an atom through a microscope, or better perhaps of cutting one in half with a knife.  There are a number of non-analytical people who would be quite prepared to believe that an atom could be visible to the eye or cut in this manner.  But any one at all conversant with physical conceptions would almost as soon think of killing the square root of 2 with a rook rifle as of cutting an atom in half with a knife.  One’s conception of an atom is reached through a process of hypothesis and analysis, and in the world of atoms there are no knives and no men to cut.  If you have thought with a strong consistent mental movement, then when you have thought of your atom under the knife blade, your knife blade has itself become a cloud of swinging grouped atoms, and your microscope lens a little universe of oscillatory and vibratory molecules.  If you think of the universe, thinking at the level of atoms, there is neither knife to cut, scale to weigh, nor eye to see.  The universe at that plane to which the mind of the molecular physicist descends has none of the shapes or forms of our common life whatever.  This hand with which I write is, in the universe of molecular physics, a cloud of warring atoms and molecules, combining and recombining, colliding, rotating, flying hither and thither in the universal atmosphere of ether.

You see, I hope, what I mean when I say that the universe of molecular physics is at a different level from the universe of common experience;—­what we call stable and solid is in that world a freely moving system of interlacing centres of force, what we call colour and sound is there no more than this length of vibration of that.  We have reached to a conception of that universe of molecular physics by a great enterprise of organised analysis, and our universe of daily experiences stands in relation to that elemental world as if it were a synthesis of those elemental things.

I would suggest to you that this is only a very extreme instance of the general state of affairs, that there may be finer and subtler differences of level between one term and another, and that terms may very well be thought of as lying obliquely and as being twisted through different levels.