A little reflection will show that knowledge in the highest perfection would consist in the *simultaneous* possession of a multitude of facts. To comprehend a science perfectly we should have every fact present with every other fact. We must write a book and we must read it successively word by word, but how infinitely higher would be our powers of thought if we could grasp the whole in one collective act of consciousness! Compared with the brutes we do possess some slight approximation to such power, and it is conceivable that in the indefinite future mind may acquire an increase of capacity, and be less restricted to the piecemeal examination of a subject. But I wish here to make plain that there is no logical foundation for the successive character of thought and reasoning unavoidable under our present mental conditions. *We are logically weak and imperfect in respect of the fact that we are obliged to think of one thing after another.* We must describe metal as “hard and opaque,” or “opaque and hard,” but in the metal itself there is no such difference of order; the properties are simultaneous and coextensive in existence. Setting aside all grammatical peculiarities which render a substantive less moveable than an adjective, and disregarding any meaning indicated by emphasis or marked order of words, we may state, as a general law of logic, that AB is identical with BA, or AB = BA. Similarly, ABC = ACB = BCA = &c. Boole first drew attention in recent years to this property of logical terms, and he called it the property of Commutativeness.[50] He not only stated the law with the utmost clearness, but pointed out that it is a Law of Thought rather than a Law of Things. I shall have in various parts of this work to show how the necessary imperfection of our symbols expressed in this law clings to our modes of expression, and introduces complication into the whole body of mathematical formulæ, which are really founded on a logical basis. [50] *Laws of Thought*, p. 29. It is pointed out in the preface to this Second Edition that Leibnitz was acquainted with the Laws of Simplicity and of Commutativeness. It is of course apparent that the power of commutation belongs only to terms related in the simple logical mode of synthesis. No one can confuse “a house of bricks” with “bricks of a house,” “twelve square feet” with “twelve feet square,” “the water of crystallization” with “the crystallization of water.” All relations which involve differences of time and space are inconvertible; the higher must not be made to change places with the lower, nor the first with the last. For the parties concerned there is all the difference in the world between A killing B and B killing A. The law of commutativeness simply asserts that difference of order does not attach to the connection between the properties and circumstances of a thing--to what I call *simple logical relation*. CHAPTER III. PROPOSITIONS.