Two classes of objects may differ in qualities, and yet they may agree in number. This point strongly confirms me in the opinion which I have already expressed, that all inference really depends upon equations, not differences. The Logical Alphabet thus enables us to make a complete analysis of any numerical problem, and though the symbolical statement may sometimes seem prolix, I conceive that it really represents the course which the mind must follow in solving the question. Although thought may outstrip the rapidity with which the symbols can be written down, yet the mind does not really follow a different course from that indicated by the symbols. For a fuller explanation of this natural system of Numerically Definite Reasoning, with more abundant illustrations and an analysis of De Morgan’s Numerically Definite Syllogism, I must refer the reader to the paper[93] in the Memoirs of the Manchester Literary and Philosophical Society, already mentioned, portions of which, however, have been embodied in the present section. [93] It has been pointed out to me by Mr. C. J. Monroe, that section 14 (p. 339) of this paper is erroneous, and ought to be cancelled. The problem concerning the number of paupers illustrates the answer which should have been obtained. Mr. A. J. Ellis, F.R.S., had previously observed that my solution in the paper of De Morgan’s problem about “men in the house” did not answer the conditions intended by De Morgan, and I therefore give in the text a more satisfactory solution. The reader may be referred, also, to Boole’s writings upon the subject in the *Laws of Thought*, chap. xix. p. 295, and in a paper on “Propositions Numerically Definite,” communicated by De Morgan, in 1868, to the Cambridge Philosophical Society, and printed in their *Transactions*, vol. xi. part ii. CHAPTER IX. THE VARIETY OF NATURE, OR THE DOCTRINE OF COMBINATIONS AND PERMUTATIONS. Nature may be said to be evolved from the monotony of non-existence by the creation of diversity. It is plausibly asserted that we are conscious only so far as we experience difference. Life is change, and perfectly uniform existence would be no better than non-existence. Certain it is that life demands incessant novelty, and that nature, though it probably never fails to obey the same fixed laws, yet presents to us an apparently unlimited series of varied combinations of events. It is the work of science to observe and record the kinds and comparative numbers of such combinations of phenomena, occurring spontaneously or produced by our interference. Patient and skilful examination of the records may then disclose the laws imposed on matter at its creation, and enable us more or less successfully to predict, or even to regulate, the future occurrence of any particular combination.