Secondly, the more immediate importance of the machine seems to consist in the unquestionable proof which it affords that correct views of the fundamental principles of reasoning have now been attained, although they were unknown to Aristotle and his followers. The time must come when the inevitable results of the admirable investigations of the late Dr. Boole must be recognised at their true value, and the plain and palpable form in which the machine presents those results will, I hope, hasten the time. Undoubtedly Boole’s life marks an era in the science of human reason. It may seem strange that it had remained for him first to set forth in its full extent the problem of logic, but I am not aware that anyone before him had treated logic as a symbolic method for evolving from any premises the description of any class whatsoever as defined by those premises. In spite of several serious errors into which he fell, it will probably be allowed that Boole discovered the true and general form of logic, and put the science substantially into the form which it must hold for evermore. He thus effected a reform with which there is hardly anything comparable in the history of logic between his time and the remote age of Aristotle. Nevertheless, Boole’s quasi-mathematical system could hardly be regarded as a final and unexceptionable solution of the problem. Not only did it require the manipulation of mathematical symbols in a very intricate and perplexing manner, but the results when obtained were devoid of demonstrative force, because they turned upon the employment of unintelligible symbols, acquiring meaning only by analogy. I have also pointed out that he imported into his system a condition concerning the exclusive nature of alternatives (p. 70), which is not necessarily true of logical terms. I shall have to show in the next chapter that logic is really the basis of the whole science of mathematical reasoning, so that Boole inverted the true order of proof when he proposed to infer logical truths by algebraic processes. It is wonderful evidence of his mental power that by methods fundamentally false he should have succeeded in reaching true conclusions and widening the sphere of reason. The mechanical performance of logical inference affords a demonstration both of the truth of Boole’s results and of the mistaken nature of his mode of deducing them. Conclusions which he could obtain only by pages of intricate calculation, are exhibited by the machine after one or two minutes of manipulation. And not only are those conclusions easily reached, but they are demonstratively true, because every step of the process involves nothing more obscure than the three fundamental Laws of Thought. *The Order of Premises.*