There is another reason for attempting to discover an instrument of reasoning (that is, of gaining new truths by means of old), which may be less vague and arbitrary than the talent and experience of the few or the common-sense of the many. As memory is not always accurate, and has on that account led to the adoption of writing, as being a _memoria technica_, unaffected by the failure of mental impressions,—as our senses at times deceive us, and have to be corrected by each other; so is it also with our reasoning faculty. The conclusions of one man are not the conclusions of another; those of the same man do not always agree together; those of ever so many who agree together may differ from the facts themselves, which those conclusions are intended to ascertain. In consequence it becomes a necessity, if it be possible, to analyze the process of reasoning, and to invent a method which may act as a common measure between mind and mind, as a means of joint investigation, and as a recognized intellectual standard,—a standard such as to secure us against hopeless mistakes, and to emancipate us from the capricious _ipse dixit_ of authority. As the index on the dial notes down the sun’s course in the heavens, as a key, revolving through the intricate wards of the lock, opens for us a treasure-house, so let us, if we can, provide ourselves with some ready expedient to serve as a true record of the system of objective truth, and an available rule for interpreting its phenomena; or at least let us go as far as we can in providing it. One such experimental key is the science of geometry, which, in a certain department of nature, substitutes a collection of true principles, fruitful and interminable in consequences, for the guesses, _pro re natâ_, of our intellect, and saves it both the labour and the risk of guessing. Another far more subtle and effective instrument is algebraical science, which acts as a spell in unlocking for us, without merit or effort of our own individually, the _arcana_ of the concrete physical universe. A more ambitious, because a more comprehensive contrivance still, for interpreting the concrete world is the method of logical inference. What we desiderate is something which may supersede the need of personal gifts by a far-reaching and infallible rule. Now, without external symbols to mark out and to steady its course, the intellect runs wild; but with the aid of symbols, as in algebra, it advances with precision and effect. Let then our symbols be words: let all thought be arrested and embodied in words. Let language have a monopoly of thought; and thought go for only so much as it can show itself to be worth in language. Let every prompting of the intellect be ignored, every _momentum_ of argument be disowned, which is unprovided with an equivalent wording, as its ticket for sharing in the common search after truth. Let the authority of nature, common-sense, experience, genius, go for nothing.