Logic Taught by Love. Mary Everest Boole

by a group of writers, among the foremost of whom may be mentioned Babbage, De Morgan, Gratry, and Boole. These philosophers have reclaimed us from bondage to the ignorant dictatorship of the opponents of "Grammarye," by proving that all the more important thought-processes can be illustrated Algebraically. Whatever can be stated in Algebraic symbols may legitimately be expressed, so far as possible, by mechanical action, or in diagrams. The practical possibilities of Algebraic notation are, it is true, far wider than those of mechanical or pictorial representation; but, when a truth has once been expressed Algebraically, it can no longer be considered fanciful to illustrate, by motion or by diagram, as much of it as is capable of such illustration. We are therefore free to teach the ​elements of the Higher Logic, to those unacquainted with the notation of Algebra, by the same methods as were used of old in schools of Free-Masonry and of Prophecy. Messrs. Benjamin Betts and Howard Hinton are creating a simple system of representation, by the use of which the study of Logic by diagrams will some day be carried much further than has ever yet been possible. In this Chapter I propose to give some idea of the elements of the Science which teaches geometrically the laws of mental Pulsation.

      A stone, escaping from a sling, exhibits tangential motion, overcoming the counteracting force of the string. According to modern definition, tangential momentum is not, properly speaking, a Force.

      "Let knowledge grow from more to more, yet more of reverence in us dwell;" reverence for the Light vouchsafed to those who had not our advantages in the way of technical knowledge. To the thinker of the far back ages, these were the facts presented as a basis for speculation:—

      If he dropped a stone from his hand, something made it fall at once, straight towards the earth. If he put it in a string and whirled it, something prevented its either falling as far as the string would allow, or yielding quite freely to the pull of the string. If it escaped from the string, something made it fly, not straight to the earth, but off towards the distant horizon. What were these rival somethings? Were they warring dæmons? And was his string a magic implement which altered the balance of power between these unseen personalities?

      If the thinker was a Hebrew Prophet, his doctrine of Unity provided him with an answer. The various ​phenomena were not the work of rival personalities, but various manifestations of the Dunamis or Power exerted by The Unity Who speaks through diversities. And when his confidence in that Unity had given him skill to conquer an opponent, both more richly endowed by Nature than himself and more amply provided with material and mechanical appliances (of learning ?), he went back to his sheepfold and sang under the silent stars: "Oh! how love I Thy Law; all the day long is my study in it." The knowledge of Science possessed by the ancient Hebrew was no doubt very elementary; but perhaps it does his more fortunate European successor no harm to reflect that, so far as it went, it was sound. Nor is it bad for the over-cultured, over-specialized, over-examined little victims of advanced education to have their hearts brought into sympathy with the emotions of the Sacred Past, while their fingers are handling its implements, and their intelligence is brought into contact with its problems. The practice of playing with such toys as the sling and stone, the sucking-valve, the old-fashioned rope-maker's wheel, and the bandalore, may be made a means of accustoming children's nerves to the feeling of Nature's opposing tendencies, and may prepare the organization for receiving knowledge, later on, into the conscious mind. By training the hand to trace out Nature's action, we train the unconscious brain to act spontaneously in accordance with Natural Law; and the unconscious mind, so trained, is the best teacher of the conscious mind.

      Another interesting exercise is that of tracing the Pentagram. Number the angles of a regular Pentagon in order; and draw straight lines from 1 to 3, from 3 to ​5, from 5 to 2, from 2 to 4, from 4 to 1. Repeat several times in succession. Choose the size of the Pentagon to suit the size of the hand. After some practice, the Pentagram should be drawn by freehand. The exercise may be varied by tracing the Heptagram, i.e. passing from one point to another of a regular Heptagon in this order—1, 4, 7, 3, 6, 2, 5, 1. Childish as the foregoing description may seem, the tracing of these figures gives a curious feeling of arriving at completeness, by a series of tentative Pulsations backwards and forwards; and in old days the idea of magic attached itself to the exercise. At a time when the ability to investigate the angles of the Pentagram represented a high degree of mathematical skill, we may imagine that some enthusiast, in a fit of that tender fun which is characteristic of scientific genius, conceived the idea of tracing the figure on his threshold, saying to his pupils, "No lying spirit can enter, nor can science degenerate into sorcery, if study is put under the safe guardianship of accurate mathematics. Very slight inaccuracies," he would add, "leave room for the entrance of any kind of treachery and deception."

      Later on it came to be believed that drawing a Pentagram on the threshold of a study prevented Satan from entering, provided it were drawn with sufficient accuracy. If at any point the junction were imperfect, the devil entered through the gap! The process by which the Pentagram degenerated from being the symbol of a scientific accuracy which shields from temptation to duplicity, into being a magic weapon of defence against a personal devil, is typical of all such degradations.

      We now pass from the Science which teaches Natural Law by training the muscles, to that which addresses ​itself more directly to the intellect, and through the intellect to the soul.

      The reform in the teaching of mathematics, now in agitation, depends essentially on getting teachers to understand that the chalk in the lecturer's hand becomes, at a given moment in the lesson, a Revealer, independent of (and, for the moment, superior to) the man who holds it; a Teacher of Teachers, King of Kings, and Lord of Lords. Yet how easily this essential doctrine of mathematics slips over into the slavish dogmas which ignorant people connect with the so-called doctrine of Transubstantiation! And how wisely did the English Church decree that the "transubstantiated" bread shall be eaten at once, not preserved as sacred! We do not wish the children to attach superstitious ideas to the chalk (or bread) when the demonstration is over; but if there is to be any vital reform in method we must make young teachers realize that, for a few moments in each lesson, he and the chalk change places; that for those moments the chalk, not he, is the true intermediary (or mediator) between the Unseen Revealer and the class. We cannot continue to boycott in England all vital mathematical teaching, just because stupid people have talked grovelling nonsense about the doctrine which is its vital essence.

      The manner in which a problem that baffles us when treated on its own level can often be solved by bringing to bear on the solution truths of a higher order than that contemplated when the question was first propounded, is well illustrated by the famous 47th Proposition of Euclid. The question proposed for solution is this:—Is there any constant relation between the length of ​the hypothenuse of a right-angled triangle and the lengths of the sides? We are now so familiar with the solution, we have so mechanicalized the process by which the answer is arrived at, that the significance of both escapes us. But let us place ourselves, in imagination, back at the time when the question was as yet nsolved and was being eagerly investigated. In studying the earlier problems of Euclid, questions about lengths of lines are settled by striking circles with compasses (which is virtually a process of measuring); and questions of area, etc., by superposition. Everything is referred to certain axioms which act as a hurdle set up for the purpose of giving children the exercise of climbing over it. The formal Logic in the beginning of Euclid exercises a certain mental agility; but everything which is really found out, is found out by trusting to the evidence of our senses aided by some mechanical process.

      But when we attempt to find a relation between the hypothenuse and sides of a right-angled triangle, all modes of measurement fail to show any fixed relation, and appear even to show that none exists. Those who were satisfied that nothing was valid except the evidence of the recognized instruments probably asserted that the existence of any fixed relation was disproved.

      But there were true Free-Masons in those days, or rather there were Free Geometers, the founders of Free-Masonry; bold, untamable spirits, who dared invoke the All-Seeing Eye of the Great Unity to enlighten their blindness; and who well knew that rules limiting the play of the human intellect were made, chiefly, to be defied. They claimed the right to seek Truth outside the limits marked by orthodox compasses; they ​knew that, when we find our way stopped in the order of thought to which we have hitherto