Mary Everest Boole

Logic Taught by Love

Published by Good Press, 2022
goodpress@okpublishing.info
EAN 4064066064655

Table of Contents


In the Beginning was the Logos
The Natural Symbols of Pulsation
Geometric Symbols of Progress by Pulsation
The Sabbath of Renewal
The Recovery of a Lost Instrument
Babbage on Miracle
Gratry on Logic
Gratry on Study
Boole and the Laws of Thought
Singular Solutions
Algebraizers
Degenerations towards Lunacy and Crime
The Redemption of Evil
The Science of Prophecy
Why the Prophet should be Lonely
Reform, False and True
Critique and Criticasters
The Sabbath of Freedom
The Art of Education
Trinity Myths
Study of Antagonistic Thinkers
Our Relation to the Sacred Tribe
Progress, False and True
The Messianic Kingdom
An Aryan Seeress to a Hebrew Prophet
Appendix I
Appendix II

In the Beginning was the Logos

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Logic Taught by Love

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CHAPTER I
IN THE BEGINNING WAS THE LOGOS

What creative Energy is, in Its own Nature, we do not know; It is The Ineffable I Am. What we do know about It is the fact that It pulsates. The very life of all that lives consists of some mode or other of Pulsation or alternate action. Without this Pulsating action, nothing grows. As the old writers said, It was in the world, and the world obeyed It by compulsion but knew it not. Then It made man, free to know It. Man, being free, sought out many inventions, all intended to substitute some fixed condition for incessant pulsation in human affairs; and to substitute the worship of some fixed entity for that of the Eternal Pulsator. But to some few the secret Wisdom revealed Itself; and to them It gave power to become Sons of God. And all the History of religion, of morals, and of Philosophy, is a history of conflict between the Seers who would teach the Law of Pulsation and the multitude who would pervert their teaching.

All Life is pulsation; and health is always rhythmic pulsation timed in accordance with the proper rhythm of the particular organ. Every baby's lungs learn this at their first contact with the air; the baby-heart has caught the secret long ago by sympathetic contagion from its mother's heart. Nature teaches her mighty secret to the baby heart and lungs; and leaves the "voluntary muscles" and the brain to learn it voluntarily. We have gone but a little way yet towards finding out how to do this; still the gymnast knows that much may be done towards hardening limbs against fatigue and disease, by a regular rhythmic alternation of extension and contraction; and logicians such as Gratry (and much greater men before him) knew that, to a large extent, the same can be done with the mental faculties. The future possibilities that open out before us as we study the great Logicians of the Pulsation doctrine, are overwhelming; one hardly dares realize all that they imply; but the fact is, that the heart and lungs do actually sing in their own language, the Eternal Hymn—Holy, Holy, Holy is the Logos, the Hidden Wisdom, the Principle of Rhythmic Pulsation, which was in the beginning, is now and ever shall be, Creator of all that is, Preserver of what has proved itself worthy, Purifier by the destruction of all that is sluggish or disorderly. The goal to which we are tending seems to be to train all our faculties, one after another, to take their parts in the same Chorus. The very antagonism of the masses to the teachers of Pulsation is a suspension which enriches the Harmony, the means by which is created the possibility of the Highest Rhythm. Humanity toys and coquets with its own bliss; it dares not let itself know what the Logos has prepared for those who love Him.

For no one really doubts the doctrine of Pulsation. Every new birth is a witness to the truth that conception (whether physical or mental) is the result of re-uniting at a suitable moment elements that have been suitably differentiated. We all know it; but we fear to let ourselves believe. History, as the Apocalyptic Seers knew, is the story of the alternate withdrawal of man's mind from the Logos-doctrine and re-union with it.

That perennial Love-Story has been intertwined with another, not less solemn and vital. Far back in the ages a Tribe was differentiated, to be to the other races of the earth what the Unseen Logos is to Humanity as a whole; the subject of incessant misunderstanding; and the object of alternate fear, dislike, contempt, and superstitious reverence. We never understand the People of Israel (nor can it be said that they ever rightly understand us); but every now and then we are made to feel that some magnetism is coming forth from the incomprehensible Race, which acts as a solvent to our metaphysical perplexities; which is the witness to and preparation for a Life higher than anything we can conceive.

The complex and variable relation between Jews and Gentiles, so unutterably sweet in some aspects, so bitter often, so unsettled and incomprehensible always, seems to be one chief means by which Humanity is being made fit for the rapture of intelligent comprehension, and able to look into the Face of Love.

The Race of Israel is the hereditary priesthood of that Unity whose action is Pulsation. There is another such priesthood: occasional, unrecognized, consecrated by no hand but that of suffering, marked out by no special observance except that of being always peculiar everywhere; High Priests for ever after that order to which all official priesthoods are forced, sooner or later, to do homage. Out of the deeps they have called; and Truth has heard. Where steady health sees solid things and enduring systems, the sick often perceive, instead, a shimmering palpitation.

The man of whom it is said that he made the greatest advance in Logic since Aristotle, said of himself, that no one could do certain kinds of work unless he would consent to be ill. The majority decide, of course, that the perceptions of illness are "abnormal"; in old days these abnormal perceptions were called "miraculous." The name matters little; the important thing for us is to see that we do not waste the gifts that God sends through suffering.

Jesus, the High Priest of Pulsation, offered himself to death rather than support any one-sided rights or any fixed doctrine. And having been slain by one set of idolaters, He was made into the object of sensational worship by another set. And now, as ever, the teachers of the Eternal Logos are alone on the earth; and yet we are not alone, because the Father is with us, and all the Seers who went before us.

If we sorrow overmuch about the idolatry of our brethren, do not we thus prove ourselves to be also idolaters who would arrest the natural Pulsations? For the conflict between Seers of New Truth and the lovers of fixed ideas is the very palpitation of human life, the great witness to the doctrine that progress takes place by pulsation.

In some of the following Chapters an attempt is made to picture past episodes in the conflict between the Logos-Seers and their antagonists; in others, suggestions are offered of means whereby that very conflict might be converted into an orderly and peaceable mental gymnastic.

The Natural Symbols of Pulsation

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CHAPTER II
THE NATURAL SYMBOLS OF PULSATION

Heaven and Earth declare the wonder of His Work.


The History of early religions is very much a history of the successive introductions into public worship of various symbols, by means of which the Seers hoped to make the masses realize the perpetual Flux or Pulsation which underlies the phenomena of Nature. The Seer perceives the Law of Pulsation by observing a certain phenomenon; that phenomenon becomes for him interesting; he tries to make the masses share his interest in it, as a revelation of Nature's fundamental Law; the masses lose sight of the idea of pulsation, and get up an idolatrous (i.e. fixed) tension on the symbol itself. To the pure in heart who see the Logos, all things are pure, because all things suggest the ineffable "process of becoming"; and those things are naturally sacred to any man, and an object of religious reverence, which most vividly suggest it to him. But to the masses things are not thus pure; because they see, in each thing, not the Creative Logos, but some special quality which is, or which they suppose to be, the especial characteristic of that object. Each Seer tries to break up the association of special Sanctity which clings round the symbol employed by his predecessor; in all good faith and innocence he tries to teach Flux-doctrine by some new symbol; and so the process begins again. It has in various forms gone on throughout the History not only of religion, but of all the intellectual and moral life of the world; it is made intelligible by studying those natural objects which at various times have been associated with religious ceremonies.

The movements of the Heavenly Bodies revealed to the Seers some mighty Principle of rhythmic motion; those whom they tried to indoctrinate with this idea worshipped Sun and Moon and Stars. The Seers erected stones to facilitate consecutive observation of the heavenly motions; the people supposed those stones to be possessed of magic virtues. It would seem that at some time in the world's history the process of becoming was taught chiefly by reference to vegetable growth. The people attached fantastic ideas to the grotesque forms of certain vegetable objects. Then the Seers selected for use in teaching certain trees distinguished by the absence of tendency to grow into suggestive shapes, and which exhibit in a severely simple form the main laws of growth.[1] The idolaters constituted these particular trees or plants sacred. Then the Seers ordered the sacred plants to be burned in homage to the Unseen Cause of growth; the masses made an idolatrous ceremonial out of the very act of destroying a sacred Symbol. The Seers would seem then to have turned from the vegetable, which only grows, and whose growth can only be inferred, not seen, to the animal, in which the life-process reveals itself by visible motion. To the medical priest, who, by dissecting a ram's heart, has caught the secret of the throbbing of his own heart, the ram is henceforward a sacred object. The mass of mankind are, however, not easily interested in abstruse and as yet imperfectly developed physiological theories; to them, a ram is — a beast of certain shape. They see his form, but not the pulsating force which constitutes his life; and, of all that the enthusiast has told them, they remember nothing, except that when they say their prayers they are to look at a ram. From that to the worship of a ram-god is an easy step for the unthinking multitude.

When the sacred beast dies, Superstition makes of him a mummy, so as to preserve as much of him as can be preserved. The Seer orders him to be burned in honour of The Unseen Giver of Life. The masses attach superstitious ideas to the very fire that consumes the offering. The Seer orders that part of the flesh shall be consumed, not by the fire, but by the very worshippers; the masses make the meal a superstitious observance. Some Seer tries to show that the important thing in the beast is not his death, but the lessons drawn from the palpitating entrails which reveal the secret of life; the next generation declares that the Prophet drew auguries from the entrails.

Another Seer tells how mere tension on the lessons of the past is idolatrous and barren, and mere following of one's personal inspirations is dangerous and misleading; that he alone is a true Prophet by whose head converge the two streams of instruction, inspiration and tradition, as two birds may fly from distant points of the horizon.[2] Posterity says that the great man of old taught how to gather knowledge from the flight of birds. And so on, ever round and round the same weary circle, the Seers rolling up the Sisyphus-stone towards true enlightenment; the masses ever plunging back into idolatry and carnalism.

There was in old times one practical difficulty connected with the conflict, which may well account for the eagerness of ancient Prophets to put an end to idolatrous conceptions. To every genuine philosopher the symbols of certain physical functions are among the most sacred of all objects, as being the perennial witness that the Logos is with man; and not with man only, but with all Creation. But the masses can see nothing in these objects except the symbols of certain pleasurable sensations; and if they are taught to think intently of them, they make their religion consist in the stimulation of mere sensation. This has been the cause of numberless disorders, and excuses much Prophetic injustice and bigotry on the subject of Idolatry.

The Founders of Judaism desired that the People should be taught, as far as possible, by symbols possessing in a very marked manner the property of evanescence. The Sun and Moon, the symbols of pure Light, had been degraded to idolatrous purposes; Moses seems to have tried to make his people feel that some phosphorescent material, which shone only rarely, was more truly sacred than the Sun and moon. In fact, the Mosaic religion may be described as one which abjures, as far as possible, the consecration of colour-and-form manifestations which are either partial or permanent; it takes, for its principal symbols, manifestations which are essentially evanescent; and it keeps permanently enshrined nothing but revealed Laws. The writer of Genesis asserts that the true symbol of God's covenant with Man is the Rainbow; which no man can capture or embalm or enshrine; which is made by the occasional breaking-up of the One Light into many colours, to fade before long into the Unity of White Light again; and which, when it departs, leaves nowhere in the world a trace of its having existed, except on man's heart an impression of spiritual beauty, and in his mind the power of attaining a knowledge of the Laws of Light.

We gain a curious side-light on the early history of religions by the study of Cornish legends. When, in the early ages, savage tribes were converted by strangers of a different religion, the priests who converted them taught them to connect the memorials of their old faith with the idea of evil magic. Where, therefore, we find Druidic stones, believed by peasants to be relics of evil magicians, we may guess that some conversionist has been trying to indoctrinate people with his views. In Cornwall there are distinct traces of a stratum of some religion intervening between the old idolatry of fixed stones and the Christian ideas imported from Rome through England. The characteristic of Cornish legends is that monoliths are people who would not pay proper respect to the Sabbath; and who, as punishment for that crime, were arrested on their way to somewhere where they wanted to go, and were struck into stone to stand on the moor for ever, to show what comes of not keeping Sabbath. Now when we know about any preacher, that he instructs his flock to expect, as the penalty for neglect of religious observances, arrestation of progress, and the falling into a permanently fixed position, we can form a tolerably clear idea what was the main character of the religion taught by him. we are not here, however, left dependent on mere inference, for the religious teachers who converted the Cornish from their early idolatry left behind them another trace besides the legend of the people who would not keep Sabbath. In contrast with these evil stones, there are others held sacred by the peasants almost to our own day; the so-called "logan-stones." A logan-stone is one so delicately poised, that a child's touch can make it sway to and fro; yet it presently returns to a position of equilibrium by virtue of its natural equipoise. The name "Logan" is derived from a word in use in Cornwall, to "log" i.e. to sway, rock, vibrate. We need not ask what was the philosophy of teachers who held sacred the logan-stone.

Perhaps the most impressive of all Natural Symbols of progress by Pulsation is the one referred to by Jesus—the Law of the circular Storm, which might be suggested to any true lover of Nature by observing the wheeling dust. The Spirit which guides man is like the whirling wind; it blows backward in one place while it is blowing forward in another; so that you cannot tell in what direction it is going as a whole, merely from feeling how it blows on you.

In connection with this subject I may mention a remark that has occurred to me in reading works of piety. All sorts of religious writers agree in describing the troubles of life as "stormy seas." The instinct of some leads them to speak of taking refuge from the storm in an Ark (which sways with the heaving sea, and yields to its every motion); while others, on the contrary, prefer to think of clinging for safety to a fixed stone or cross, or other immovable object. The writers of "clinging" symbolism are of the properly orthodox type; if such a man should happen to disagree with the ecclesiastical superior who is in authority over him, it will be owing to the disturbing accident of some other having gained a stronger hold on his mind. But the man who, like Baxter, writes hymns about taking refuge in an Ark, is normally a heretic by the very nature of his mind; a natural Free-thinker, born to be a reformer and an Apostle of the Hidden Logos. There are, indeed, some who express the sense of trust in God without reference even to an intervening Ark; they find sufficient security in the very Law of the Storm itself. He who is scientific enough to know the rhythmic pulsation which is revealed in the Law of the Storm, feels sure that it will cease when the appointed time has come. Suggestions of this feeling are common in the Hebrew Scriptures; the following is a modern English instance:—

"O'er this fair and blooming earth,
When the rushing storm has birth,
And the winged lightning flies,
And the tempest rends the skies,
And the sea with deafening roar
Rolls its strength along the shore;
Yet within its limits' bound
Raves that storm its little round.
O'er the flood Jehovah reigns,
Ever He a King remains.

"From the sphere of human things,
When Peace waves her parting wings,
Bidding mighty Nations quail
At the Future's opening veil;
Famine lift her withered hand,
Battle waste a sinking land,

Social warfare, civil strife,
Wither all the flowers of life;
Yet within its bounds assigned
Is that tempest's wrath confined;
And in limits sealed and set
Human passions roll and fret;
O'er the Water-flood Who reigns
Evermore a King remains.

"When above my fainting head
Gathering clouds of ill are spread,
Wild and dark the Heavens around,
Rough my path on alien ground;
Still, O Lord of Hosts, in Thee
Shall my trust unwavering be;
For the dwelling of Thy Throne
Is where tempests are unknown;
And Thy sceptre and Thy sway
All life's waves and storms obey;
O'er the Water-flood Who reigns
Evermore a King remains."

George Boole.
  1. Such is the characteristic of all the sacred Trees which I have been able to examine.
  2. Odin's birds were "Thought and "Tradition."

Geometric Symbols of Progress by Pulsation

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CHAPTER III
GEOMETRIC SYMBOLS OF PROGRESS BY PULSATION

"When He made a decree for the rain, and a way for the lightning, He saw Wisdom; and to man He said, The fear of the Lord is Wisdom."
Job xxviii. 26—28.

While such Seers as Moses, Isaiah, and Odin were struggling to make the masses attend to the Genesis of things, or process of becoming, to give them some sort of faith in the very existence of any Laws of moral development by reaction, certain thinkers of less actively social and philanthropic temperament retired into solitude to study those Laws in detail, and to impart their knowledge to a few chosen pupils. Many of them studied the Laws of mental development by the method of mathematical analysis. The vulgar called such students Wizards and other harsh names. The pursuit of mathematical Logic was often forbidden; the books of "Grammarye" were burned; and sometimes the writers and readers of them. At other times Wizards were held in high honour. Is it not possible that the famous breast-plate of Aaron, which was consulted in mental difficulties, may have had inscribed on it a selection of the Natural and Geometric Symbols of orderly mental sequence?

In modern times it has been assumed that the study of mathematical Logic must have been "mystical" or "fanciful." But in the middle of last century the Science was revived 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 highersquare