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The Bottom of the Mind.—1. Pure Reason.—2. Burla Burla.—3. Perfect Certainty.—4. The Leak.—5. The Child's Prayer.

PURE Earthmeasure, instead of affording a true starting point, has turned out to be a mere balloon arising from the real earth. But there is another kind of measure which seems to come before earthmeasure, more truly than Euclid's point before his lines and flats. If measure be the handmaid of knowledge, number is the handmaid of measure. Here, surely, we touch bottom; if not the bottom of the All-Thing, at least the bottom of the mind, so often mistaken for the bottom of the All-Thing. Did not Pythagoras strive to build the All-Thing out of numbers? And did not the chief architect of the Roman school, Boethius, choose ciphering for his foundation stone; for the first tread of that curriculum which the imprisoned squirrels turned round so painfully in the Logical Age?


Because I shrank from using the Babu word Arithmetic, I cast about for the child's name for the same thing: and no sooner had I written it down than I

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saw it foretold what I was going to say. For among us the word cipher has come to mean the figure 0; and children tell each other that nought stands for nothing.

Arithmetic is Pure Reasoning, as the children would have told Kant, if he had stooped to ask them. When they are going to rob a bird's nest, they excuse themselves by saying that, if they leave one egg in the nest, the bird will not know it has been robbed, because birds cannot count. At heart they know very well that the bird is not so stupid as that; but they have learned from grown-up people that you can lull your sense of right and wrong to sleep with words; and the grown-up people have told them that birds have instinct instead of reason. And so they have gone to the point, and put it plainly that birds cannot count. Which is absurd.

The greatest Pure Reasoner ever known was not Kant, but Babbage's machine. The Calculating Machine, as its creator named it, not only reckoned more carefully than Babbage himself, but when it reached a stage at which new laws of number came into play, laws which had been unknown to Babbage when he made it, it discovered those laws for itself, and went right on. That is to say, it was infallible.

If it be the peculiar distinction and glory of man that he is the reckoning animal, one sees that Babbage did a far more wonderful thing than was thought of by the learned men who hoped that they

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could create life out of the contents of a chemist's shop. Because all they hoped to create was the lowest kind of life; in their own words, the protozoon, or forelife; whereas Babbage created the highest kind of life; as it should seem, the afterlife,—ta meta ta phusika in very deed!

In many ages and countries Babbage's machine would have been worshipped as a god. In the age from which we are escaping it would have been burnt for witchcraft. And yet all the time this reasoning creature could not have told its creator how many buttons he had on his waistcoat. It was much stupider than the birds, really. It could only go on saying what Babbage told it to say. It had no going strength; no soul.

It would be easy to make a more energetic machine than Babbage's, out of a millwheel and a roll of paper, which would go on multiplying by ten, by the simple process of stamping noughts on the paper, as long as the paper lasted and the stream ran. Indeed, the Buddhists long ago took a far higher flight than Babbage, with their famous praying-wheel, which says a prayer every time the wheel turns round, and so may fairly lay claim to being Pure Religion.


Here then is the ogre at last, in his true shape.

Pure Ciphering is the last word, or, verily speaking,

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the first word, in the Andronican lexicon. If there be such a thing as metaphysics, ciphering is Pure Metaphysics. It is the science of Absolute Truth, of Verihood By Itself.

I cannot show this better than by means of a saying which has always been revered as a sample of Absolute Truth, a foundation-stone of Logic, a genuine fulcrum for the human mind. It is put forward as such by Descartes, and it is still popular in quarters where Descartes has always been unpopular—Two and two are four.

It is hard for one whose mind is childlike, and all untrained in exact reasoning, to take this aged play upon words quite seriously. Nevertheless, in case there should be still some sleep-walkers abroad, not able to withstand this kind of conjuring, I have taken the trouble to ask myself a question,—Suppose there should be savages who had got distinct names only for two or three numbers, and whose name for four was consequently "two and two", would not this unanswerable proposition then stand thus,—Two and two are two and two? I made the practical experiment; I went to a book about savages, and sure enough I found that among the Queensland black-fellows the name for two is burla, and the name for four is burla burla.

And so now, copying the pleasant vein of a distinguished Mediterranean cardinal, I am able to picture a Queensland Champion of Positivism calling his dusky congregation round him, and addressing them

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in this wise: "My brethren, I grieve to hear that some among us have denied that the Kangaroo in the Moon ought rightly to be called a Kangaroo. And I find that they have fallen into this distressing heresy through doubting if there be such a thing as Absolute Truth known to men. Let me therefore, while the secular arm is making ready the fagots, silence these unhappy infidels; and confirm the wavering faith of such as still wish to believe; by reminding them and you of this unalterable, this irrefragable, this Untied Truth By Itself,—Burla and burla, at all times and in all places, and to all men and kangaroos, are burla burla!"

That little fable may help us to understand the difference between the kind of Absolute Truth which was known even to Babbage's machine, and the kind of Absolute Truth which has to fall back on fagots for Absolute Proof.


There is a very famous art or mystery of ciphering in words which has been known for more than two thousand years as Logic.

Very many treatises have been, and are still being, written on this art, but when we look into them we find that no two of them are agreed as to what Logic is, or what it does, or how it ought to do it. The learned and distinguished writers have fared no better

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than the members of the Metaphysical Society. And I am afraid the reason is the same in both cases. They have not asked what the word itself meant.

Logic sounds like the Babu for wordiness. But it also means orderliness. It is connected with law, much as arithmetic is connected with rhythm. Now the history of logic is the history of an attempt to make an arithmetic of words.

The aim of the logicians has been to learn from words instead of things. They have sought for what they call certainty, or Perfect Certainty, which is of course our old friend Absolute Truth or Pure Assurance under another name. And they have believed that they could arrive at it by the tidy arrangement of words.

Their grand achievement has been the syllogism, which is, as its name half confesses, a mere saying again. To use their own language, every logical proposition is an identical proposition. The reasoning machine can only say what its creator tells it to say. You cannot get more out of the words than you have put into them; as the logicians themselves confess altogether when they say that the conclusion must be contained in the premises. And the more tidily the premises are arranged, the more self-evident the conclusion will be, till Pure Logic attains to Perfect Certainty in—Burla burla.

In the old conjuring books one meets this kind of thing as a specimen of what the logical mind believes to be proof:—

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All men are mortal:
Socrates is a man:
Therefore Socrates is mortal.

Now that is quite true. But it is not a proof of anything; it is merely a vain repetition. If all men are sure to die, then in saying that Socrates is a man you have said that he is sure to die. If not, the syllogism would stand thus

All who are not sure to die are sure to die:
Socrates is one who is not sure to die:
Therefore Socrates is sure to die.

Which is absurd.

There is no such thing as logical proof. Demonstration is not proof, it is pointing out, and pure reason is the pointing out of pure samenesses, like those of arithmetic and measure. Logic does this in words, and the better it does it, the more the words themselves will be the same, till they end by saying nothing at all.

As soon as we pass from words to things, we find that we are dealing not with samenesses but with likenesses. The art of pointing them out in words is called by the logicians rhetoric; and perhaps the greatest triumph of rhetoric has been in persuading mankind that there is such a thing as logic. But all the time the surest demonstration is that which points out the thing itself; and, if we may believe the greatest of all rhetoricians, the surest rhetoric is that which moves the man himself by other means than words.

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For all this time there has to be a man.

It is because Demosthenes declared the secret of oratory to be the orator's thump upon the table, that I believe this bag of gold thrown down among the logicians will explode all their syllogisms, and that, a stronger than I having thumped the table, I am adding these few words.


My slight acquaintance with treatises on logic leads me to the conclusion that the art was invented by some one living among savages whose minds were incapable of distinguishing between puns and sense. The writers are all hard at work refuting the nursery riddle—When is a door not a door? When it is ajar. That riddle, I think, like other things one hears in the nursery, must be a relic, what Darwin calls a rudiment, of old cannibal metaphysics. It is the kind of thing that would have made the fortune of a Greek sophist, or a Roman theologian, or. a modern physicist. When is The Good not Good? When it is an abstract noun. When is bread not bread? When it is a grin. When is elastic not elastic? When it is a scientific conception.

In so far as the tidy arrangement of words helps us to tell sense from nonsense, logic is a useful part of grammar. If it pretended to be nothing more, I should not have found it in my path in this inquiry. The brazen serpent made by Moses in the wilderness,

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[paragraph continues] (in seeming carelessness of his Commandments) was very well as a cure for snake-bites. But when the people were found burning incense to it in the house of Yahweh, it was time to call it not Snake but Brass, and to break it in pieces. (Hebraists seem to have missed the play upon words in rachash and rehustan.)

Logic is such a medicine, and the people are burning incense to it in the house of Verihood. They are mistaking samenesses in words for samenesses in things. The mistake is made in theology, it is made in morality, it is made by the lawyers, it is made by the scientists.

Logic is like a straight line which can only touch the round of verihood at one point. The farther you prolong the line, the farther you are going from verihood. The definitions break down; the efforts to enclose reality in words run into endless decimals. There is a perpetual flaw which cannot be patched up. There is a leak which cannot be stopped. The lawyers cannot stop the leak with all their codes and cases; nor the theologians with all their General Councils and their Privy Councils; nor the moralists with all their altruism; nor the materialists with all their Ether and Ethereon, their necessary assumptions and their scientific conceptions. That is the answer to the spell of the enchanters; when men have taken to heart that lesson the enchantment will be broken, and the Mediterranean nightmare will vex sleep no more.

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The more Logic is asked to do, the worse it does it. Pure Reckoning is seen at its best in the Multiplication Table. It is seen at its worst in such a would-be science as Political Economy. There are two schools of this science, known respectively as Individualists and Socialists. Their conclusions are diametrically opposed; both are thoroughly logical, and both are thoroughly wrong. Both take it for granted that men are right-angled triangles; and setting out in opposite directions from this common ground, both end in absurdity. One holds that men are perfectly selfish, and the other that they are perfectly unselfish; but both are agreed that men are perfectly wise. A world of men who were all ruled by enlightened selfishness would be a heaven, more so, perhaps, than a world of men ruled by enlightened unselfishness. Unhappily the case is that most men are intensely stupid. Some of them may be more selfish, and others more unselfish, but stupidity is master of them all, and master of the world.


Is there, then, nothing to be done? Surely there is.

Once when I was seated in one of our public pleasure-grounds a little fellow, whose hoop had got bent out of shape, ran up to me and asked, "Please, sir, will you make my hoop round?" I

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could not forbear from smiling at the thought that I was being asked to do that which God has not yet done. But I did not tell the little fellow that what he wanted was beyond the power of logic, or mathematics, or physics or metaphysics. Instead, I set to work, and made his hoop round; that is to say, I made it round enough for him to play with, which was all he wanted.

The prayer of that little fellow is still sounding in my ears. I think it has been sounding in them all my life. I hear it coming from many quarters, and in many languages. I hear it in the Fourth Clause of Nobel's Will.

Next: 13. Ontology: The End