Science and mathematics writer Martin Gardner was a noted Chestertonian, and reprinted about one-third of the chapter "The Ethics of Elfland" (from GKC's book Orthodoxy) in his 1948 anthology Great Essays in Science, entitling the selection "The Logic of Elfland". While Gardner's statement concerning Chesterton's scientific views should be more nuanced, nevertheless I wished to include below his preface to the selection.

It may come as a shock to many readers to find a selection by Gilbert Keith Chesterton (1874-1936) included here. The rotund British writer was not noted for his knowledge of things scientific. He never, for example, could quite bring himself to accept the theory of man's descent from lower animals. Yet there are times, as in the following selection, when he startles you with unexpected scientific insight.

Chesterton's topic is nothing less than the fundamental contrast between deductive logic, true of all possible worlds, and inductive logic, capable only of telling us how we may reasonably expect this world to behave. Let us hasten to add that Chesterton's analysis is in full agreement with the views of modern logicians. Perhaps his "test of the imagination" is not strictly accurate— who can "imagine" the four-dimensional constructions of relativity?-but in essence his position is unassailable. Logical and mathematical statements are true by definition. They are "empty tautologies," to use a current phrase, like the impressive maxim that there are always six eggs in half a dozen. Nature, on the other hand, is under no similar constraints. Fortunately, her "weird repetitions," as GK calls them, often conform to surprisingly low-order equations. But as Hume and others before Hume made clear, there is no logical reason why she should behave so politely.

The following selection is taken from, of all places, Orthodoxy, Chesterton's most famous work of Christian (it was published fourteen years before he became a Catholic) apologetics. The style is that for which the author is justly famous-brilliant, witty, alliterative, dazzling in its metaphors and verbal swordplay, and a joy to read even when you disagree with him.

Thinking in isolation and with pride ends in being an idiot. Every man who will not have softening of the heart must at last have softening of the brain.

-Orthodoxy (1908)

...if we wish to protect the poor we shall be in favour of fixed rules and clear dogmas. The rules of a club are occasionally in favour of the poor member. The drift of a club is always in favour of the rich one.

-Orthodoxy (1908)

How much larger your life would be if your self could become smaller in it...

-Orthodoxy (1908)

"The more transcendental is your patriotism, the more practical are your politics."

The man who is most likely to ruin the place he loves is exactly the man who loves it with a reason. The man who will improve the place is the man who loves it without a reason. If a man loves some feature of Pimlico (which seems unlikely), he may find himself defending that feature against Pimlico itself. But if he simply loves Pimlico itself, he may lay it waste and turn it into the New Jerusalem. I do not deny that reform may be excessive; I only say that it is the mystic patriot who reforms [...] The more transcendental is your patriotism, the more practical are your politics."

-Orthodoxy (1908)

Pope Francis quotes GKC

Recently Pope Francis quoted Chesterton, as reported in this link on the Vatican's website (Well, an allusion, as far as I can make out for sure, not a direct quote, but still...):

http://www.vatican.va/holy_father/francesco/cotidie/2013/en/papa-francesco-cotidie_20131205_words-mad_en.html

Pope Francis then recalled the prophet Isaiah who, in the first Reading (26:1-6) says: “Trust in the Lord for ever, for the Lord is an everlasting rock”. “The rock is Jesus Christ, the rock is the Lord. Our word is forceful, it bestows life, it continues on, it can tolerate any attack if this word is rooted in Jesus Christ”. However, he said, “a Christian word whose life-giving roots are not grounded in a person, in Jesus Christ, is a Christian word without Christ. And Christian words without Christ deceive, they do harm”.

The Pontiff then quoted the English author G. K. Chesterton (1874-1936), when speaking about heresy once said that a heresy is a truth, a word, a truth gone mad. “When Christian words lack Christ, they begin to head down the road of madness”. The prophet Isaiah, he added, clearly describes the nature of this madness. He says: “The Lord is an everlasting rock. For he has brought low the inhabitants of the height, the lofty city” (26:4-5). “The inhabitants of the height. A Christian word without Christ leads to vanity, to self assuredness, to pride, and to power for power’s sake. And the Lord brings these people low”.

Presumably the Pope is making reference is to the third chapter of Orthodoxy:

The modern world is not evil; in some ways the modern world is far too good. It is full of wild and wasted virtues. When a religious scheme is shattered (as Christianity was shattered at the Reformation), it is not merely the vices that are let loose. The vices are, indeed, let loose, and they wander and do damage. But the virtues are let loose also; and the virtues wander more wildly, and the virtues do more terrible damage. The modern world is full of the old Christian virtues gone mad. The virtues have gone mad because they have been isolated from each other and are wandering alone. Thus some scientists care for truth; and their truth is pitiless. Thus some humanitarians only care for pity; and their pity (I am sorry to say) is often untruthful. For example, Mr. Blatchford attacks Christianity because he is mad on one Christian virtue: the merely mystical and almost irrational virtue of charity. He has a strange idea that he will make it easier to forgive sins by saying that there are no sins to forgive. Mr. Blatchford is not only an early Christian, he is the only early Christian who ought really to have been eaten by lions. For in his case the pagan accusation is really true: his mercy would mean mere anarchy. He really is the enemy of the human race -- because he is so human. At the other extreme, we may take the acrid realist, who has deliberately killed in himself all human pleasure in happy tales or in the healing of the heart. Torquemada tortured people physically for the sake of moral truth. Zola tortured people morally for the sake of physical truth. But in Torquemada's time there was at least a system that could to some extent make righteousness and peace kiss each other. Now they do not even bow.

"As long as the vision of heaven is always changing, the vision of earth will be exactly the same."

...the man we see every day -- the worker in Mr. Gradgrind's factory, the little clerk in Mr. Gradgrind's office -- he is too mentally worried to believe in freedom. He is kept quiet with revolutionary literature. He is calmed and kept in his place by a constant succession of wild philosophies. He is a Marxian one day, a Nietzscheite the next day, a Superman (probably) the next day; and a slave every day. The only thing that remains after all the philosophies is the factory. The only man who gains by all the philosophies is Gradgrind. It would be worth his while to keep his commercial helotry supplied with sceptical literature. And now I come to think of it, of course, Gradgrind is famous for giving libraries. He shows his sense. All modern books are on his side. As long as the vision of heaven is always changing, the vision of earth will be exactly the same. No ideal will remain long enough to be realized, or even partly realized. The modern young man will never change his environment; for he will always change his mind.

This, therefore, is our first requirement about the ideal towards which progress is directed; it must be fixed. Whistler used to make many rapid studies of a sitter; it did not matter if he tore up twenty portraits. But it would matter if he looked up twenty times, and each time saw a new person sitting placidly for his portrait. So it does not matter (comparatively speaking) how often humanity fails to imitate its ideal; for then all its old failures are fruitful. But it does frightfully matter how often humanity changes its ideal; for then all its old failures are fruitless. The question therefore becomes this: How can we keep the artist discontented with his pictures while preventing him from being vitally discontented with his art? How can we make a man always dissatisfied with his work, yet always satisfied with working? How can we make sure that the portrait painter will throw the portrait out of window instead of taking the natural and more human course of throwing the sitter out of window?

-Orthodoxy (1908)

Just wanted to link to a wonderful review of Orthodoxy which I happened to come across, and enjoyed greatly. :-)

"A Tribute to G.K. Chesterton"

"...in all that welter of inconsistent and incompatible heresies, the one and only really unpardonable heresy was orthodoxy."

I began to examine more exactly the general Christian theology which many execrated and few examined. I soon found that it did in fact correspond to many of these experiences of life; that even its paradoxes corresponded to the paradoxes of life. Long afterwards Father Waggett (to mention another very able man of the old Anglo-Catholic group), once said to me, as we stood on the Mount of Olives in view of Gethsemane and Aceldama, “Well, anyhow, it must be obvious to anybody that the doctrine of the Fall is the only cheerful view of human life.” It is indeed obvious to me; but the thought passed over me at the moment, that a very large proportion of that old world of sceptical sects and cliques, to which I had once belonged, would find it a much more puzzling paradox than the paradoxes of Oscar Wilde and Bernard Shaw. I will not develop the argument here, which I have so often developed elsewhere; I merely mention it to suggest my general sense, even at this stage, that the old theological theory seemed more or less to fit into experience, while the new and negative theories did not fit into anything, least of all into each other. It was about this time that I had published some studies on contemporary writers, such as Kipling and Shaw and Wells; and feeling that each of them erred through an ultimate or religious error, I gave the book the title of Heretics. It was reviewed by Mr. G. S. Street, the very delightful essayist, who casually used the expression that he was not going to bother about his theology until I had really stated mine. With all the solemnity of youth, I accepted this as a challenge; and wrote an outline of my own reasons for believing that the Christian theory, as summarised in the Apostles’ Creed, would be found to be a better criticism of life than any of those that I had criticised. I called it Orthodoxy, but even at the time I was very much dissatisfied with the title. It sounded a thinnish sort of thing to be defending through thick and thin. Even then I fancy I had a dim foreshadowing that I should have to find some better name for it before I died. As it was, the only interesting effect of the title, or the book, that I ever heard of, occurred on the frontiers of Russia. There I believe the Censor, under the old Russian regime, destroyed the book without reading it. From its being called Orthodoxy, he naturally inferred that it must be a book on the Greek Church. And from its being a book on the Greek Church, he naturally inferred that it must be an attack on it.

But there did remain one rather vague virtue about the title, from my point of view; that it was provocative. And it is an exact test of that extraordinary modern society that it really was provocative. I had begun to discover that, in all that welter of inconsistent and incompatible heresies, the one and only really unpardonable heresy was orthodoxy. A serious defence of orthodoxy was far more startling to the English critic than a serious attack on orthodoxy was to the Russian censor. And through this experience I learned two very interesting things, which serve to divide all this part of my life into two distinct periods. Very nearly everybody, in the ordinary literary and journalistic world, began by taking it for granted that my faith in the Christian creed was a pose or a paradox. The more cynical supposed that it was only a stunt. The more generous and loyal warmly maintained that it was only a joke. It was not until long afterwards that the full horror of the truth burst upon them; the disgraceful truth that I really thought the thing was true. And I have found, as I say, that this represents a real transition or border-line in the life of the apologists. Critics were almost entirely complimentary to what they were pleased to call my brilliant paradoxes; until they discovered that I really meant what I said. Since then they have been more combative; and I do not blame them.

-Autobiography (1936)

"Orthodoxy" on Chuck Norris's website

On Chuck Norris's official website one can find the entirety of Chesterton's book Orthodoxy:

http://www.chucknorris.com/Christian/Christian/ebooks/chesterton_orthodox.pdf

Presumably, he is recommending that you read it. And, let's face it, do you really want to say no to Chuck Norris? :-)

"But now I really was happy, for I had learnt that man is a monstrosity."

I had often called myself an optimist, to avoid the too evident blasphemy of pessimism. But all the optimism of the age had been false and disheartening for this reason, that it had always been trying to prove that we fit in to the world. The Christian optimism is based on the fact that we do not fit in to the world. I had tried to be happy by telling myself that man is an animal, like any other which sought its meat from God. But now I really was happy, for I had learnt that man is a monstrosity. I had been right in feeling all things as odd, for I myself was at once worse and better than all things. The optimist's pleasure was prosaic, for it dwelt on the naturalness of everything; the Christian pleasure was poetic, for it dwelt on the unnaturalness of everything in the light of the supernatural. The modern philosopher had told me again and again that I was in the right place, and I had still felt depressed even in acquiescence. But I had heard that I was in the wrong place, and my soul sang for joy, like a bird in spring. The knowledge found out and illuminated forgotten chambers in the dark house of infancy. I knew now why grass had always seemed to me as queer as the green beard of a giant, and why I could feel homesick at home.

-Orthodoxy (1908)

"It is quite futile to argue that man is small compared to the cosmos; for man was always small compared to the nearest tree."

But modern thought also hit my second human tradition. It went against the fairy feeling about strict limits and conditions. The one thing it loved to talk about was expansion and largeness. Herbert Spencer would have been greatly annoyed if any one had called him an imperialist, and therefore it is highly regrettable that nobody did. But he was an imperialist of the lowest type. He popularized this contemptible notion that the size of the solar system ought to over-awe the spiritual dogma of man. Why should a man surrender his dignity to the solar system any more than to a whale? If mere size proves that man is not the image of God, then a whale may be the image of God; a somewhat formless image; what one might call an impressionist portrait. It is quite futile to argue that man is small compared to the cosmos; for man was always small compared to the nearest tree. But Herbert Spencer, in his headlong imperialism, would insist that we had in some way been conquered and annexed by the astronomical universe. He spoke about men and their ideals exactly as the most insolent Unionist talks about the Irish and their ideals. He turned mankind into a small nationality. And his evil influence can be seen even in the most spirited and honourable of later scientific authors; notably in the early romances of Mr. H. G. Wells. Many moralists have in an exaggerated way represented the earth as wicked. But Mr. Wells and his school made the heavens wicked. We should lift up our eyes to the stars from whence would come our ruin.

-Orthodoxy (1908)

"We have a censorship by the press."

...we have almost up to the last instant trusted the newspapers as organs of public opinion. Just recently some of us have seen (not slowly, but with a start) that they are obviously nothing of the kind. They are, by the nature of the case, the hobbies of a few rich men. We have not any need to rebel against antiquity; we have to rebel against novelty...It will not be necessary for any one to fight again against the proposal of a censorship of the press. We do not need a censorship of the press. We have a censorship by the press.

-Orthodoxy (1908)

"Men who begin to fight the Church for the sake of freedom and humanity end by flinging away freedom and humanity if only they may fight the Church."

These can be called the essentials of the old orthodoxy, of which the chief merit is that it is the natural fountain of revolution and reform; and of which the chief defect is that it is obviously only an abstract assertion. Its main advantage is that it is the most adventurous and manly of all theologies. Its chief disadvantage is simply that it is a theology. It can always be urged against it that it is in its nature arbitrary and in the air. But it is not so high in the air but that great archers spend their whole lives in shooting arrows at it -- yes, and their last arrows; there are men who will ruin themselves and ruin their civilization if they may ruin also this old fantastic tale. This is the last and most astounding fact about this faith; that its enemies will use any weapon against it, the swords that cut their own fingers, and the firebrands that burn their own homes. Men who begin to fight the Church for the sake of freedom and humanity end by flinging away freedom and humanity if only they may fight the Church. This is no exaggeration; I could fill a book with the instances of it. Mr. Blatchford set out, as an ordinary Bible-smasher, to prove that Adam was guiltless of sin against God; in manoeuvring so as to maintain this he admitted, as a mere side issue, that all the tyrants, from Nero to King Leopold, were guiltless of any sin against humanity. I know a man who has such a passion for proving that he will have no personal existence after death that he falls back on the position that he has no personal existence now. He invokes Buddhism and says that all souls fade into each other; in order to prove that he cannot go to heaven he proves that he cannot go to Hartle-pool. I have known people who protested against religious education with arguments against any education, saying that the child's mind must grow freely or that the old must not teach the young. I have known people who showed that there could be no divine judgment by showing that there can be no human judgment, even for practical purposes. They burned their own corn to set fire to the church; they smashed their own tools to smash it; any stick was good enough to beat it with, though it were the last stick of their own dismembered furniture. We do not admire, we hardly excuse, the fanatic who wrecks this world for love of the other. But what are we to say of the fanatic who wrecks this world out of hatred of the other? He sacrifices the very existence of humanity to the non-existence of God. He offers his victims not to the altar, but merely to assert the idleness of the altar and the emptiness of the throne. He is ready to ruin even that primary ethic by which all things live, for his strange and eternal vengeance upon some one who never lived at all.

And yet the thing hangs in the heavens unhurt. Its opponents only succeed in destroying all that they themselves justly hold dear. They do not destroy orthodoxy; they only destroy political courage and common sense. They do not prove that Adam was not responsible to God; how could they prove it? They only prove (from their premises) that the Czar is not responsible to Russia. They do not prove that Adam should not have been punished by God; they only prove that the nearest sweater should not be punished by men. With their oriental doubts about personality they do not make certain that we shall have no personal life hereafter; they only make certain that we shall not have a very jolly or complete one here. With their paralysing hints of all conclusions coming out wrong they do not tear the book of the Recording Angel; they only make it a little harder to keep the books of Marshall & Snelgrove. Not only is the faith the mother of all worldly energies, but its foes are the fathers of all worldly confusion. The secularists have not wrecked divine things; but the secularists have wrecked secular things, if that is any comfort to them. The Titans did not scale heaven; but they laid waste the world.

-Orthodoxy (1908)

"How can we say that the Church wishes to bring us back into the Dark Ages? The Church was the only thing that ever brought us out of them."

I take in order the next instance offered: the idea that Christianity belongs to the Dark Ages. Here I did not satisfy myself with reading modern generalisations; I read a little history. And in history I found that Christianity, so far from belonging to the Dark Ages, was the one path across the Dark Ages that was not dark. It was a shining bridge connecting two shining civilizations. If any one says that the faith arose in ignorance and savagery the answer is simple: it didn't. It arose in the Mediterranean civilization in the full summer of the Roman Empire. The world was swarming with sceptics, and pantheism was as plain as the sun, when Constantine nailed the cross to the mast. It is perfectly true that afterwards the ship sank; but it is far more extraordinary that the ship came up again: repainted and glittering, with the cross still at the top. This is the amazing thing the religion did: it turned a sunken ship into a submarine. The ark lived under the load of waters; after being buried under the debris of dynasties and clans, we arose and remembered Rome. If our faith had been a mere fad of the fading empire, fad would have followed fad in the twilight, and if the civilization ever re-emerged (and many such have never re-emerged) it would have been under some new barbaric flag. But the Christian Church was the last life of the old society and was also the first life of the new. She took the people who were forgetting how to make an arch and she taught them to invent the Gothic arch. In a word, the most absurd thing that could be said of the Church is the thing we have all heard said of it. How can we say that the Church wishes to bring us back into the Dark Ages? The Church was the only thing that ever brought us out of them.

-Orthodoxy (1908)

"The test of all happiness is gratitude..."

Here I am only trying to describe the enormous emotions which cannot be described. And the strongest emotion was that life was as precious as it was puzzling. It was an ecstacy because it was an adventure; it was an adventure because it was an opportunity. The goodness of the fairy tale was not affected by the fact that there might be more dragons than princesses; it was good to be in a fairy tale. The test of all happiness is gratitude; and I felt grateful, though I hardly knew to whom. Children are grateful when Santa Claus puts in their stockings gifts of toys or sweets. Could I not be grateful to Santa Claus when he put in my stockings the gift of two miraculous legs? We thank people for birthday presents of cigars and slippers. Can I thank no one for the birthday present of birth?

-Orthodoxy (1908)

"...it is necessary whether we wish the king's orders to be promptly executed or whether we only wish the king to be promptly executed."

A strict rule is not only necessary for ruling; it is also necessary for rebelling. This fixed and familiar ideal is necessary to any sort of revolution. Man will sometimes act slowly upon new ideas; but he will only act swiftly upon old ideas. If I am merely to float or fade or evolve, it may be towards something anarchic; but if I am to riot, it must be for something respectable....Thus we may say that a permanent ideal is as necessary to the innovator as to the conservative; it is necessary whether we wish the king's orders to be promptly executed or whether we only wish the king to be promptly executed...There must at any given moment be an abstract right and wrong if any blow is to be struck; there must be something eternal if there is to be anything sudden.

-Orthodoxy (1908)

"We are not altering the real to suit the ideal. We are altering the ideal: it is easier."

Progress should mean that we are always changing the world to suit the vision. Progress does mean (just now) that we are always changing the vision. It should mean that we are slow but sure in bringing justice and mercy among men: it does mean that we are very swift in doubting the desirability of justice and mercy: a wild page from any Prussian sophist makes men doubt it. Progress should mean that we are always walking towards the New Jerusalem. It does mean that the New Jerusalem is always walking away from us. We are not altering the real to suit the ideal. We are altering the ideal: it is easier.

-Orthodoxy (1908)

"The Church had to be careful, if only that the world might be careless."

Last and most important, it is exactly this which explains what is so inexplicable to all the modern critics of the history of Christianity. I mean the monstrous wars about small points of theology, the earthquakes of emotion about a gesture or a word. It was only a matter of an inch; but an inch is everything when you are balancing. The Church could not afford to swerve a hair's breadth on some things if she was to continue her great and daring experiment of the irregular equilibrium. Once let one idea become less powerful and some other idea would become too powerful. It was no flock of sheep the Christian shepherd was leading, but a herd of bulls and tigers, of terrible ideals and devouring doctrines, each one of them strong enough to turn to a false religion and lay waste the world. Remember that the Church went in specifically for dangerous ideas; she was a lion tamer. The idea of birth through a Holy Spirit, of the death of a divine being, of the forgiveness of sins, or the fulfilment of prophecies, are ideas which, any one can see, need but a touch to turn them into something blasphemous or ferocious. The smallest link was let drop by the artificers of the Mediterranean, and the lion of ancestral pessimism burst his chain in the forgotten forests of the north. Of these theological equalisations I have to speak afterwards. Here it is enough to notice that if some small mistake were made in doctrine, huge blunders might be made in human happiness. A sentence phrased wrong about the nature of symbolism would have broken all the best statues in Europe. A slip in the definitions might stop all the dances; might wither all the Christmas trees or break all the Easter eggs. Doctrines had to be defined within strict limits, even in order that man might enjoy general human liberties. The Church had to be careful, if only that the world might be careless.

-Orthodoxy (1908)

"Almost every contemporary proposal to bring freedom into the church is simply a proposal to bring tyranny into the world."

Almost every contemporary proposal to bring freedom into the church is simply a proposal to bring tyranny into the world. For freeing the church now does not even mean freeing it in all directions. It means freeing that peculiar set of dogmas loosely called scientific, dogmas of monism, of pantheism, or of Arianism, or of necessity. And every one of these (and we will take them one by one) can be shown to be the natural ally of oppression. In fact, it is a remarkable circumstance (indeed not so very remarkable when one comes to think of it) that most things are the allies of oppression. There is only one thing that can never go past a certain point in its alliance with oppression -- and that is orthodoxy. I may, it is true, twist orthodoxy so as partly to justify a tyrant. But I can easily make up a German philosophy to justify him entirely.

-Orthodoxy (1908)