An Introduction to Mathematics (1911)

• The study of mathematics is apt to commence in disappointment... We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it.
  • ch. 1.

• By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race.
  • ch. 5.

• It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle — they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.
  • ch. 5.

• It is a safe rule to apply that, when a mathematical or philosophical author writes with a misty profundity, he is talking nonsense.
  • ch. 15.

The Principles of Natural Knowledge (1919)

• Life is complex in its expression, involving more than percipience, namely desire, emotion, will, and feeling.

• Identification of rhythm as the causal counterpart of life; wherever there is some life, only perceptible to us when the analogies are sufficiently close.

• The rhythm is then the life, in the sense in which it can be said to be included within nature.

Science and the Modern World (1925)

It requires a very unusual mind to undertake the analysis of the obvious.

All the world over and at all times there have been practical men, absorbed in 'irreducible and stubborn facts': all the world over and at all times there have been men of philosophic temperament, who have been absorbed in the weaving of general principles.

Religion is the vision of something which stands beyond, behind and within the passing flux of immediate things; something which is real, and yet waiting to be realized; something which is a remote possibility, and yet the greatest of present facts; something that gives meaning to all that passes, and yet eludes apprehension...

• Nature gets credit which should in truth be reserved for ourselves: the rose for its scent, the nightingale for its song, and the sun for its radiance. The poets are entirely mistaken. They should address their lyrics to themselves and should turn them into odes of self-congratulation on the excellence of the human mind.
  • as cited in History, Humanity and Evolution (1989), p. 383.

• Philosophy, in one of its functions, is the critic of cosmologies. It is its function to harmonise, refashion, and justify divergent intuitions as to the nature of things. It has to insist on the scrutiny of the ultimate ideas, and on the retention of the whole of the evidence in shaping our cosmological scheme. Its business is to render explicit, and — so far as may be — efficient, a process which otherwise is unconsciously performed without rational tests.
  • Preface

• It requires a very unusual mind to undertake the analysis of the obvious.
  • Preface (p. 4)

• The worst that happened to men of science was that Galileo suffered an honorable detention and a mild reproof, before dying peacefully in his bed.
  • Ch. 1: "The Origins of Modern Science"

• The new tinge to modern minds is a vehement and passionate interest in the relation of general principles to irreducible and stubborn facts. All the world over and at all times there have been practical men, absorbed in 'irreducible and stubborn facts'; all the world over and at all times there have been men of philosophic temperament, who have been absorbed in the weaving of general principles. It is this union of passionate interest in the detailed facts with equal devotion to abstract generalisation which forms the novelty of our present society.
  • Ch. 1: "The Origins of Modern Science"

• More and more it is becoming evident that what the West can most readily give to the East is its science and its scientific outlook. This is transferable from country to country, and from race to race, wherever there is a rational society.
  • Ch. 1: "The Origins of Modern Science"

• The science of pure mathematics, in its modern developments, may claim to be the most original creation of the human spirit.

• Mathematics as an Element in the History of Thought.

• ...The pursuit of mathematics is a divine madness of the human spirit...
  • Ch. 2: "Mathematics as an Element in the History of Thought"

• The relevant poems are Milton's Paradise Lost, Pope's Essay on Man, Wordsworth's Excursion, Tennyson's In Memoriam.
  • Ch. 5: "The Romantic Reaction"

• The greatest invention of the nineteenth century was the invention of the method of invention.
  • Ch. 6: "The Nineteenth Century"

• Every human being is the natural guardian of his own importance.
  • Ch. 9: "Science and Philosophy"

• He has been named respectively, Jehovah, Allah, Brahma, Father in Heaven, Order of Heaven, First Cause, Supreme Being, Chance. Each name corresponds to a system of thought derived from the experiences of those who have used it.... He has been conceived as the foundation of the metaphysical situation with its ultimate activity. If this conception be adhered to, there can be no alternative except to discern in Him the origin of all evil as well as of all good. He is then the supreme author of the play, and to him must therefore be ascribed its shortcomings as well as its success.
  • Ch. 11: "God"

• In formal logic, a contradiction is the signal of a defeat; but in the evolution of real knowledge it marks the first step in progress towards victory.

• ...We cannot think first and act afterwards. From the moment of birth we are immersed in action and can only fitfully guide it by taking thought.

• Religion will not regain its old power until it can face change in the same spirit as does science. Its principles may be eternal, but the expression of those principles requires continual development.

• ...The modern fading of interest in religion.

• Religion is the reaction of human nature to its search for God. The presentation of God under the aspect of power awakens every modern instinct of critical reaction. This is fatal; for religion collapses unless its main positions command immediacy of assent. In this respect the old phraseology is at variance with the psychology of modern civilisations. This change in psychology is largely due to science, and is one of the chief ways in which the advance of science has weakened the hold of the old religious forms of expression.

• Religion is the vision of something which stands beyond, behind and within the passing flux of immediate things; something which is real, and yet waiting to be realized; something which is a remote possibility, and yet the greatest of present facts; something that gives meaning to all that passes, and yet eludes apprehension; something whose possession is the final good, and yet is beyond all reach; something which is the ultimate ideal, and the hopeless quest.

• The fact of the religious vision, and its history of persistent expansion, is our one ground for optimism. Apart from it, human life is a flash of occasional enjoyments lighting up a mass of pain and misery, a bagatelle of transient experience.

• The power of God is the worship He inspires.... The worship of God is not a rule of safety — it is an adventure of the spirit, a flight after the unattainable. The death of religion comes with the repression of the high hope of adventure.
  • Ch. 12: Religion and Science.

• It is the business of the future to be dangerous; and it is among the merits of science that it equips the future for its duties.
  • Ch. 13: Requisites for Social Progress.

• Nothing is more impressive than the fact that as mathematics withdrew increasingly into the upper regions of ever greater extremes of abstract thought, it returned back to earth with a corresponding growth of importance for the analysis of concrete fact. ...The paradox is now fully established that the utmost abstractions are the true weapons with which to control our thought of concrete fact.

The Aims of Education (1929)

The essence of education is that it be religious.

That knowledge which adds greatness to character is knowledge so handled as to transform every phase of immediate experience.

• Education is the acquisition of the art of the utilisation of knowledge.

• For successful education there must always be a certain freshness in the knowledge dealt with. It must be either new in itself or invested with some novelty of application to the new world of new times. Knowledge does not keep any better than fish. You may be dealing with knowledge of the old species, with some old truth; but somehow it must come to the students, as it were, just drawn out of the sea and with the freshness of its immediate importance.

• The consequences of a plethora of half-digested theoretical knowledge are deplorable.

• The essence of education is that it be religious. Pray, what is religious education? A religious education is an education which inculcates duty and reverence. Duty arises from our potential control over the course of events. Where attainable knowledge could have changed the issue, ignorance has the guilt of vice. And the foundation of reverence is this perception, that the present holds within itself the complete sum of existence, backwards and forwards, that whole amplitude of time, which is eternity.

• That knowledge which adds greatness to character is knowledge so handled as to transform every phase of immediate experience.

• The universities are schools of education, and schools of research. But the primary reason for their existence is not to be found either in the mere knowledge conveyed to the students or in the mere opportunities for research afforded to the members of the faculty. Both these functions could be performed at a cheaper rate, apart from these very expensive institutions. Books are cheap, and the system of apprenticeship is well understood. So far as the mere imparting of information is concerned, no university has had any justification for existence since the popularization of printing in the fifteenth century. Yet the chief impetus to the foundation of universities came after that date, and in more recent times has even increased. The justification for a university is that it preserves the connection between knowledge and the zest of life, by uniting the young and the old in the imaginative consideration of learning.

• In training a child to activity of thought, above all things we must beware of what I will call "inert ideas"—that is to say, ideas that are merely received into the mind without being utilised, or tested, or thrown into fresh combinations.
  In the history of education, the most striking phenomenon is that schools of learning, which at one epoch are alive with a ferment of genius, in a succeeding generation exhibit merely pedantry and routine. The reason is, that they are overladen with inert ideas. Education with inert ideas is not only useless: it is, above all things, harmful—Corruptio optimi, pessima [the corruption of the best is the worst].

• Every intellectual revolution which has ever stirred humanity into greatness has been a passionate protest against inert ideas. Then, alas, with pathetic ignorance of human psychology, it has proceeded by some educational scheme to bind humanity afresh with inert ideas of its own fashioning.

• What the learned world tends to offer is one second-hand scrap of information illustrating ideas derived from another second-hand scrap of information. The second-handedness of the learned world is the secret of its mediocrity.

• The main importance of Francis Bacon’s influence does not lie in any peculiar theory of inductive reasoning which he happened to express, but in the revolt against second-hand information of which he was a leader.

Process and Reality: An Essay in Cosmology (1929)

In all philosophic theory there is an ultimate which is actual in virtue of its accidents.

Consciousness is only the last and greatest of such elements by which the selective character of the individual obscures the external totality from which it originates and which it embodies.

• There remains the final reflection, how shallow, puny, and imperfect are efforts to sound the depths in the nature of things. In philosophical discussion, the merest hint of dogmatic certainty as to finality of statement is an exhibition of folly.
  • Preface, p. 16 (Corrected Edition)

The chief danger to philosophy is narrowness in the selection of evidence.

In the inescapable flux, there is something that abides; in the overwhelming permanence, there is an element that escapes into flux.

The art of progress is to preserve order amid change, and to preserve change amid order.

• The chief error in philosophy is overstatement.
  • Pt. I, ch. 1, sec. 1.

• In all philosophic theory there is an ultimate which is actual in virtue of its accidents. It is only then capable of characterization through its accidental embodiments, and apart from these accidents is devoid of actuality. In the philosophy of organism this ultimate is termed creativity; and [[God] is its primordial, non-temporal accident. In monistic philosophies, Spinoza's or absolute idealism, this ultimate is God, who is also equivalently termed The Absolute. In such monistic schemes, the ultimate is illegitimately allowed a final, eminent reality, beyond that ascribed to any of its accidents. In this general position the philosophy of organism seems to approximate more to some strains of Indian, or Chinese, thought, than to western Asiatic, or European, thought. One side makes process ultimate; the other side makes fact ultimate.
  • Pt. I, ch. 1, sec. 2.

• Rationalism is an adventure in the clarification of thought.
  • Pt. I, ch. 1, sec. 3.

• Our habitual experience is a complex of failure and success in the enterprise of interpretation. If we desire a record of uninterpreted experience, we must ask a stone to record its autobiography.
  • Pt. I, ch. 1, sec. 6.

• Philosophy is the self-correction by consciousness of its own initial excess of subjectivity. Each actual occasion contributes to the circumstances of its origin additional formative elements deepening its own peculiar individuality. Consciousness is only the last and greatest of such elements by which the selective character of the individual obscures the external totality from which it originates and which it embodies. An actual individual, of such higher grade, has truck with the totality of things by reason of its sheer actuality; but it has attained its individual depth of being by a selective emphasis limited to its own purposes. The task of philosophy is to recover the totality obscured by the selection.
  • Pt. I, ch. 1, sec. 6.

• Philosophy finds religion, and modifies it; and conversely religion is among the data of experience which philosophy must weave into its own scheme. Religion is an ultimate craving to infuse into the insistent particularity of emotion that non-temporal generality which primarily belongs to conceptual thought alone. In the higher organisms the differences of tempo between the mere emotions and the conceptual experiences produce a life-tedium, unless this supreme fusion has been effected. The two sides of the organism require a reconciliation in which emotional experiences illustrate a conceptual justification, and conceptual experiences find an emotional illustration.
  • Pt. I, ch. 1, sec. 6.

• The term many presupposes the term one, and the term one presupposes the term many.
  • Pt. I, ch. 2, sec. 2.

• Creativity is the universal of universals characterizing ultimate matter of fact. It is that ultimate principle by which the many, which are the universe disjunctively, become the one actual occasion, which is the universe conjunctively. It lies in the nature of things that the many enter into complex unity.
  • Pt. I, ch. 2, sec. 2.

• The ultimate metaphysical principle is the advance from disjunction to conjunction, creating a novel entity other than the entities given in disjunction.
  • Pt. I, ch. 2, sec. 2.

• The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato.
  • Pt. II, ch. 1, sec. 1.

• Without doubt, if we are to go back to that ultimate, integral experience, unwarped by the sophistications of theory, that experience whose elucidation is the final aim of philosophy, the flux of things is one ultimate generalization around which we must weave our philosophical system.
  • Pt. II, ch. 10, sec. 1.

• The oneness of the universe, and the oneness of each element of the universe, repeat themselves to the crack of doom in the creative advance from creature to creature, each creature including in itself the whole of history and exemplifying the self-identity of things and their mutual diversities.
  • Pt. III, ch. 1, sec. 7.

• The chief danger to philosophy is narrowness in the selection of evidence.
  • Pt. V, ch. 1, sec. 1.

• There is a greatness in the lives of those who build up religious systems, a greatness in action, in idea and in self-subordination, embodied in instance after instance through centuries of growth. There is a greatness in the rebels who destroy such systems: they are the Titans who storm heaven, armed with passionate sincerity. It may be that the revolt is the mere assertion by youth of its right to its proper brilliance, to that final good of immediate joy. Philosophy may not neglect the multifariousness of the world — the fairies dance, and Christ is nailed to the cross.
  • Pt. V, ch. 1, sec. 1.

• The theme of Cosmology, which is the basis of all religions, is the story of the dynamic effort of the World passing into everlasting unity, and of the static majesty of God's vision, accomplishing its purpose of completion by absorption of the World's multiplicity of effort.
  • Pt. V, ch. II, sec. V.

• Some philosophers fail to distinguish propositions from judgments; … But in the real world it is more important that a proposition be interesting than that it be true. The importance of truth is that it adds to interest.
  • p. 259.
  • Variant: It is more important that a proposition be interesting than that it be true. This statement is almost a tautology. For the energy of operation of a proposition in an occasion of experience is its interest, and its importance. But of course a true proposition is more apt to be interesting than a false one.
    • As extended upon in Adventures of Ideas (1933), Pt. 4, Ch. 16.

• There is nothing in the real world which is merely an inert fact. Every reality is there for feeling: it promotes feeling; and it is felt.
  • Chapter IV, p. 310.

• A precise language awaits a completed metaphysics.

• In the inescapable flux, there is something that abides; in the overwhelming permanence, there is an element that escapes into flux. Permanence can be snatched only out of flux; and the passing moment can find its adequate intensity only by its submission to permanence.

• Thus the universe is to be conceived as attaining the active self-expression of its own variety of opposites of its own freedom and its own necessity, of its own multiplicity and its own unity, of its own imperfection and its own perfection. All the opposites are elements in the nature of things, and are incorrigibly there. The concept of God is the way in which we understand this incredible fact that what cannot be, yet is.

• Error is the price we pay for progress.

• The art of progress is to preserve order amid change, and to preserve change amid order.

• Whether or no it be for the general good, life is robbery. It is at this point that with life morals become acute. The robber requires justification.

• For the kingdom of heaven is with us today.

• We find here the final application of the doctrine of objective immortality. Throughout the perishing occasions in the life of each temporal Creature, the inward source of distaste or of refreshment, the judge arising out of the very nature of things, redeemer or goddess of mischief, is the transformation of Itself, everlasting in the Being of God. In this way, the insistent craving is justified — the insistent craving that zest for existence be refreshed by the ever-present, unfading importance of our immediate actions, which perish and yet live for evermore.

Adventures of Ideas (1933)

Life is an offensive, directed against the repetitious mechanism of the Universe.

• Intolerance is the besetting sin of moral fervour.
  • p. 63, Ch. 4

• In the study of ideas, it is necessary to remember that insistence on hard-headed clarity issues from sentimental feeling, as if it were a mist, cloaking the perplexities of fact. Insistence on clarity at all costs is based on sheer superstition as to the mode in which human intelligence functions. Our reasoning grasps at straws for premises and float on gossamer for deductions.
  • p. 91.

• Life is an offensive, directed against the repetitious mechanism of the Universe.
  • p. 102.

• Systems, scientific and philosophic, come and go. Each method of limited understanding is at length exhausted. In its prime each system is a triumphant success: in its decay it is an obstructive nuisance.
  • p. 203.

• The deliberate aim at Peace very easily passes into its bastard substitute, Anesthesia.
  • p. 284.

• The deepest definition of youth is life as yet untouched by tragedy.
  • p. 285.

• The human body is an instrument for the production of art in the life of the human soul.
  • p. 349.

• A general definition of civilization: a civilized society is exhibiting the five qualities of truth, beauty, adventure, art, peace.
  • p. 353.

• A race preserves its vigour so long as it harbours a real contrast between what has been and what may be, and so long as it is nerved by the vigour to adventure beyond the safeties of the past. Without adventure, civilization is in full decay.
  • p. 360.

Dialogues of Alfred North Whitehead (1954)

Lucien Price (1954). Dialogues of Alfred North Whitehead

Intelligence is quickness to apprehend as distinct from ability, which is capacity to act wisely on the thing apprehended.

Art is the imposing of a pattern on experience, and our aesthetic enjoyment in recognition of the pattern.

A philosopher of imposing stature doesn't think in a vacuum. Even his most abstract ideas are, to some extent, conditioned by what is or is not known in the time when he lives.

• There are no whole truths; all truths are half-truths. It is trying to treat them as whole truths that plays the devil.
  • Prologue.

• A man really writes for an audience of about ten persons. Of course if others like it, that is clear gain. But if those ten are satisfied, he is content.
  • p. 66

• The vitality of thought is in adventure. Ideas won't keep. Something must be done about them. When the idea is new, its custodians have fervor, live for it, and, if need be, die for it.
  • p. 100; Ch. 12, April 28, 1938.

• Intelligence is quickness to apprehend as distinct from ability, which is capacity to act wisely on the thing apprehended.
  • p. 135; Ch. 17, December 15, 1939.

• Our minds are finite, and yet even in these circumstances of finitude we are surrounded by possibilities that are infinite, and the purpose of human life is to grasp as much as we can out of the infinitude.
  • Ch. 21, June 28, 1941.

• A culture is in its finest flower before it begins to analyze itself.
  • Ch. 22, August 17, 1941.

• What is morality in any given time or place? It is what the majority then and there happen to like, and immorality is what they dislike.
  • Ch. 22, August 30, 1941.

• The ideas of Freud were popularized by people who only imperfectly understood them, who were incapable of the great effort required to grasp them in their relationship to larger truths, and who therefore assigned to them a prominence out of all proportion to their true importance.
  • Ch. 28, June 3, 1943.

• Art is the imposing of a pattern on experience, and our aesthetic enjoyment in recognition of the pattern.
  • Ch. 29, June 10, 1943.

• A philosopher of imposing stature doesn't think in a vacuum. Even his most abstract ideas are, to some extent, conditioned by what is or is not known in the time when he lives.
  • Ch. 29, June 10, 1943.

• With the sense of sight, the idea communicates the emotion, whereas, with sound, the emotion communicates the idea, which is more direct and therefore more powerful.
  • Ch. 29, June 10, 1943.

• Ninety percent of our lives is governed by emotion. Our brains merely register and act upon what is telegraphed to them by our bodily experience. Intellect is to emotion as our clothes are to our bodies; we could not very well have civilized life without clothes, but we would be in a poor way if we had only clothes without bodies.
  • Ch. 29, June 10, 1943.

• No period of history has ever been great or ever can be that does not act on some sort of high, idealistic motives, and idealism in our time has been shoved aside, and we are paying the penalty for it.
  • Ch. 32, January 13, 1944.

• The English never abolish anything. They put it in cold storage.
  • Ch. 36, January 19, 1945.

• Shakespeare wrote better poetry for not knowing too much; Milton, I think, knew too much finally for the good of his poetry.
  • Ch. 43, November 11, 1947.