The remembrance of forbidden fruit is the earliest thing in the memory of each of us, as it is in that of mankind.

The present contains nothing more than the past, and what is found in the effect was already in the cause.

Men do not sufficiently realise that their future is in their own hands. Theirs is the task of determining first of all whether they want to go on living or not. Theirs is the responsibility, then, for deciding if they want merely to live, or intend to make just the extra effort required for fulfilling, even on their refractory planet, the essential function of the universe, which is a machine for the making of gods.

Every good mathematician is at least half a philosopher, and every good philosopher is at least half a mathematician.

The historical approach, with its aim of detecting how things began and arriving from these origins at a knowledge of their nature, is certainly perfectly legitimate; but it also has its limitations. If everything were in continual flux, and nothing maintained itself fixed for all time, there would no longer be any possibility of getting to know about the world, and everything would be plunged into confusion.

A judgment, for me is not the mere grasping of a thought, but the admission of its truth.

If the task of philosophy is to break the domination of words over the human mind, then my concept notation, being developed for these purposes, can be a useful instrument for philosophers. I believe the cause of logic has been advanced already by the invention of this concept notation.

We suppose, it would seem, that concepts grow in the individual mind like leaves on a tree, and we think to discover their nature by studying their growth; we seek to define them psychologically, in terms of the human mind. But this account makes everything subjective, and if we follow it through to the end, does away with truth. What is known as the history of concepts is really a history either of our knowledge of concepts or of the meanings of words.

Without some affinity in human ideas art would certainly be impossible; but it can never be exactly determined how far the intentions of the poet are realized.

I hope I may claim in the present work to have made it probable that the laws of arithmetic are analytic judgments and consequently a priori. Arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic, albeit a derivative one. To apply arithmetic in the physical sciences is to bring logic to bear on observed facts; calculation becomes deduction.

Often it is only after immense intellectual effort, which may have continued over centuries, that humanity at last succeeds in achieving knowledge of a concept in its pure form, by stripping off the irrelevant accretions which veil it from the eye of the mind.

Being true is different from being taken as true, whether by one or by many or everybody, and in no case is it to be reduced to it. There is no contradiction in something's being true which everybody takes to be false. I understand by 'laws of logic' not psychological laws of takings-to-be-true, but laws of truth. ...If being true is thus independent of being acknowledged by somebody or other, then the laws of truth are not psychological laws: they are boundary stones set in an eternal foundation, which our thought can overflow, but never displace. It is because of this that they have authority for our thought if it would attain truth. They do not bear the relation to thought that the laws of grammar bear to language; they do not make explicit the nature of our human thinking and change as it changes.

Facts, facts, facts,' cries the scientist if he wants to emphasize the necessity of a firm foundation for science. What is a fact? A fact is a thought that is true. But the scientist will surely not recognize something which depends on men's varying states of mind to be the firm foundation of science.

Gottlob Frege created modern logic including "for all," "there exists," and rules of proof. Leibniz and Boole had dealt only with what we now call "propositional logic" (that is, no "for all" or "there exists"). They also did not concern themselves with rules of proof, since their aim was to reach truth by pure calculation with symbols for the propositions. Frege took the opposite track: instead of trying to reduce logic to calculation, he tried to reduce mathematics to logic, including the concept of number.

The ideal of strictly scientific method in mathematics which I have tried to realise here, and which perhaps might be named after Euclid I should like to describe in the following way... The novelty of this book does not lie in the content of the theorems but in the development of the proofs and the foundations on which they are based... With this book I accomplish an object which I had in view in my Begriffsschrift of 1879 and which I announced in my Grundlagen der Arithmetik. I am here trying to prove the opinion on the concept of number that I expressed in the book last mentioned.

It really is worth the trouble to invent a new symbol if we can thus remove not a few logical difficulties and ensure the rigour of the proofs. But many mathematicians seem to have so little feeling for logical purity and accuracy that they will use a word to mean three or four different things, sooner than make the frightful decision to invent a new word.

A scientist can hardly meet with anything more undesirable than to have the foundations give way just as the work is finished. I was put in this position by a letter from Mr. Bertrand Russell when the work was nearly through the press.

If I compare arithmetic with a tree that unfolds upward into a multitude of techniques and theorems while its root drives into the depths, then it seems to me that the impetus of the root.

Is it always permissible to speak of the extension of a concept, of a class? And if not, how do we recognize the exceptional cases? Can we always infer from the extension of one concept's coinciding with that of a second, that every object which falls under the first concept also falls under the second?

Although a poem be not made by counting of syllables upon the fingers, yet "numbers" is the most poetical synonym we have for verse, and "measure" the most significant equivalent for beauty, for goodness, and perhaps even for truth. Those early and profound philosophers, the followers of Pythagoras, saw the essence of all things in number, and it was by weight, measure, and number, as we read in the Bible, that the Creator first brought Nature out of the void.

Religions are not true or false, but better or worse.

There is nothing impossible in the existence of the supernatural: its existence seems to me decidedly probable.

They [the wise spirits of antiquity in the first circle of Dante's Inferno] are condemned, Dante tells us, to no other penalty than to live in desire without hope, a fate appropriate to noble souls with a clear vision of life.

Skepticism, like chastity, should not be relinquished too readily.

I leave you but the sound of many a word In mocking echoes haply overheard, I sang to heaven. My exile made me free,from world to world, from all worlds carried me.

O world, thou choosest not the better part! It is not wisdom to be only wise, And on the inward vision close the eyes, But it is wisdom to believe the heart. Columbus found a world, and had no chart, Save one that faith deciphered in the skies; To trust the soul's invincible surmise Was all his science and his only art.

The idea of Christ is much older than Christianity.

In the Gospels, for instance, we sometimes find the kingdom of heaven illustrated by principles drawn from observation of this world rather than from an ideal conception of justice; ... They remind us that the God we are seeking is present and active, that he is the living God; they are doubtless necessary if we are to keep religion from passing into a mere idealism and God into the vanishing point of our thought and endeavour.

A child educated only at school is an uneducated child.

Culture is on the horns of this dilemma: if profound and noble, it must remain rare, if common, it must become mean.

The truth is cruel, but it can be loved, and it makes free those who have loved it.

When Socrates and his two great disciples composed a system of rational ethics they were hardly proposing practical legislation for mankind...They were merely writing an eloquent epitaph for their country.

The living have never shown me how to live.

The pint would call the quart a dualist, if you tried to pour the quart into him.

Fashion is something barbarous, for it produces innovation without reason and imitation without benefit.

Liberal philosophy, at this point, ceases to be empirical and British in order to become German and transcendental. Moral life, it now believes, is not the pursuit of liberty and happiness of all sorts by all sorts of different creatures; it is the development of a single spirit in all life through a series of necessary phases, each higher than the preceding one. No man, accordingly, can really or ultimately desire anything but what the best people desire. This is the principle of the higher snobbery; and in fact, all earnest liberals are higher snobs.

Beauty is a pledge of the possible conformity between the soul and nature, and consequently a ground of faith in the supremacy of the good.

Professional philosophers are usually only apologists: that is, they are absorbed in defending some vested illusion or some eloquent idea. Like lawyers or detectives, they study the case for which they are retained.

The young man who has not wept is a savage, and the old man who will not laugh is a fool.

What renders man an imaginative and moral being is that in society he gives new aims to his life which could not have existed in solitude: the aims of friendship, religion, science, and art.

England is the paradise of individuality, eccentricity, heresy, anomalies, hobbies, and humors.

Oblivious of Democritus, the unwilling materialists of our day have generally been awkwardly intellectual and quite incapable of laughter. If they have felt anything, they have felt melancholy. Their allegiance and affection were still fixed on those mythical sentimental worlds which they saw to be illusory. The mechanical world they believed in could not please them, in spite of its extent and fertility. Giving rhetorical vent to their spleen and prejudice, they exaggerated nature's meagreness and mathematical dryness. When their imagination was chilled they spoke of nature, most unwarrantably, as dead, and when their judgment was heated they took the next step and called it unreal.

Profound skepticism is favorable to conventions, because it doubts that the criticism of conventions is any truer than they are.

Every moment celebrates obsequies over the virtues of its predecessor.

It is not politics that can bring true liberty to the soul; that must be achieved, if at all, by philosophy;

Everything ideal has a natural basis and everything natural an ideal development.

No system would have ever been framed if people had been simply interested in knowing what is true, whatever it may be. What produces systems is the interest in maintaining against all comers that some favourite or inherited idea of ours is sufficient and right.

All living souls welcome whatsoever they are ready to cope with; all else they ignore, or pronounce to be monstrous and wrong, or deny to be possible.

Let a man once overcome his selfish terror at his own finitude, and his finitude is, in one sense, overcome.

Friendship is almost always the union of a part of one mind with the part of another; people are friends in spots.