L.E.J. Brouwer > Quotes

“Most philosophers and moralists believe as little in what they write as the manufacturers of baby foods and meat extracts believe in their own products; neither do they act with more good faith than those who lead spiritualist séance; and very few poets have themselves experienced the happiness they describe.”
― L.E.J. Brouwer, Vita, arte e mistica

“Alas, the spheres of truth are less transparent than those of illusion.”
― L.E.J. Brouwer

“Mathematics is created by a free action independent of experience; it develops from a single aprioristic basic intuition [Ur-intuition], which may be called invariance in change as well as unity in multitude.”
― L.E.J. Brouwer

“Mathematics is nothing more, nothing less, than the exact part of our thinking.”
― L.E.J. Brouwer

“It [logical reasoning] serves only lawyers and demagogues, not to instruct other people but to deceive them, and that is because the vulgar herd unconsciously reasons: the language with its logical figures is there, so it will be useful and so they meekly let themselves be deceived; just as I heard several people defend their habit of gin drinking with the words: ‘What else is gin for?’ Whoever has the illusion to improve the world, may just as well agitate against the language of logical reasoning as against alcohol.”
― L.E.J. Brouwer, The Selected Correspondence of L.E.J. Brouwer

“Look at this world, full of wretched people, who imagine that they have possessions, worried that they might lose them and ever toiling in the hope of acquiring more. Look at all these people, striving after luxury and wealth, those whose riches are secured, whose stocks and shares are safely deposited, and who now nurture an insatiable appetite for knowledge, power, health, glory and pleasure.

Only he who recognizes that he has nothing, that he cannot possess anything, that security is unattainable, only he who completely resigns himself and sacrifices all, who gives everything, who does not know anything, who does not want anything and does not want to know anything, who abandons and neglects all, he will receive all. The world of freedom is opened to him, the world of painless contemplation and―of nothing.”
― L.E.J. Brouwer, Vita, arte e mistica

“We have now reached the point where everyone has power but at the same time suffers oppression. The old instinct of separation and isolation now lives only as pale envy and jealousy.”
― L.E.J. Brouwer, Vita, arte e mistica

“Regarding your remark that the name of Kant doesn’t belong in a mathematical dissertation: you will see that the 'Foundations' of Russell deal repeatedly with Kant, & that ‘The Principles of Mathematics’ of Couturat are completed with an Appendix of over 100 pages about Kant. And when you compare the Transcendental Aesthetics of Kant to these, you will see that he speaks about exactly the same things as Russell and Couturat. And Poincaré points out that the present struggle about the foundations is a continuation of the old mathematical-philosophical controversy between Kant & Leibniz. Even though the name of Kant can be avoided here—his subjects are touched upon; is it then necessary to avoid his name because he is known as a philosopher? (Brouwer, 1906 letter to Korteweg)”
― L.E.J. Brouwer, The Selected Correspondence of L.E.J. Brouwer

“Mathematics, science and language constitute the main functions of the activity of mankind, by means of which it dominates nature and maintains order in its midst. These functions find their origin in three forms of action of the will to live of the individual: 1. mathematical attention, 2. mathematical abstraction, and 3. the imposing of will by means of sounds.”
― L.E.J. Brouwer

“[Neo-intuitionism] considers the falling aparts of moments of life into qualitatively different parts, to be reunited only while remaining separated by time, as the fundamental phenomenon of the human intellect, passing by abstracting from its emotional content into the fundamental phenomenon of mathematical thinking, the intuition of the bare two-oneness. This intuition of two-oneness, the basal intuition of mathematics, creates not only the numbers one and two, but also all finite ordinal numbers, inasmuch as one of the elements of the two-oneness may be thought of as a new two-oneness, which process may be repeated indefinitely.”
― L.E.J. Brouwer

“The mathematical attention comes about as an act of will serving the instinct of self-preservation of the individual in two phases: the temporal disposition and the causal disposition.
The first one is nothing but the intellectual principal phenomenon of the falling apart of a moment of life into two qualitatively distinct things, of which the one is experienced as giving way to the other, and nonetheless is experienced as preserved by the act of memory. At the same time the split moment of life is separated from the Ego and shifted to a world of its own, called the world of perception [Anschauungswelt].
Now the causal disposition consists of the act of the will to ‘identify’ certain of these temporal sequences of phenomena which extend over the past as well as the future. Thereby comes into being a common substratum of these identified sequences, which is denoted by a ‘causal sequence’.”
― L.E.J. Brouwer

“One cannot inquire into the foundations and nature of mathematics without delving into the question of the operations by which the mathematical activity of the mind is conducted. If one failed to take that into account, then one would be left studying only the language in which mathematics is represented rather than the essence of mathematics.”
― L.E.J. Brouwer

“It is part of the balance of the eternal and omnipresent life that everyone is called away from this earthly existence when one’s time has come. Until then man suffers in mind and body as befits his evil mood of thrift, his lust for power, his vanity and fear.”
― L.E.J. Brouwer, Leven, Kunst en Mystiek

“The fullest constructional beauty is the introspective beauty of mathematics, where [...] the basic intuition of mathematics is left to free unfolding. This unfolding is not bound to the exterior world, and thereby to finiteness and responsibility; consequently its introspective harmonies can attain any degree of richness and clearness.”
― L.E.J. Brouwer

“An incorrect theory, even if it cannot be inhibited by any contradiction that would refute it, is none the less incorrect, just as a criminal policy is none the less criminal even if it cannot be inhibited by any court that would curb it.”
― L.E.J. Brouwer

“Die Mathematik ist mehr ein Tun als eine Lehre.”
― L.E.J. Brouwer

“One knows well that the world is not a logical system and one cannot argue logically about it.”
― L.E.J. Brouwer, The Selected Correspondence of L.E.J. Brouwer

“The question where mathematical exactness does exist, is answered differently by the two sides; the intuitionist says: in the human intellect, the formalist says: on paper.”
― L.E.J. Brouwer

“Intuitionistic mathematics is inner architecture, and research in the foundations of mathematics is inner inquiry.”
― L.E.J. Brouwer

“Science places whatever is perceived, outside the self, in a world of perception independent of the self; the bond with the self, its only source and guide, is lost. It then constructs a mathematical-logical substratum which is completely alien to life, an illusion, one which acts in life as a Tower of Babel with its confusion of tongues.”
― L.E.J. Brouwer

“Science [...] makes sense only when man in his struggle against nature and his fellow men, uses the calculations of counting and measuring; in other words, physical science has value only as a weapon, it does not concern life – indeed it is a disturbing and distracting factor like everything in any way connected with struggle. But mathematics practised for its own sake can achieve all the harmony (i.e., an overwhelming multiplicity of different visible, simple structures within one and the same all-embracing edifice) such as can be found in architecture and music, and also yield all the illicit pleasures which ensue from the free and full development of one’s faculties without external force.”
― L.E.J. Brouwer

“(...), dat alle woorduitingen meer of minder ontwikkelde verbale imperatieven zijn, dat dus toespreken altijd neerkomt op bevelen of bedreigen, en begrijpen op gehoorzamen; (...)”
― L.E.J. Brouwer

“Intellect has done mankind a devil's service by linking the two phantasies of means and end... there are others [scientists] who do not know when to stop, who keep on and on until they go mad. They grow bald, short-sighted and fat, their stomachs stop working, and moaning with asthma and gastric trouble they fancy that in this way equilibrium is within reach and almost reached.... So much for science, the last flower and ossification of culture.”
― L.E.J. Brouwer, Vita, arte e mistica

“Nothing in art or science that is true has value (i.e. commercial value).”
― L.E.J. Brouwer

“Let the motivation behind mathematics be the craving for the good, not passion or brains.”
― L.E.J. Brouwer

“The mathematics of whole and part [=syllogistic] does not teach us through its theory anything new for application. Once the system is applied to a part of the observational world, even a very mediocre intellect can immediately read off all the consequences: no intermediary logical reasoning is necessary.”
― L.E.J. Brouwer, The Selected Correspondence of L.E.J. Brouwer

“The question where mathematical exactness exists is answered differently by the two sides; the intuitionist says: in the human intellect; the formalist says: on paper.”
― L.E.J. Brouwer

“The question where mathematical exactness does exist is answered differently by the two sides; the intuitionist says: in the human intellect; the formalist says: on paper”
― L.E.J. Brouwer