A Quote by David Hilbert

In mathematics ... we find two tendencies present. On the one hand, the tendency towards abstraction seeks to crystallise the logical relations inherent in the maze of materials ... being studied, and to correlate the material in a systematic and orderly manner. On the other hand, the tendency towards intuitive understanding fosters a more immediate grasp of the objects one studies, a live rapport with them, so to speak, which stresses the concrete meaning of their relations.
Conservatism is pessimistic, with a negative tendency - which we mostly resist - towards despair. Liberals are optimists, with a negative tendency, rarely resisted, towards utopianism.
The best way to think about anarchism is as a combination of three levels. On the one hand, the sort of instinctual revulsion against forms of inequality in power; on the other hand, a reappraisal of what one is already doing in egalitarian relations; and then the projection of these principles on all sorts of relations.
I understand that the tendency of foreign countries in recent years has been to establish particularly close relations with one or two others among all the countries which have general relations. In time of peace, they make secret treaties in advance, and in wartime, they aid one another with military provisions and armaments.
The natural tendency of representative government, as of modern civilisation, is towards collective mediocrity: and this tendency is increased by all reductions and extensions of the franchise, their effect being to place the principal power in the hands of classes more and more below the highest level of instruction in the community.
There is nothing to be known about anything except an initially large, and forever expandable, web of relations to other things. Everything that can serve as a term of relation can be dissolved into another set of relations, and so on for ever. There are, so to speak, relations all the way down, all the way up, and all the way out in every direction: you never reach something which is not just one more nexus of relations.
Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long the relations don't change. Matter is not important, only form interests them.
The story of Noah, like other stories in the first 11 chapters of Genesis, are archetypal. Noah's story tells us that human beings have an inherent tendency towards violence both towards their fellow human beings and towards the creation itself. The story tells us that this violence grieves God.
Science studies the relations of things to each other: but art studies only their relations to man.
Mathematicians do not deal in objects, but in relations between objects; thus, they are free to replace some objects by others so long as the relations remain unchanged. Content to them is irrelevant: they are interested in form only.
The spontaneous tendency to invoke a Final Cause in explanation of every difficulty is characteristic of metaphysical philosophy. It arises from a general tendency towards the impersonation of abstractions which is visible throughout History.
Modem science, then, maintains on the one hand that nature, both organic and inorganic, strives towards a state of order and that man's actions are governed by the same tendency.
...man is an analogist, and studies relations in all objects. He is placed in the center of beings, and a ray of relation passes from every other being to him. And neither can man be understood without these objects, nor these objects without man.
If on one day we find the fast-spreading recognition of popular rights accompanied by a silent, growing perception of the rights of women, we also find it accompanied by a tendency towards a system of non-coercive education--that is, towards a practical illustration of the rights of children.
There are two things that seem to be at the bottom of our constitutions; one is a continual tendency towards politics; the other is family pride; and it is strange how these two feelings run through all of us.
While, on the one hand, the end of scientific investigation is the discovery of laws, on the other, science will have reached its highest goal when it shall have reduced ultimate laws to one or two, the necessity of which lies outside the sphere of our cognition. These ultimate laws-in the domain of physical science at least-will be the dynamical laws of the relations of matter to number, space, and time. The ultimate data will be number, matter, space, and time themselves. When these relations shall be known, all physical phenomena will be a branch of pure mathematics.
[Mathematics is] purely intellectual, a pure theory of forms, which has for its objects not the combination of quantities or their images, the numbers, but things of thought to which there could correspond effective objects or relations, even though such a correspondence is not necessary.
This site uses cookies to ensure you get the best experience. More info...
Got it!