Conflicting intellectual positions may actually come to supplement one another. It is imperative in the present transitional period to make use of the intellectual twilight which dominates our epoch and in which all values and points of view appear in their genuine relativity. We must realize once and for all that the meanings which make up our world are simply an historically determined and continuously developing structure in which man develops, and are in no sense absolute.
Karl MannheimRelated topics
absolute appear developing epoch imperative intellectual man once period present relativity sense structure supplement twilight use view world pointsRelated quotes
I shall now address you on the subject of the present situation in research in the foundations of mathematics. Since there remain open questions in this field, I am not in a position to paint a definitive picture of it for you. But it must be pointed out that the situation is not so critical as one could think from listening to those who speak of a foundational crisis. From certain points of view, this expression can be justified; but it could give rise to the opinion that mathematical science is shaken at its roots.
Paul Bernays
When scientists need to explain difficult points of theory, illustration by hypothetical example - rather than by total abstraction - works well (perhaps indispensably) as a rhetorical device. Such cases do not function as speculations in the pejorative sense - as silly stories that provide insight into complex mechanisms - but rather as idealized illustrations to exemplify a difficult point of theory. (Other fields, like philosophy and the law, use such conjectural cases as a standard device.)
Stephen Jay Gould
Once efficiency is universally accepted as a rule, it becomes an inner compulsion and weighs like a sense of sin, simply because no one can ever be efficient enough, just as no one can ever be virtuous enough. And this new sense of sin only contributes further to the enervation of leisure, for the rich as well as the poor.The difficulty of carrying on a leisure-oriented tradition of culture in a work-oriented society is enough in itself to keep the present crisis in our culture unresolved.
Clement Greenberg
Depth, in a pictorial, plastic sense, is not created by the arrangement of objects one after another toward a vanishing point, in the sense of the Renaissance perspective, but on the contrary (and in absolute denial of this doctrine) by the creation of forces in the sense of push and pull . Nor is depth created by tonal gradation (another doctrine of the academician which, at its culmination, degraded the use of color to a mere function of expressing dark and light).
Hans Hofmann
At this point in history when all things which concern man and the structure and elements of history itself are suddenly revealed to us in a new light, it behooves us in our scientific thinking to become masters of the situation, for it is not inconceivable that sooner than we suspect, as has often been the case before in history, this vision may disappear, the opportunity may be lost, and the world will once again present a static, uniform, and inflexible countenance.
Karl Mannheim
