A Quote by Socrates
The understanding of mathematics is necessary for a sound grasp of ethics.
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...mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics. Every other science, even logic, especially in its early stages, is in danger of evaporating into airy nothingness, degenerating, as the Germans say, into an arachnoid film, spun from the stuff that dreams are made of. There is no such danger for pure mathematics; for that is precisely what mathematics ought to be.
As to ethics, unfortunately, we are still at sea. We never did have any popular base for what little ethics we knew, except the religious theories, and now that our faith is shaken in those theories we cannot account for ethics at all. It is no wonder we behave badly, we are literally ignorant of the laws of ethics, which is the simplest of sciences, the most necessary, the most continuously needed. The childish misconduct of our 'revolted youth' is quite equaled by that of older people, and neither young nor old seem to have any understanding of the reasons why conduct is 'good' or 'bad.
Mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics.
The product of mathematics is clarity and understanding. Not theorems, by themselves. ... In short, mathematics only exists in a living community of mathematicians that spreads understanding and breathes life into ideas both old and new.
If scientific reasoning were limited to the logical processes of arithmetic, we should not get very far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability.
The study of geometry is a petty and idle exercise of the mind, if it is applied to no larger system than the starry one. Mathematics should be mixed not only with physics but with ethics; that is mixed mathematics.
There's so many things about Babymetal you cannot just grasp with the sound. The visual has to compliment the sound, the costumes have to compliment the sound.
In order to contract, It is necessary first to expand. In order to weaken, It is necessary first to strengthen. In order to destroy, It is first necessary to promote. In order to grasp, It is necessary first to give. This is called subtle light. The weak and the tender overcome the hard and the strong.
. . . the membership relation for sets can often be replaced by the composition operation for functions. This leads to an alternative foundation for Mathematics upon categories -- specifically, on the category of all functions. Now much of Mathematics is dynamic, in that it deals with morphisms of an object into another object of the same kind. Such morphisms (like functions) form categories, and so the approach via categories fits well with the objective of organizing and understanding Mathematics. That, in truth, should be the goal of a proper philosophy of Mathematics.
Mathematics should be mixed not only with physics but with ethics.
Art is a form of understanding like philosophy and science and mathematics are an understanding but the difference is that art has the capacity to hold all these different things. It is the form of understanding that is best suited for the contemporary time.
The rejection of all abstract formalism. Materialism reminds every science of its real source: the world men transform. No science can, whether in its history or its object, grasp its own origins within itself or constitute itself as a closed world, exhaustively defined by internal rules. Materialism refers every science and every activity to the reality they depend on, even if this dependence is masked by a great many abstract mediations: mathematics as well as logic, aesthetics as well as ethics and politics.
No code of ethics and no effort are justifiable a priori in the face of the cruel mathematics that command our condition.
As a writer who writes poetry, nonfiction, and fiction, I think it's important to always maintain a firm grasp on genre and ethics.
How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.
Theology is faith seeking understanding, but understanding is more than theoretical. If we really grasp who and where we are as disciples, we should know how to live out our faith.
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