A Quote by Richard M. Nixon

We do not learn by inference and deduction and the application of mathematics to philosophy, but by direct intercourse and sympathy.

Richard M. Nixon

Quote Topics

Sympathy Application Deduction Direct Inference Intercourse Learn Mathematics Philosophy

Quote Author

Richard M. Nixon
American - President
January 9, 1913 - April 22, 1994

The true man of science will know nature better by his finer organization; he will smell, taste, see, hear, feel, better than other men. His will be a deeper and finer experience. We do not learn by inference and deduction and the application of mathematics to philosophy, but by direct intercourse and sympathy. It is with science as with ethics,--we cannot know truth by contrivance and method; the Baconian is as false as any other, and with all the helps of machinery and the arts, the most scientific will still be the healthiest and friendliest man, and possess a more perfect Indian wisdom.

Henry David Thoreau

He is not a true man of science who does not bring some sympathy to his studies, and expect to learn something by behavior as well as by application. It is childish to rest in the discovery of mere coincidences, or of partial and extraneous laws. 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. The fact which interests us most is the life of the naturalist. The purest science is still biographical.

Henry David Thoreau

The history of mathematics, lacking the guidance of philosophy, [is] blind, while the philosophy of mathematics, turning its back on the most intriguing phenomena in the history of mathematics, is empty.

Imre Lakatos

He is not a true man of science who does not bring some sympathy to his studies, and expect to learn something by behaviour as well as application.

Henry David Thoreau

To criticize mathematics for its abstraction is to miss the point entirely. Abstraction is what makes mathematics work. If you concentrate too closely on too limited an application of a mathematical idea, you rob the mathematician of his most important tools: analogy, generality, and simplicity. Mathematics is the ultimate in technology transfer.

Ian Stewart

in certain crises direct expression of sympathy is the least possible to those who most feel sympathy.

George Eliot

One of the most amazing things about mathematics is the people who do math aren't usually interested in application, because mathematics itself is truly a beautiful art form. It's structures and patterns, and that's what we love, and that's what we get off on.

Danica McKellar

For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics?

Richard Courant

No amount of reading and intelligent deduction could supplant the direct experience.

John Fowles

Mathematics may be defined as the economy of counting. There is no problem in the whole of mathematics which cannot be solved by direct counting.

Ernst Mach

. . . 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.

Saunders Mac Lane

The philosophy of protectionism is a philosophy of war. The wars of our age are not at variance with popular economic doctrines; they are, on the contrary, the inescapable result of a consistent application of these doctrines.

Ludwig von Mises

There are areas of philosophy that are important, but I think of them as being subsumed by other fields. In the case of descriptive philosophy, you have literature or logic, which, in my view, is really mathematics.

Lawrence M. Krauss

It is difficult to distinguish deduction from what in other circumstances is called problem-solving. And concept learning, inference, and reasoning by analogy are all instances of inductive reasoning. (Detectives typically induce, rather than deduce.) None of these things can be done separately from each other, or from anything else. They are pseudo-categories.