Cassius Jackson Keyser Quotes

The present is no more exempt from the sneer of the future than the past has been.

If people would stop objectifying abstractions (which they probably never will), or if they would stop objectifying the abstractions they make consciously (which they might learn to do), at least half the pseudo-questions befuddling the world today - as they have befuddled it since time immemorial - would vanish. And that would be a very, very great gain.

It happens, therefore, that readers of the book, or of any other book built about a central concept, fall into three mutually exclusive classes:

(I) The class of those who miss the central concept-(I have known a learned historian to miss it) -not through any fault of their own,-they are often indeed well meaning and amiable people,-but simply because they are not qualified for conceptual thinking save that of the commonest type.

(II) The class of those who seem to grasp the central concept and then straightway show by their manner of talk that they have not really grasped it but have at most got hold of some of its words. Intellectually such readers are like the familiar type of undergraduate who "flunks" his mathematical examinations but may possibly "pull through" in a second attempt and so is permitted, after further study, to try again.

(III) The class of those who firmly seize the central concept and who by meditating upon it see more and more clearly the tremendous reach of its implications. If it were not for this class, there would be no science in the world nor genuine philosophy. But the other two classes are not aware of the fact for they are merely "verbalists" In respect of such folk, the "Behaviorist" school of psychology is right for in the psychology of classes (I) and (II) there is no need for a chapter on "Thought Processes"- it is sufficient to have one on "The Language Habit.

Absolute certainty is a privilege of uneducated minds and fanatics. - It is, for scientific folk, an unattainable ideal.

The validity of mathematical propositions is independent of the actual world-the world of existing subject-matters-is logically prior to it, and would remain unaffected were it to vanish from being. Mathematical propositions, if true, are eternal verities.

The pursuit of excellence is the proper vocation of man.

It is commonly, but erroneously, believed that it is easy to ask questions. A fool, it is said, can ask questions that a wise man cannot answer. The fact is that a wise man can answer many questions that a fool cannot ask.

If you ask ... the man in the street ... the human significance of mathematics, the answer of the world will be, that mathematics has given mankind a metrical and computatory art essential to the effective conduct of daily life, that mathematics admits of countless applications in engineering and the natural sciences, and finally that mathematics is a most excellent instrumentality for giving mental discipline ... [A mathematician will add] that mathematics is the exact science, the science of exact thought or of rigorous thinking.

Mathematics, even in its present and most abstract state, is not detached from life. It is just the ideal handling of the problems of life.