Morris Raphael Cohen Quotes

Powerful Morris Raphael Cohen for Daily Growth

About Morris Raphael Cohen

Morris Raphael Cohen (1880-1947), a prominent mathematician and logician, was born in Montreal, Canada on August 22, 1880. Growing up, he displayed an exceptional aptitude for mathematics, leading to his early acceptance at McGill University at the age of just fifteen. There, he studied under influential mathematicians like Leonard Eugene Dickson and James Dickson Inglis. Cohen's academic journey took him to the University of Chicago in 1902, where he worked under George David Birkhoff. His research focused on algebraic topology and number theory, making significant contributions to these fields. Notably, his work "On the Convergence of Certain Series Representing Functions of a Complex Variable" was published in the American Journal of Mathematics in 1907. In 1913, Cohen moved to Columbia University as an assistant professor. Here, he delved into set theory, logic, and mathematical foundations, becoming one of the pioneers of modern axiomatic set theory. His most significant work, "Set Theory and the Continuum Problem", published in 1946, is still regarded as a cornerstone in this field. Cohen's work on the independence of the continuum hypothesis from the standard axioms of set theory had profound implications for mathematics and philosophy. Despite facing challenges due to anti-Semitism during his academic career, Cohen's intellect, determination, and groundbreaking contributions cemented his legacy as one of the most influential mathematicians of the 20th century.

Interpretations of Popular Quotes

"In mathematics, you don't understand things. You just get used to them."

This quote by Morris Raphael Cohen suggests that in the field of mathematics, deep comprehension or "understanding" may not always be achievable. Instead, one becomes proficient and comfortable with mathematical concepts through practice, exposure, and repetition. In other words, mastery of mathematical ideas is often a matter of familiarity and habit rather than a complete grasp of their underlying principles.

"Mathematical logic is not a part of mathematics, it is mathematics."

This quote by Morris Raphael Cohen emphasizes that Mathematical Logic is the fundamental foundation upon which all mathematics rests. It signifies that mathematical logic is not just a subset or branch of mathematics but rather, it encapsulates the very essence of mathematics as a discipline. In other words, mathematical logic defines and establishes the rules, principles, and structures that give mathematics its unique nature and rigor. Without mathematical logic, mathematics would lack the precision, consistency, and formalism necessary for proofs, reasoning, and problem-solving.

"It is more important to have a million-dollar idea than a million dollars."

This quote suggests that having an exceptional, groundbreaking idea (a "million-dollar idea") is more valuable than possessing a large amount of money (a "million dollars"). The implication is that with the right idea, one can potentially create wealth or make significant impact, whereas money alone may not yield the same results. It emphasizes the power and potential of creativity, innovation, and original thinking over mere financial resources.

"The greatest of all mathematical discoveries is that we are quite incapable of understanding anything really valuable."

This quote by Morris Raphael Cohen suggests that the most profound mathematical discoveries, or perhaps any significant knowledge, may surpass our human capacity to fully comprehend them. It implies that as humans, there is a limit to our understanding when it comes to truly grasping complex ideas or concepts, even those of great value. This idea challenges us to appreciate the depth and mystery that lies within the vast expanse of knowledge we strive to explore.

"There is no such thing as applied mathematics, only applications of mathematics."

This quote by Morris Raphael Cohen suggests that mathematics itself is not a discipline that can be directly applied to solve practical problems; rather, it's the principles, theories, and methods derived from mathematics that are applied in real-world situations. In other words, we don't have "applied mathematics," but instead use mathematical concepts to tackle various applications across different fields such as physics, engineering, computer science, economics, etc.

The method of exposition which philosophers have adopted leads many to suppose that they are simply inquiries, that they have no interest in the conclusions at which they arrive, and that their primary concern is to follow their premises to their logical conclusions.

- Morris Raphael Cohen

Conclusions, Which, Method, Premises

Cruel persecutions and intolerance are not accidents, but grow out of the very essence of religion, namely, its absolute claims.

- Morris Raphael Cohen

Cruel, Grow, Very, Claims

It is not impossible to think that the minds of philosophers sometimes act like those of other mortals, and that, having once been determined by diverse circumstances to adopt certain views, they then look for and naturally find reasons to justify these views.

- Morris Raphael Cohen

Other, Been, Reasons, Mortals

Liberalism is an attitude rather than a set of dogmas - an attitude that insists upon questioning all plausible and self-evident propositions, seeking not to reject them but to find out what evidence there is to support them rather than their possible alternatives.

- Morris Raphael Cohen

Evidence, Liberalism, Set, Plausible

If religion cannot restrain evil, it cannot claim effective power for good.

- Morris Raphael Cohen

Effective, Cannot, Restrain, Claim

Literature and philosophy both allow past idols to be resurrected with a frequency which would be truly distressing to a sober scientist.

- Morris Raphael Cohen

Past, Allow, Which, Sober

Lastly, literature and philosophy both allow past idols to be resurrected with a frequency which would be truly distressing to a sober scientist.

- Morris Raphael Cohen

Past, Allow, Which, Sober

This open eye for possible alternatives which need to be scrutinized before we can determine which is the best grounded is profoundly disconcerting to all conservatives and to almost all revolutionaries.

- Morris Raphael Cohen

Almost All, Which, Determine, Disconcerting

It has generally been assumed that of two opposing systems of philosophy, e.g., realism and idealism, one only can be true and one must be false; and so philosophers have been hopelessly divided on the question, which is the true one.

- Morris Raphael Cohen

Been, Opposing, Which, Philosophers

In thus pointing out certain respects in which philosophy resembles literature more than science, I do not mean, of course, to imply that it would be well for philosophy if it ceased to aim at scientific rigor.

- Morris Raphael Cohen

Which, Imply, Thus, Respects

If a philosophic theory is once ruled out of court, no one can tell when it will appear again.

- Morris Raphael Cohen

Will, Tell, Again, Philosophic

Conservatism clings to what has been established, fearing that, once we begin to question the beliefs that we have inherited, all the values of life will be destroyed.

- Morris Raphael Cohen

Question, Been, Established, Fearing

Liberalism, on the other hand, regards life as an adventure in which we must take risks in new situations, in which there is no guarantee that the new will always be the good or the true, in which progress is a precarious achievement rather than inevitability.

- Morris Raphael Cohen

Always, Liberalism, Which, Precarious

Liberalism regards life as an adventure in which we must take risks in new situation, in which there is no guarantee that the new will always be the good or the true, in which progress is a precarious achievement rather than inevitability.

- Morris Raphael Cohen

Always, Liberalism, Which, Precarious

The picture which the philosopher draws of the world is surely not one in which every stroke is necessitated by pure logic.

- Morris Raphael Cohen

Philosopher, Which, Surely, Draws

A creative element is surely present in all great systems, and it does not seem possible that all sympathy or fundamental attitudes of will can be entirely eliminated from any human philosophy.

- Morris Raphael Cohen

Will, Surely, Eliminated, Element

Law is a formless mass of isolated decisions.

- Morris Raphael Cohen

Law, Isolated, Mass, Decisions

To be sure, the vast majority of people who are untrained can accept the results of science only on authority.

- Morris Raphael Cohen

People, Sure, Vast Majority, Untrained

Let philosophy resolutely aim to be as scientific as possible, but let her not forget her strong kinship with literature.

- Morris Raphael Cohen

Strong, Forget, Literature, Kinship

Again, both literature and philosophy work by appealing to certain reigning idols.

- Morris Raphael Cohen

Work, Literature, Reigning, Philosophy

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