"Our knowledge springs from two fundamental sources of the mind; the first is the capacity of receiving representations (receptivity for impressions), the second is the power of knowing an object through these representations (spontaneity [in the production] of concepts)." (Immanuel Kant, "Critique of Pure Reason", 1781)
"Thoughts without content are empty, intuitions without concepts are blind. The understanding can intuit nothing, the senses can think nothing. Only through their unison can knowledge arise." (Immanuel Kant, "Critique of Pure Reason", 1781)
"No hypothesis can lay claim to any value unless it assembles many phenomena under one concept." (Johann Wolfgang von Goethe, [letter to Sommering] 1795)
"Every word instantly becomes a concept precisely insofar as it is not supposed to serve as a reminder of the unique and entirely individual original experience to which it owes its origin; but rather, a word becomes a concept insofar as it simultaneously has to fit countless more or less similar cases - which means, purely and simply, cases which are never equal and thus altogether unequal. Every concept arises from the equation of unequal things. Just as it is certain that one leaf is never totally the same as another, so it is certain that the concept 'leaf' is formed by arbitrarily discarding these individual differences and by forgetting the distinguishing aspects." (Friedrich Nietzsche, "On Truth and Lie in an Extra-Moral Sense", 1873)
"A theory is the more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended is its area of applicability. Therefore the deep impression which classical thermodynamics made upon me. It is the only physical theory of universal content concerning which I am convinced that, within the framework of the applicability of its basic concepts, it will never be overthrown (for the special attention of those who are skeptics on principle)." (Albert Einstein, "Autobiographical Notes", 1949)
"What distinguishes the language of science from language as we ordinarily understand the word? […] What science strives for is an utmost acuteness and clarity of concepts as regards their mutual relation and their correspondence to sensory data." (Albert Einstein, "Ideas and Opinions", 1954)
"Awareness of universals is called conceiving, and a universal of which we are aware is called a concept." (Bertrand Russell, "Basic writings", 1961)
"The view is often defended that sciences should be built up on clear and sharply defined basal concepts. In actual fact no science, not even the most exact, begins with such definitions. The true beginning of scientific activity consists rather in describing phenomena and then in proceeding to group, classify and correlate them." (Sigmund Freud, "General Psychological Theory", 1963)
"From time immemorial, man has desired to comprehend the complexity of nature in terms of as few elementary concepts as possible." (Abdus Salam, "Ideals and Realities", 1989)
"On their way toward modern science human beings have discarded meaning. The concept is replaced by the formula, the cause by rules and probability." (Theodor W Adorno, "Dialectic of Enlightenment", 2002)
Quotes and Resources Related to Mathematics, (Mathematical) Sciences and Mathematicians
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Douglas T Ross - Collected Quotes
"Automatic design has the computer do too much and the human do too little, whereas automatic programming has the human do too much and...
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