10 April 2021

On Generalization (1800-1849)

"An idea is always a generalization, and generalization is a property of thinking. To generalize means to think." (Georg W F Hegel, "The Philosophy of Right", 1820)

"To minds of a certain cast there is nothing so captivating as simplification and generalization." (Thomas R Malthus, "Principles of Political Economy", 1820)

"General assertions, like general truths, are not always applicable to individual cases; though Fortune's wheel is generally on the turn, sometimes when it gets into the mud, it sticks there." (Letitia E Landon, "Romance and Reality", 1831)

"It is not easy to anatomize the constitution and the operations of a mind which makes such an advance in knowledge. Yet we may observe that there must exist in it, in an eminent degree, the elements which compose the mathematical talent. It must possess distinctness of intuition, tenacity and facility in tracing logical connection, fertility of invention, and a strong tendency to generalization." (William Whewell, "History of the Inductive Sciences" Vol. 1, 1837)

"Every theorem in geometry is a law of external nature, and might have been ascertained by generalizing from observation and experiment, which in this case resolve themselves into comparisons and measurements. But it was found practicable, and being practicable was desirable, to deduce these truths by ratiocination from a small number of general laws of nature, the certainty and universality of which was obvious to the most careless observer, and which compose the first principles and ultimate premises of the science." (John S Mill, "System of Logic", 1843)

"The mere accumulation of unconnected observations of details, devoid of generalization of ideas, may doubtlessly have tended to create and foster the deeply rooted prejudice, that the study of the exact sciences must necessarily chill the feelings, and diminish the nobler enjoyments attendant upon a contemplation of nature." (Alexander von Humboldt, "Cosmos: A Sketch of a Physical Description of the Universe", 1845)

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