On Analogy (Unsourced)

"A fact is not novel if it has an analogue which could have some interest. A fact which does not fi t in with a series of known facts is a fact which deserves particular attention. If the mind had to retain all individual facts, it could not manage and science would not exist; but when these facts can be connected by general laws and by theories, when a large number of these facts can be represented by a single one, one can remember them more easily, one can generalise one’s ideas, one can compare one general fact with another general fact and discoveries can succeed each other. It is only when laws can be introduced into a science that it assumes the true character of science." (Joseph L Gay-Lussac)

"A good analogy is stretching a rubber band. You can stretch and stretch and even feel the tension increase in the muscles in your hands and arms as the gap from one end of the band to the other widens. But at some point you reach the limits of elasticity of the band and it snaps. The same thing happens with human systems." (John L Casti)

"Analogy has two errors to fear - the one when it contents itself with being serviceable to wit, in which case it floats away in futile sport; the other, when it shrouds itself in tropes and similes: this last is the less dangerous of the two." (Johann Wolfgang von Goethe)

"By observation, facts are distinctly and minutely impressed in the mind; by analogy, similar facts are connected; by experiment, new facts are discovered; and, in the progression of knowledge, observation, guided by analogy, leads to experiment, and analogy, confirmed by experiment, becomes scientific truth." (Sir Humphry Davy)

“Good mathematicians see analogies between theorems or theories, the very best ones see analogies between analogies.” (Stefan Banach)

"Imagination, as well as reason, is necessary to perfection in the philosophical mind. A rapidity of combination, a power of perceiving analogies, and of comparing them by facts, is the creative source of discovery." (Sir Humphry Davy)

"No discovery has been made in mathematics, or anywhere else for that matter, by an effort of deductive logic; it results from the work of creative imagination which builds what seems to be truth, guided sometimes by analogies, sometimes by an esthetic ideal, but which does not hold at all on solid logical bases. Once a discovery is made, logic intervenes to act as a control; it is logic that ultimately decides whether the discovery is really true or is illusory; its role therefore, though considerable, is only secondary." (Henri Lebesgue)

"The arguments […] by which you support my theories, are most ingenious, but not founded on demonstrated facts; analogy is no proof." (Louis Pasteur)

"The law of analogy is a priceless key to the divine mysteries." (Hermes Trismegistus)

"The way to determine the secret workings of Nature is from analogous cases where one has caught her in act." (Georg C Lichtenberg)

"Thinking by analogy is not to be despised. Analogy has this merit, that it does not settle things - does not pretend to be conclusive. On the other hand, that induction is pernicious which, with a preconceived end in view, and working right forward for only that,  drags in its train a number of unsifted observations, both false and true." (Johann Wolfgang von Goethe)

"To communicate knowledge by means of analogy appears to me a process equally useful and pleasant. The analogous case is not there to force itself on the attention or prove anything; it offers a comparison with some other cases, but it is not in union with it." (Johann Wolfgang von Goethe)