On Insight (-1899)

"[…] it is from long experience chiefly that we are to expect the most certain rules of practice, yet it is withal to be remembered, that observations, and to put us upon the most probable means of improving any art, is to get the best insight we can into the nature and properties of those things which we are desirous to cultivate and improve." (Stephen Hales, "Vegetable Staticks", 1727)

"Reason in a creature is a faculty of widening the rules and purposes of the use of all its powers far beyond natural instinct; it acknowledges no limits to its projects. Reason itself does not work instinctively, but requires trial, practice, and instruction in order gradually to progress from one level of insight to another." (Immanuel Kant, "Idea for a Universal History from a Cosmopolitan Point of View", 1784)

"Complete knowledge of the nature of an analytic function must also include insight into its behavior for imaginary values of the arguments. Often the latter is indispensable even for a proper appreciation of the behavior of the function for real arguments. It is therefore essential that the original determination of the function concept be broadened to a domain of magnitudes which includes both the real and the imaginary quantities, on an equal footing, under the single designation complex numbers." (Carl F Gauss, cca. 1831)

"[...] it should be noted that the seeds of wisdom that are to bear fruit in the intellect are sown less by critical studies and learned monographs than by insights, broad impressions, and flashes of intuition." (Carl von Clausewitz, "On War", 1832)

"The insights gained and garnered by the mind in its wanderings among basic concepts are benefits that theory can provide. Theory cannot equip the mind with formulas for solving problems, nor can it mark the narrow path on which the sole solution is supposed to lie by planting a hedge of principles on either side. But it can give the mind insight into the great mass of phenomena and of their relationships, then leave it free to rise into the higher realms of action." (Carl von Clausewitz, "On War", 1832)

"The desire to explain what is simple by what is complex, what is easy by what is difficult, is a calamity affecting the whole body of science, known, it is true, to men of insight, but not generally admitted." (Johann Wolfgang von Goethe, "Maxims and Reflections", 1833)

"This science, Geometry, is one of indispensable use and constant reference, for every student of the laws of nature; for the relations of space and number are the alphabet in which those laws are written. But besides the interest and importance of this kind which geometry possesses, it has a great and peculiar value for all who wish to understand the foundations of human knowledge, and the methods by which it is acquired. For the student of geometry acquires, with a degree of insight and clearness which the unmathematical reader can but feebly imagine, a conviction that there are necessary truths, many of them of a very complex and striking character; and that a few of the most simple and self-evident truths which it is possible for the mind of man to apprehend, may, by systematic deduction, lead to the most remote and unexpected results." (William Whewell, "The Philosophy of the Inductive Sciences", 1858)

"The mysterious complexity of our life is not to be embraced by maxims... to lace ourselves up in formulas of that sort is to repress all the divine promptings and inspirations that spring from growing insight and sympathy." (George Eliot, "The Mill on the Floss", 1860)

"The sciences are said, and they are truly said, to have a mutual connection, that any one of them may be the better understood, for an insight into the rest." (Samuel Horsley, "Sermons", 1860)

"It often happens that the pursuit of the beautiful and appropriate, or, as it may be otherwise expressed, the endeavor after the perfect, is rewarded with a new insight into the true." (James J Sylvester, "Separation of the Roots of an Algebraical Equation", Philosophical Magazine, 1866)

"A law of nature, however, is not a mere logical conception that we have adopted as a kind of memoria technical to enable us to more readily remember facts. We of the present day have already sufficient insight to know that the laws of nature are not things which we can evolve by any speculative method. On the contrary, we have to discover them in the facts; we have to test them by repeated observation or experiment, in constantly new cases, under ever-varying circumstances; and in proportion only as they hold good under a constantly increasing change of conditions, in a constantly increasing number of cases with greater delicacy in the means of observation, does our confidence in their trustworthiness rise." (Hermann von Helmholtz, "Popular Lectures on Scientific Subjects", 1873)

"Science corrects the old creeds, sweeps away, with every new perception, our infantile catechisms, and necessitates a faith commensurate with the grander orbits and universal laws which it discloses yet it does not surprise the moral sentiment that was older and awaited expectant these larger insights." (Ralph Waldo Emerson, "Letters and Social Aims", 1876)

"Our power of scientific insight is but feeble when compared with the profundity of nature, because deep truths require deep thought to enable us to understand and value them." (George Gore, 'The Art of Scientific Discovery", 1878)

"The aim of proof is, in fact, not merely to place the truth of a proposition beyond all doubt, but also to afford us insight into the dependence of one truth upon another. After we have convinced ourselves that a boulder is immovable, by trying unsuccessfully to move it, there remains the further question, what is it that supports it so securely." (Gottlob Frege, "The Foundations of Arithmetic", 1884)

"By thus thinking [by analogy] you will get a more real grasp of the subject and insight into the actual processes occurring in Nature - unknown though these may still strictly be - than if you employed the old ideas of action at a distance, or contented yourselves with no theory at all on which to link the facts. You will have made a step in the direction of the truth, but I must beg you to understand that it is only a step; that what modifications and additions will have to be made to it before it becomes a complete theory of electricity I am unable fully to tell you." (Oliver J Lodge, "Modern Views of Electricity", 1889)

"The history of science shows that great discoveries are made by means of imaginative insight, but it also teaches that mere imagination without dependence upon known facts is frequently a source of much mischief." (James E Creighton, "An Introductory Logic", 1898)