On Experiments (1700-1749)

"The calculation of probabilities is of the utmost value, […] but in statistical inquiries there is need not so much of mathematical subtlety as of a precise statement of all the circumstances. The possible contingencies are too numerous to be covered by a finite number of experiments, and exact calculation is, therefore, out of the question. Although nature has her habits, due to the recurrence of causes, they are general, not invariable. Yet empirical calculation, although it is inexact, may be adequate in affairs of practice." (Gottfried W Leibniz [letter to Bernoulli], 1703)

"As in Mathematics, so in Natural Philosophy, the Investigation of difficult Things by the Method of Analysis, ought ever to precede the Method of Composition. This Analysis consists in making Experiments and Observations, and in drawing general Conclusions from them by Induction, and admitting of no Objections against the Conclusions but such as are taken from Experiments, or other certain Truths." (Sir Isaac Newton, "Opticks", 1704)

"For chemistry is no science form’d à priori; ’tis no production of the human mind, framed by reasoning and deduction: it took its rise from a number of experiments casually made, without any expectation of what follow’d; and was only reduced into an art or system, by collecting and comparing the effects of such unpremeditated experiments, and observing the uniform tendency thereof. So far, then, as a number of experimenters agree to establish any undoubted truth; so far they may be consider'd as constituting the theory of chemistry." (Hermann Boerhaave, "A New Method of Chemistry", 1727)

"Beware of determining and declaring your Opinion suddenly on any Object; for Imagination often gets the Start of judgment, and makes People believe they see Things, which better Observations will convince them could not possibly be seen: Therefore assert nothing till after repeated Experiments and Examinations in all Lights and in all Positions." (Henry Baker, "The Microscope Made Easy", 1742)

"From causes which appear similar we expect similar effects. This is the sum of all our experimental conclusions." (David Hume, "An Enquiry Concerning Human Understanding", 1748)

"In reality, all arguments from experience are founded on the similarity which we discover among natural objects, and by which we are induced to expect effects similar to those, which we have found to follow from such objects. And though none but a fool or madman will ever pretend to dispute the authority of experience, or to reject that great guide of human life; it may surely be allowed a philosopher to have so much curiosity at least, as to examine the principle of human nature, which gives this mighty authority to experience, and makes us draw advantage from that similarity, which nature has placed among different objects. From causes, which appear similar, we expect similar effects. This is the sum of all our experimental conclusions." (David Hume, "An Enquiry Concerning Human Understanding", 1748)

"Those who have not imbibed the prejudices of philosophers, are easily convinced that natural knowledge is to be founded on experiment and observation." (Colin Maclaurin, "An Account of Sir Isaac Newton’s Philosophical Discoveries", 1748)