“Robert [Grosseteste] became much interested in science and scientific method … He was conscious of the dual approach by means of induction and deduction (resolution and composition); i. e., from the empirical knowledge one proceeds to probable general principles, and from these as premises one them derives conclusions which constitute verifications or falsifications of the principles. This approach to science was not that far removed from Aristotle …”

—  Carl B. Boyer

Source: The Rainbow: From Myth to Mathematics (1959), p. 88

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Carl B. Boyer photo
Carl B. Boyer 15
American mathematician 1906–1976

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“In its application to natural science Grosseteste based his method of verification and falsification on two assumptions about the nature of reality. (a) The first was the principle of the uniformity of nature, meaning that forms are always uniform in their operations…. In support of this principle he quoted 'Aristotles II de Generat.:…'the same cause, provided it remains in the same condition, cannot produce anything but the same effect.' (b) The second assumption Grosseteste made was that of the principle of economy, or lex parsimoniae. This he also derived from Aristotle, who stated it as a pragmatic principle.”

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“We tend to believe the premises because we can see that their consequences are true, instead of believing the consequences because we know the premises to be true. But the inferring of premises from consequences is the essence of induction; thus the method in investigating the principles of mathematics is really an inductive method, and is substantially the same as the method of discovering general laws in any other science.”

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“Grosseteste's contribution was to emphasize the importance of falsification in the search for true causes and to develop the method of verification and falsification into a systematic method of experimental procedure.”

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“The method of viewing things which proceeds in accordance with the principle of sufficient reason is the rational method, and it alone is valid and of use in practical life and in science. The method which looks away from the content of this principle is the method of genius, which is only valid and of use in art.”

Arthur Schopenhauer book The World as Will and Representation

Die dem Satz vom Grunde nachgehende ist die vernünftige Betrachtungsart, welche im praktischen Leben, wie in der Wissenschaft, allein gilt und hilft: die vom Inhalt jenes Satzes wegsehende ist die geniale Betrachtungsart, welche in der Kunst allein gilt und hilft.
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The World as Will and Representation (1819; 1844; 1859)

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“It would be better, I think, for the man who really seeks the truth not to ask what the poets say; rather, he should first learn the method of finding the scientific premises that I discussed in the second book; then he should train and exercise himself in this method; and when his training is sufficiently advanced, then, as he approaches each particular problem, he should enquire into the premise needed for proving it, which premise he should take from simple sense-perception, which from experience, whether drawn from life or from the arts, which from the truths clearly apprehended by the mind, in order to draw out from them the desired conclusion.”

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Galen, On the Doctrines of Hippocrates and Plato,: PHP III 8.35.1-11 translation: De Lacy, Phillip (1978- 1984) Galen, On the Doctrines of Hippocrates and Plato, Berlin. p. 233; cited in: Christopher Jon Elliott. "Galen, Rome and the Second Sophistic." p. 147-8.

“Both induction and deduction, reasoning from the particular and the general, and back again from the universal to the specific, form the essence to scientific thinking.”

Hans Christian von Baeyer (1938) American physicist

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“The historical approach to understanding of scientific fact is what differentiates the scholar in science from the mere experimenter.”

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Source: Psychologist at large, 1961, p. 3

Honoré de Balzac photo

“Thinking is seeing," said he one day, carried away by some objection raised as to the first principles of our organisation."Every human science is based on deduction, which is a slow process of seeing by which we work up from the effect to the cause; or, in a wider sense, all poetry like every work of art proceeds from a swift vision of things.”

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Penser, c'est voir! me dit-il un jour emporté par une de nos objections sur le principe de notre organisation. Toute science humaine repose sur la déduction, qui est une vision lente par laquelle on descend de la cause à l'effet, par laquelle on remonte de l'effet à la cause; ou, dans une plus large expression, toute poésie comme toute oeuvre d'art procède d'une rapide vision des choses.
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“Robert Grosseteste … was born at the decisive moment when Greek and Arabic science became accessible in Latin versions.”

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Source: The Rainbow: From Myth to Mathematics (1959), p. 88

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“By this way of Analysis we may proceed from Compounds to Ingredients, and from Motions to the Forces producing them; and in general, from Effects to their Causes, and from particular Causes to more general ones, till the Argument end in the most general. This is the Method of Analysis: and the Synthesis consists in assuming the Causes discover'd, and establish'd as Principles, and by them explaining the Phænomena proceeding from them, and proving the Explanations.”

Isaac Newton book Opticks, or a Treatise of the Reflections, Refractions, Inflections and Colours of Light

Query 31
Opticks (1704)

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