“We consider it a good principle to explain the phenomena by the simplest hypothesis possible.”

— Ptolemy , book Almagest

Book III, sec 1 (trans. Gerald J. Toomer)
Almagest

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Ptolemy 8

Greco-Egyptian writer and astronomer of Alexandria 100–170

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“Although to penetrate into the intimate mysteries of nature and thence to learn the true causes of phenomena is not allowed to us, nevertheless it can happen that a certain fictive hypothesis may suffice for explaining many phenomena.”
Quanquam nobis in intima naturae mysteria penetrare, indeque veras caussas Phaenomenorum agnoscere neutiquam est concessum: tamen evenire potest, ut hypothesis quaedam ficta pluribus phaenomenis explicandis aeque satisfaciat, ac si vera caussa nobis esset perspecta.

Leonhard Euler (1707–1783) Swiss mathematician

§1
A conjecture about the nature of air (1780)

“This ideal theory of the true and real being that hides behind phenomena, Professor James, I repeat, puts forward only as a possible hypothesis, to point and emphasise his contention that "when we think of the law that thought is a function of the brain, we are not required to think of productive function only; we are entitled also to consider permissive or transmissive function."”

George Holmes Howison (1834–1916) American philosopher

Source: The Limits of Evolution, and Other Essays, Illustrating the Metaphysical Theory of Personal Ideaalism (1905), Human Immortality: its Positive Argument, p.282

“In whatever manner God created the world, it would always have been regular and in a certain general order. God, however, has chosen the most perfect, that is to say, the one which is at the same time the simplest in hypothesis and the richest in phenomena.”

Gottfried Leibniz book Discourse on Metaphysics

De quelque manière que Dieu aurait créé le monde, il aurait toujours été régulier et dans un certain ordre général. Mais Dieu a choisi celui qui est le plus parfait, c’est-à-dire celui qui est en même temps le plus simple en hypothèses et le plus riche en phénomènes...
Discours de métaphysique (1686); Leibniz famously tried to show that ours is the best of all possible worlds (see also Monadologie (53 & 54) below and compare Maimonides from Guide for the Perplexed (c. 1190), "Whatever is formed of matter receives the most perfect form possible in that species of matter.") These attempts were mercilessly parodied in Voltaire's Candide. Quotations from Voltaire's novel are often mistakenly attributed to Leibniz. Other statements by Leibniz upon the subject include these:
S'il n'y avait pas le meilleur (optimum) parmi tous les mondes possibles, Dieu n'en aurait produit aucun.
If there were no best among all possible worlds, God would not have created one.
Théodicée (1710)ː I. 8
I do not believe that a world without evil, preferable in order to ours, is possible; otherwise it would have been preferred. It is necessary to believe that the mixture of evil has produced the greatest possible good: otherwise the evil would not have been permitted.
The combination of all the tendencies to the good has produced the best; but as there are goods that are incompatible together, this combination and this result can introduce the destruction of some good, and as a result some evil.
Letter to Bourguet (late 1712)], as translated in The Shorter Leibniz Texts (2006) http://books.google.com/books?id=oFoCY3xJ8nkC&dq edited by Lloyd H. Strickland, p. 208

“The word hypothesis has now a somewhat different significance from that given it by Newton. We are now accustomed to understand by hypothesis all thoughts connected with the phenomena.
Newton was far from the crude thought that explanation of phenomena could be attained by abstraction.”

Bernhard Riemann (1826–1866) German mathematician

Causality
Gesammelte Mathematische Werke (1876)

“Ptolemy… against the champions of this or that cosmology of the heavens… had dared to claim that it is legitimate to interpret the facts of astronomy by the simplest geometrical scheme which will 'save the phenomena,' no matter whose metaphysics might be upset. His conception of the physical structure of the earth, however, prevented him from carrying through in earnest this principle of relativity, as his objections to the hypothesis that the earth moves amply show.”

Edwin Arthur Burtt (1892–1989) American philosopher

Source: The Metaphysical Foundations of Modern Physical Science (1925), p. 35

“The aim of the scientist is to express, in as simple a statement as possible, the principles underlying the order and arrangement of phenomena.”

Herbert Dingle (1890–1978) British astronomer

page 39 https://books.google.com/books?id=hwpKAAAAIAAJ&pg=PA39
Relativity for All, London, 1922

“It is possible to express the laws of thermodynamics in the form of independent principles, deduced by induction from the facts of observation and experiment, without reference to any hypothesis as to the occult molecular operations with which the sensible phenomena may be conceived to be connected; and that course will be followed in the body of the present treatise. But, in giving a brief historical sketch of the progress of thermodynamics, the progress of the hypothesis of thermic molecular motions cannot be wholly separated from that of the purely inductive theory.”

William John Macquorn Rankine (1820–1872) civil engineer

Source: A Manual of the Steam Engine and Other Prime Movers (1859), p. 27

“(Coining phrase "null hypothesis") In relation to any experiment we may speak of this hypothesis as the “null hypothesis,” and it should be noted that the null hypothesis is never proved or established, but is possibly disproved, in the course of experimentation. Every experiment may be said to exist only in order to give the facts a chance of disproving the null hypothesis.”

Ronald Fisher book The Design of Experiments

The Design of Experiments, Edinburgh: Oliver and Boyd, 1935, p. 18
1930s

“One finds in this subject a kind of demonstration which does not carry with it so high a degree of certainty as that employed in geometry; and which differs distinctly from the method employed by geometers in that they prove their propositions by well-established and incontrovertible principles, while here principles are tested by inferences which are derivable from them. The nature of the subject permits of no other treatment. It is possible, however, in this way to establish a probability which is little short of certainty. This is the case when the consequences of the assumed principles are in perfect accord with the observed phenomena, and especially when these verifications are numerous; but above all when one employs the hypothesis to predict new phenomena and finds his expectations realized.”

Christiaan Huygens book Treatise on Light

Treatise on Light (1690) - preface, Translated by Michael R. Matthews, Scientific Background to Modern Philosophy. 1989. p. 126

“Mr. Darwin and Mr. Wallace say that the opposite hypothesis, which assumes that every species is capable of varying indefinitely from its original type, is not a whit more arbitrary, and has this manifest claim to be preferred, that it will account for a multitude of phenomena which the ordinary theory is incapable of explaining.”

Charles Lyell (1797–1875) British lawyer and geologist

Source: The Geological Evidences of the Antiquity of Man (1863), Ch.21, p. 411
Context: Every naturalist admits that there is a general tendency in animals and plants to vary; but it is usually taken for granted, though we have no means of proving the assumption to be true, that there are certain limits beyond which each species cannot pass under any circumstances, or in any number of generations. Mr. Darwin and Mr. Wallace say that the opposite hypothesis, which assumes that every species is capable of varying indefinitely from its original type, is not a whit more arbitrary, and has this manifest claim to be preferred, that it will account for a multitude of phenomena which the ordinary theory is incapable of explaining.

“We consider it a good principle to explain the phenomena by the simplest hypothesis possible.”

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Ptolemy 8

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