“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

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "One finds in this subject a kind of demonstration which does not carry with it so high a degree of certainty as that em…" by Christiaan Huygens?

Christiaan Huygens 16

Dutch mathematician and natural philosopher 1629–1695

Related quotes

“You well know … for which reason I began searching for a number of demonstrations proving a statement due to the ancient Greeks … and which passion I felt for the subject … so that you reproached me my preoccupation with these chapters of geometry, not knowing the true essence of these subjects, which consists precisely in going in each matter beyond what is necessary. … Whatever way he [the geometer] may go, through exercise will he be lifted from the physical to the divine teachings, which are little accessible because of the difficulty to understand their meaning … and because the circumstance that not everybody is able to have a conception of them, especially not the one who turns away from the art of demonstration.”

Al-Biruni (973–1048) Persian scholar and polymath

Book on the Finding of Chords.

“Reason may be employed in two ways to establish a point: firstly, for the purpose of furnishing sufficient proof of some principle, as in natural science, where sufficient proof can be brought to show that the movement of the heavens is always of uniform velocity. Reason is employed in another way, not as furnishing a sufficient proof of a principle, but as confirming an already established principle, by showing the congruity of its results, as in astrology the theory of eccentrics and epicycles is considered as established, because thereby the sensible appearances of the heavenly movements can be explained; not, however, as if this proof were sufficient, forasmuch as some other theory might explain them.”

Thomas Aquinas book Summa Theologica

I, q. 32, art. 1, reply obj. 2
Summa Theologica (1265–1274)

“Ostensive demonstration is that which concludes directly to that which is in question. Reduction ad impossibile is that which, when something the opposite of that which is in question has been assumed, concludes with some other proposition directly to a known and manifest impossibility, from the opposite of which the investigator is led back to the original proposition in question. But there is a difference between ostensive demonstration and reduction ad impossibile, because the former proves from things prior in the order of nature but the latter from things posterior in the order of nature. When things prior in nature are better known in the intellect of the person making the demonstration the process is carried out ostensively; but when posterior things are better known to his intellect then the demonstration is carried out per impossibile… in demonstration carried out per impossibile the showing of the original thing in question is carried out by means of things posterior to it in the order of nature… And there is in the contrary, falsely supposed in predicate of subject, a connecting term by which something is implied to be which impossible in the nature of things.”

Robert Grosseteste (1175–1253) English bishop and philosopher

i. 17, f. 18<sup>r</sup>
Commentarius in Posteriorum Analyticorum Libros (c. 1217-1220)

“From principles is derived probability, but truth or certainty is obtained only from facts.”

Tom Stoppard (1937) British playwright

From principles is derived probability, but truth is obtained only from facts. - Jesse Olney (1798 - 1872), The National Preceptor (Goodwin, 1830), Lesson LXXXV: "Select Sentences," rule # 19 (p. 171).
Misattributed

“A psychological space is established for any set of stimuli by determining metric distances between the stimuli such that the probability that a response learned to any stimulus will generalize to any other is an invariant monotonic function of the distance between them. To a good approximation, this probability of generalization (i) decays exponentially with this distance, and (ii) does so in accordance with one of two metrics, depending on the relation between the dimensions along which the stimuli vary. These empirical regularities are mathematically derivable from universal principles of natural kinds and probabilistic geometry that may, through evolutionary internalization, tend to govern the behaviors of all sentient organisms.”

Roger Shepard (1929) American psychologist

Source: "Toward a universal law of generalization for psychological science," 1987, p. 1317

“No power of government ought to be employed in the endeavor to establish any system or article of belief on the subject of religion.”

Jeremy Bentham (1748–1832) British philosopher, jurist, and social reformer

Source: Constitutional Code; For the Use All Nations and All Governments Professing Liberal Opinions Volume 1

“In all matters but particularly in architecture …that which is signified is the subject of which we may be speaking and that which gives significance is a demonstration on scientific principles. …One who professes himself an architect should be well versed in both directions.”

Vitruvius book De architectura

Source: De architectura (The Ten Books On Architecture) (~ 15BC), Book I, Chapter I, Sec. 3

“The difference between mind and brain is that brain deals only with memorized, subjective, special-case experiences and objective experiments, while mind extracts and employs the generalized principles and integrates and interrelates their effective employment.”

Buckminster Fuller (1895–1983) American architect, systems theorist, author, designer, inventor and futurist

1960s, Operating Manual for Spaceship Earth (1963)
Context: The difference between mind and brain is that brain deals only with memorized, subjective, special-case experiences and objective experiments, while mind extracts and employs the generalized principles and integrates and interrelates their effective employment. Brain deals exclusively with the physical, and mind exclusively with the metaphysical.

“That miracles are things in themselves possible, must be allowed so long as it is evident that there is in nature a power equal to the working of them. And certainly the power, principle, or being, by whatever name it be denominated, which produced the universe, and established the laws of it, is fully equal to any occasional departures from them.”

Joseph Priestley book An History of the Corruptions of Christianity

General Conclusions, Part I : Containing Considerations addressed to Unbelievers and especially to Mr. Gibbon
An History of the Corruptions of Christianity (1782)
Context: That miracles are things in themselves possible, must be allowed so long as it is evident that there is in nature a power equal to the working of them. And certainly the power, principle, or being, by whatever name it be denominated, which produced the universe, and established the laws of it, is fully equal to any occasional departures from them. The object and use of those miracles on which the christian religion is founded, is also maintained to be consonant to the object and use of the general system of nature, viz. the production of happiness. We have nothing, therefore to do, but to examine, by the known rules of estimating the value of testimony whether there be reason to think that such miracles have been wrought, or whether the evidence of Christianity, or of the christian history, does not stand upon as good ground as that of any other history whatever.

“[T]he ancient philosophers… all of them assert that the elements, and those things which are called by them principles, are contraries, though they establish them without reason, as if they were compelled to assert this by truth itself. They differ, however… that some of them assume prior, and others posterior principles; and some of them things more known according to reason, but others such as are more known according to sense: for some establish the hot and the cold, others the moist and the dry, others the odd and the even, and others strife and friendship, as the causes of generation. …in a certain respect they assert the same things, and speak differently from each other. They assert different things… but the same things, so far as they speak analogously. For they assume principles from the same co-ordination; since, of contraries, some contain, and others are contained.”

Aristotle book Physics

Book I, Ch. VI, pp. 57-59.
Physics

Help us to complete the source, original and additional information

Christiaan Huygens 16

Related quotes

Related topics