A Quote by Bertrand Russell
Bacon not only despised the syllogism, but undervalued mathematics, presumably as insufficiently experimental. He was virulently hostile to Aristotle , but he thought very highly of Democritus , Although he did not deny that the course of nature exemplifies a Divine purpose, he objected to any admixture of teleological explanation in the actual investigation of phenomena; everything, he held, should be explained as following necessarily from efficient causes .
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Any theory which causes solipsism to seem just as likely an explanation for the phenomena it seeks to describe ought to be held in the utmost suspicion.
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.
The Scientific Revolution, that remarkable transformation of European thought that occurred between approximately 1550 and 1700, brought with it an ascendancy of the experimental method and the refusal to believe any explanation of natural phenomena that could not be proven to the satisfaction of the empirical observer.
Statistics is, or should be, about scientific investigation and how to do it better, but many statisticians believe it is a branch of mathematics. Now I agree that the physicist, the chemist, the engineer, and the statistician can never know too much mathematics, but their objectives should be better physics, better chemistry, better engineering, and in the case of statistics, better scientific investigation. Whether in any given study this implies more or less mathematics is incidental.
[We need not think] that there is any Contradiction, when Philosophy teaches that to be done by Nature; which Religion, and the Sacred Scriptures, teach us to be done by God: no more, than to say, That the balance of a Watch is moved by the next Wheel, is to deny that Wheel, and the rest, to be moved by the Spring; and that both the Spring, and all the other Parts, are caused to move together by the Maker of them. So God may be truly the Cause of This Effect, although a Thousand other Causes should be supposed to intervene: For all Nature is as one Great Engine, made by, and held in His Hand.
Our alleged facts might be true in all kinds of ways without contradicting any truth already known. I will dwell now on only one possible line of explanation, - not that I see any way of elucidating all the new phenomena I regard as genuine, but because it seems probable I may shed a light on some of those phenomena. All the phenomena of the universe are presumably in some way continuous; and certain facts, plucked as it were from the very heart of nature, are likely to be of use in our gradual discovery of facts which lie deeper still.
The very hope of experimental philosophy, its expectation of constructing the sciences into a true philosophy of nature, is basedon induction, or, if you please, the a priori presumption, that physical causation is universal; that the constitution of nature is written in its actual manifestations, and needs only to be deciphered by experimental and inductive research; that it is not a latent invisible writing, to be brought out by the magic of mental anticipation or metaphysical mediation.
In experimental philosophy, propositions gathered from phenomena by induction should be considered either exactly or very nearly true notwithstanding any contrary hypotheses, until yet other phenomena make such propositions either more exact or liable to exceptions.
Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity-- to pose their own problems, to make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs-- you deny them mathematics itself.
The evolutionary explanation for origins, although impossible either to prove or to test scientifically, is nevertheless defended by its proponents on the basis that it is the only explanation which is naturalistic, not involving the 'supernatural' element of a divine Creator.
Archimedes to Eratosthenes greeting. ... certain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards because their investigation by the said method did not furnish an actual demonstration. But it is of course easier, when we have previously acquired by the method, some knowledge of the questions, to supply the proof than it is to find it without any previous knowledge.
Design can never be an ultimate explanation for anything. It can only be a proximate explanation. A plane or a car is explained by a designer but that's because the designer himself, the engineer, is explained by natural selection.
The simplicity of nature is not to be measured by that of our conceptions. Infinitely varied in its effects, nature is simple only in its causes, and its economy consists in producing a great number of phenomena, often very complicated, by means of a small number of general laws.
To develop an empiricist account of science is to depict it as involving a search for truth only about the empirical world, aboutwhat is actual and observable.... It must involve throughout a resolute rejection of the demand for an explanation of the regularities in the observable course of nature, by means of truths concerning a reality beyond what is actual and observable, as a demand which plays no role in the scientific enterprise.
Although I was four years at the University [of Wisconsin], I did not take the regular course of studies, but instead picked out what I thought would be most useful to me, particularly chemistry, which opened a new world, mathematics and physics, a little Greek and Latin, botany and and geology. I was far from satisfied with what I had learned, and should have stayed longer.
A highly developed moral nature joined to an undeveloped intellectual nature, an undeveloped artistic nature, and a very limited religious nature, is of necessity repulsive. It represents a bit of human nature a good bit, of course, but a bit only in disproportionate, unnatural and revolting prominence.
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