A Quote by Nassau William Senior
But that the reasoning from these facts, the drawing from them correct conclusions, is a matter of great difficulty, may be inferred from the imperfect state in which the Science is now found after it has been so long and so intensely studied.
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The very foundation of our science is only an inference; far the whole of it rests an the unprovable assumption that, all through the inferred lapse of time which the inferred performance of inferred geological processes involves, they have been going on in a manner consistent with the laws of nature as we know them now.
The one [the logician] studies the science of drawing conclusions, the other [the mathematician] the science which draws necessary conclusions.
Mathematical study and research are very suggestive of mountaineering. Whymper made several efforts before he climbed the Matterhorn in the 1860's and even then it cost the life of four of his party. Now, however, any tourist can be hauled up for a small cost, and perhaps does not appreciate the difficulty of the original ascent. So in mathematics, it may be found hard to realise the great initial difficulty of making a little step which now seems so natural and obvious, and it may not be surprising if such a step has been found and lost again.
... if you insist that the inference is made by a chain of reasoning, I desire you to produce that reasoning. The connection between the two is not intuitive. There is required a medium, which may enable the mind to draw such an inference, if indeed it be drawn by reasoning and argument. What that medium is, I must confess, passes my comprehension; and it is incumbent on those to produce it, who assert that it really exists, and is the origin of all our conclusions concerning matter of fact.
Though it is only in a very imperfect state of the world's arrangements that anyone can best serve the happiness of others by the absolute sacrifice of his own, yet, so long as the world is in that imperfect state, I fully acknowledge that the readiness to make such a sacrifice is the highest virtue which can be found in man.
It surely can be no offence to state, that the progress of science has led to new views, and that the consequences that can be deduced from the knowledge of a hundred facts may be very different from those deducible from five. It is also possible that the facts first known may be the exceptions to a rule and not the rule itself, and generalisations from these first-known facts, though useful at the time, may be highly mischievous, and impede the progress of the science if retained when it has made some advance.
This is the problem with the way you educate your children. You don't want your young ones drawing their own conclusions. You want them to come to the same conclusions that you came to. Thus you doom them to repeat the mistakes to which your own conclusions led you.
Every work of science great enough to be well remembered for a few generations affords some exemplification of the defective state of the art of reasoning of the time when it was written; and each chief step in science has been a lesson in logic.
You will be right, over the course of many transactions, if your hypotheses are correct, your facts are correct, and your reasoning is correct. True conservatism is only possible through knowledge and reason.
It is ... a sign of the times-though our brothers of physics and chemistry may smile to hear me say so-that biology is now a science in which theories can be devised: theories which lead to predictions and predictions which sometimes turn out to be correct. These facts confirm me in a belief I hold most passionately-that biology is the heir of all the sciences.
Philosophy, for Plato, is a kind of vision, the 'vision of truth'...Everyone who has done any kind of creative work has experienced, in a greater or less degree, the state of mind in which, after long labour, truth or beauty appears, or seems to appear, in a sudden glory - it may only be about some small matter, or it may be about the universe. I think that most of the best creative work, in art, in science, in literature, and in philosophy, has been a result of just such a moment.
Much of economics isn't difficult, or rather, the difficulty is in cooking up arguments to "prove" that commonsense conclusions are wrong. The fact is that many commonsense conclusions are quite correct, and it takes a lot of education to get you to believe different.
There is an inconvenience which attends all abstruse reasoning. that it may silence, without convincing an antagonist, and requires the same intense study to make us sensible of its force, that was at first requisite for its invention. When we leave our closet, and engage in the common affairs of life, its conclusions seem to vanish, like the phantoms of the night on the appearance of the morning; and 'tis difficult for us to retain even that conviction, which we had attain'd with difficulty.
In the final, the positive, state, the mind has given over the vain search after absolute notions, the origin and destination of the universe, and the causes of phenomena, and applies itself to the study of their laws - that is, their invariable relations of succession and resemblance. Reasoning and observation, duly combined, are the means of this knowledge. What is now understood when we speak of an explanation of facts is simply the establishment of a connection between single phenomena and some general facts.
Nothing before had ever made me thoroughly realise, though I had read various scientific books, that science consists in grouping facts so that general laws or conclusions may be drawn from them.
Upon the whole, Chymistry is as yet but an opening science, closely connected with the usefull and ornamental arts, and worthy the attention of the liberal mind. And it must always become more and more so: for though it is only of late, that it has been looked upon in that light, the great progress already made in Chymical knowledge, gives us a pleasant prospect of rich additions to it. The Science is now studied on solid and rational grounds. While our knowledge is imperfect, it is apt to run into error: but Experiment is the thread that will lead us out of the labyrinth.
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