...it is rare that mathematicians are intuitive, and that men of intuition are mathematicians, because mathematicians wish to treat matters of intuition mathematically, and make themselves ridiculous, wishing to begin with definitions and then with axioms, which is not the way to proceed in this kind of reasoning. Not that the mind does not do so, but it does it tacitly, naturally, and without technical rules; for the expression of it is beyond all men, and only a few can feel it. .
There are then two kinds of intellect: the one able to penetrate acutely and deeply into the conclusions of given premises, and this is the precise intellect; the other able to comprehend a great number of premises without confusing them, and this is the mathematical intellect. The one has force and exactness, the other comprehension. Now the one quality can exist without the other; the intellect can be strong and narrow, and can also be comprehensive and weak. .
Those who are accustomed to judge by feeling do not understand the process of reasoning, for they would understand at first sight, and are not used to seek for principles. And others, on the contrary, who are accustomed to reason from principles, do not at all understand matters of feeling, seeking principles, and being unable to see at a glance. .
The understanding and the feelings are moulded by intercourse; the understanding and feelings are corrupted by intercourse. Thus good or bad society improves or corrupts them. It is, then, all-important to know how to choose in order to improve and not to corrupt them; and we cannot make this choice, if they be not already improved and not corrupted. Thus a circle is formed, and those are fortunate who escape it. .
When we wish to correct with advantage, and to show another that he errs, we must notice from what side he views the matter, for on that side it is usually true, and admit that truth to him, but reveal to him the side on which it is false. He is satisfied with that, for he sees that he was not mistaken, and that he only failed to see all sides. .
...no one is offended at not seeing everything; but one does not like to be mistaken, and that perhaps arises from the fact that man naturally cannot see everything, and that naturally he cannot err in the side he looks at, since the perceptions of our senses are always true. .
When a natural discourse paints a passion or an effect, one feels within oneself the truth of what one reads, which was there before, although one did not know it. Hence one is inclined to love him who makes us feel it, for he has not shown us his own riches, but ours. ...such community of intellect that we have with him necessarily inclines the heart to love. .
It [eloquence] consists, then, in a correspondence which we seek to establish between the head and the heart of those to whom we speak on the one hand, and, on the other, between the thoughts and the expressions which we employ. ...We must put ourselves in the place of those who are to hear us, and make trial on our own heart... We ought to restrict ourselves, so far as possible, to the simple and natural, and not to magnify that which is little, or belittle that which is great. It is not enough that a thing be beautiful; it must be suitable to the subject, and there must be in it nothing of excess or defect. .
Since we cannot be universal and know all that is to be known of everything, we ought to know a little about everything. For it is far better to know something about everything than to know all about one thing. This universality is the best. If we can have both, still better; but if we must choose, we ought to choose the former. And the world feels this and does so; for the world is often a good judge. .
...when we wish to demonstrate a general theorem, we must give the rule as applied to a particular case; but if we wish to demonstrate a particular case, we must begin with the general rule. For we always find the thing obscure which we wish to prove, and that clear which we use for the proof; for, when a thing is put forward to be proved, we first fill ourselves with the imagination that it is therefore obscure, and on the contrary that what is to prove it, is clear, and so we understand it easily. .
Certain authors, speaking of their works, say, "My book," "My commentary," "My history," etc. They resemble middle-class people who have a house of their own, and always have "My house" on their tongue. They would do better to say, "Our book," "Our commentary," "Our history," etc., because there is in them usually more of other people's than their own. .
I might well have taken this discourse in an order like this: to show the vanity of all conditions of men, to show the vanity of ordinary lives, and then the vanity of philosophic lives, sceptics, stoics; but the order would not have been kept. I know a little what it is, and how few people understand it. No human science can keep it.did not keep it. Mathematics keep it, but they are useless on account of their depth. .
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