Let us work without theorizing, 'Tis the only way to make life endurable.
A conception not reducible to the small change of daily experience is like a currency not exchangeable for articles of consumption; it is not a symbol, but a fraud.
Good tests kill flawed theories; we remain alive to guess again.
The Theory of Groups is a branch of mathematics in which one does something to something and then compares the result with the result obtained from doing the same thing to something else, or something else to the same thing.
The surface of the earth is soft and impressible by the feet of men; and so with the paths which the mind travels. How worn and dusty, then, must be the highways of the world, how deep the ruts of tradition and conformity! I did not wish to take a cabin passage, but rather to go before the mast and on the deck of the world, for there I could best see the moonlight amid the mountains.
I never guess. It is a shocking habit -- destructive to the logical faculty.
Power of generalizing gives men so much the superiority in mistake over the dumb animals.
Treat with utmost respect your power of forming opinions, for this power alone guards you against making assumptions that are contrary to nature and judgments that overthrow the rule of reason.
You must stick to your conviction, but be ready to abandon your assumptions.
It had never occurred to him that he should live in any other than what he would have called an ordinary way, with green glasses for hock, and excellent waiting at table. In warming himself at French social theories he had brought away no smell of scorching. We may handle even extreme opinions with impunity while our furniture, our dinner-giving, and preference for armorial bearings in our own ease, link us indissolubly with the established order.
When speculation has done its worst, two and two still make four.
The narrower the mind, the broader the statement.
Some theories are good for nothing except to be argued about.
Delight at having understood a very abstract and obscure system leads most people to believe in the truth of what it demonstrates.
A theory is the more impressive the greater is the simplicity of its premises, the more different are the kinds of things it relates and the more extended the range of its applicability.
Creating a new theory is not like destroying an old barn and erecting a skyscraper in its place. It is rather like climbing a mountain, gaining new and wider views, discovering unexpected connections between our starting points and its rich environment. But the point from which we started out still exists and can be seen, although it appears smaller and forms a tiny part of our broad view gained by the mastery of the obstacles on our adventurous way up.
It is theory that decides what can be observed.
Our minds have the need to know. When we dont know we make assumptions - they make us feel safer than not knowing. And we are pretty much always making assumptions.
Another great evil arising from this desire to be thought rich; or rather, from the desire not to be thought poor, is the destructive thing which has been honored by the name of speculation; but which ought to be called Gambling.
The dull mind, once arriving at an inference that flatters the desire, is rarely able to retain the impression that the notion from which the inference started was purely problematic.
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