The Laws of Reasoning consist of the ground, the path, and the result. ...Suffering is in the mind. How we perceive happiness determines our suffering or not.
Mathematics may be compared to a mill of exquisite workmanship, which grinds your stuff to any degree of fineness.
Nothing has afforded me so convincing a proof of the unity of the Deity as these purely mental conceptions of numerical and mathematical science.
Tis evident that all reasonings concerning matter of fact are founded on the relation of cause and effect, and that we can never infer the existence of one object from another, unless they be connected together, either mediately or immediately... Here is a billiard ball lying on the table, and another ball moving toward it with rapidity. They strike; and the ball which was formerly at rest now acquires a motion. This is as perfect an instance of the relation of cause and effect as any which we know, either by sensation or reflection.
There are also two kinds of truths, those of reasoning and those of fact. Truths of reasoning are necessary and their opposite is impossible, and those of fact are contingent and their opposite is possible. When a truth is necessary its reason can be found by analysis, resolving it into more simple ideas and truths until we reach those which are primitive.
Were we incapable of empathy – of putting ourselves in the position of others and seeing that their suffering is like our own – then ethical reasoning would lead nowhere. If emotion without reason is blind, then reason without emotion is impotent.
The mathematician is entirely free, within the limits of the imagination, to construct what worlds he pleases.
All exact science is dominated by the idea of approximation.
The fact is there are few more popular subjects than mathematics. Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune.
The concept of number is the obvious distinction between the beast and man.
It is our nature to defy gravity, to transcend the limitations of the reasoning mind and connect with the realm of the mystical truth.
By no amount of reasoning can we altogether eliminate all contingency from our world. Moreover, pure speculation alone will not enable us to get a determinate picture of the existing world. We must eliminate some of the conflicting possibilities, and this can be brought about only by experiment and observation.
Our garden was debated territory between five local cats, and we'd heard that the best way to keep other cats out of the garden was to have one yourself. A moment's rational thought here will spot the slight flaw in this reasoning.
Man does not limit himself to seeing; he thinks and insists on learning the meaning of phenomena whose existence has been revealed to him by observation. So he reasons, compares facts, puts questions to them, and by the answers which he extracts, tests one by another. This sort of control, by means of reasoning and facts, is what constitutes experiment, properly speaking; and it is the only process that we have for teaching ourselves about the nature of things outside us.
... scientific research is compounded of ... empirical procedures, general speculative ideas, and mathematical or abstract reasoning.
Special qualities are required of the essayist. A poem or a novel may spring from the inner consciousness of an author. Reasoning poers must be brought to reinforce imagination.
If you think that moral reasoning is something we do to figure out the truth, you’ll be constantly frustrated by how foolish, biased, and illogical people become when they disagree with you.
The deep paradox uncovered by AI research: the only way to deal efficiently with very complex problems is to move away from pure logic.... Most of the time, reaching the right decision requires little reasoning.... Expert systems are, thus, not about reasoning: they are about knowing.... Reasoning takes time, so we try to do it as seldom as possible. Instead we store the results of our reasoning for later reference.
I now understand the need for faith - pure, blind, fly-in-the-face-of-reason faith - as a small life preserver in the wild and endless sea of a universe ruled by unfeeling laws and totally indifferent to the small, reasoning beings that inhabit it.
Of course all such conclusions about appropriate actions against the rich and powerful are based on a fundamental flaw: This is us, and that is them. This crucial principle, deeply embedded in Western culture, suffices to undermine even the most precise analogy and the most impeccable reasoning.
Pure logic is the ruin of the spirit.
Victor smiled through the pain and the blood. "Of course you have. I used to think Belikov was the savage one, but it's really you, isn't it? You're the animal with no control, no higher reasoning except to fight and kill.
To arrive at the simplest truth, as Newton knew and practiced, requires years of contemplation. Not activity Not reasoning. Not calculating. Not busy behaviour of any kind. Not reading. Not talking. Not making an effort. Not thinking. Simply bearing in mind what it is one needs to know.
I said that he was my superior in observation and deduction. If the art of the detective began and ended in reasoning from an armchair, my brother would be the greatest criminal agent that ever lived. But he has no ambition and no energy. He will not even go out of his way to verify his own solutions, and would rather be considered wrong than take the trouble to prove himself right.
For the flowers are great blessings. For the Lord made a Nosegay in the meadow with his disciples and preached upon the lily. For the flowers have great virtues for all senses. For the flower glorifies God and the root parries the adversary. For the flowers have their angels even the words of God's creation. For there is a language of flowers. For there is a sound reasoning upon all flowers. For flowers are peculiarly the poetry of Christ.
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