President Nixon in his inaugural address indicated that he wanted an era of negotiation. Our reasoning was that whatever our ideological differences, whatever our geopolitical differences, we were condemned to coexistence by nuclear weapons.
Ignorance lies at the bottom of all human knowledge, and the deeper we penetrate the nearer we arrive unto it. For what do we truly know, or what can we clearly affirm, of any one of those important things upon which all our reasonings must of necessity be built--time and space, life and death, matter and mind?
It is curious how tyrannical the habit of reading is...
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.
Perhaps the most surprising thing about mathematics is that it is so surprising.
The best defense against logic is ignorance.
The concept of number is the obvious distinction between the beast and man.
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 mathematician is entirely free, within the limits of the imagination, to construct what worlds he pleases.
What sets us against one another is not our aims - they all come to the same thing - but our methods, which are the fruit of our varied reasoning.
Do not expect to arrive at certainty in every subject which you pursue. There are a hundred things wherein we mortals. . . must be content with probability, where our best light and reasoning will reach no farther.
The culture and educational system of the contemporary West are based almost exclusively upon the training of the reasoning brain and, to a lesser degree, of the aesthetic emotions. Most of us have forgotten that we are not only brain and will, senses and feelings; we are also spirit. Modern man has for the most part lost touch with the truest and highest aspect of himself; and the result of this inward alienation can be seen all too plainly in his restlessness, his lack of identity and his loss of hope.
The required techniques of effective reasoning are pretty formal, but as long as programming is done by people that don't master them, the software crisis will remain with us and will be considered an incurable disease. And you know what incurable diseases do: they invite the quacks and charlatans in, who in this case take the form of Software Engineering gurus.
TEF is predicated on logic, a simple wager that every human faces: If a reasoning human being loves and values life, they will want to live as long as possible-the desire to be immortal. Nevertheless, it's impossible to know if they're going to be immortal once they die. To do nothing doesn't help the odds of attaining immortality-since it seems evident that everyone will die someday and possibly cease to exist. To try to do something scientifically constructive towards ensuring immortality beforehand is the most logical conclusion.
If plants could be credited with reasoning powers, we would marvel at the imaginative ways they bribe or ensnare other creatures to carry out their wishes.
Play stimulates the parts of the brain involved in both careful, logical reasoning and carefree, unbound exploration.
A human group transforms itself into a crowd when it suddenly responds to a suggestion rather than to reasoning, to an image rather than to an idea, to an affirmation rather than to proof, to the repetition of a phrase rather than to arguments, to prestige rather than to competence.
There are three basic approaches to AI: Case-based, rule-based, and connectionist reasoning.
Preaching is compelling to young secular adults ... - not if preachers use video clips from their favorite movies and dress informally and sound sophisticated, - but if the preachers understand their hearts and culture so well that listeners feel the force of the sermon's reasoning, even if in the end they don't agree with it.
Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation.
Let him cry whoever feels like crying, for we were animals before we became reasoning beings, and the shedding of a tear, whether of forgiveness or of pity or of sheer delight at beauty, will do him a lot of good.
If scientific reasoning were limited to the logical processes of arithmetic, we should not get very far in our understanding of the physical world
Our scientific world is our world of reasoning. It has its greatness and uses and attractions. We are ready to pay homage due to it. But when it claims to have discovered the real world for us and laughs at the worlds of all simple-minded men, then we must say it is like a general grown intoxicated with his power, usurping the throne of his king
God is intelligent; but in what manner? Man is intelligent by the act of reasoning, but the supreme intelligence lies under no necessity to reason. He requires neither premise nor consequences; nor even the simple form of a proposition. His knowledge is purely intuitive. He beholds equally what is and what will be. All truths are to Him as one idea, as all places are but one point, and all times one moment.
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