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If you use a trick in logic, whom can you be tricking other than yourself?
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p. 24e

 

Ludwig Wittgenstein

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What magical trick makes us intelligent? The trick is that there is no trick. The power of intelligence stems from our vast diversity, not from any single, perfect principle.

 

Marvin Minsky

 

Not knowing what one is looking for is pure agony. Too much analytical thinking, too much logic, too many meanings! Life has no logic, so why does there have to be logic to explain what it means? Also, what is logic? I think I may need to break away from analytical thinking; this is the cause of all my anxieties.

 

Gao Xingjian

 

So much of modern mathematical work is obviously on the border-line of logic, so much of modern logic is symbolic and formal, that the very close relationship of logic and mathematics has become obvious to every instructed student. The proof of their identity is, of course, a matter of detail: starting with premisses which would be universally admitted to belong to logic, and arriving by deduction at results which as obviously belong to mathematics, we find that there is no point at which a sharp line can be drawn, with logic to the left and mathematics to the right. If there are still those who do not admit the identity of logic and mathematics, we may challenge them to indicate at what point, in the successive definitions and deductions of Principia Mathematica, they consider that logic ends and mathematics begins. It will then be obvious that any answer must be quite arbitrary.

 

Bertrand Russell

 

The whole thing never happened and I can prove it — now. But Ira De Kalb made me wait a billion years to write the story.
So we start with a paradox. But the strangest thing of all is that there are no real paradoxes involved, not one. This is a record of logic. Not human logic, of course, not the logic of this time or this space.

 

Henry Kuttner

 

There is a logic of language and a logic of mathematics. The former is supple and lifelike, it follows our experience. The latter is abstract and rigid, more ideal. The latter is perfectly necessary, perfectly reliable: the former is only sometimes reliable and hardly ever systematic. But the logic of mathematics achieves necessity at the expense of living truth, it is less real than the other, although more certain. It achieves certainty by a flight from the concrete into abstraction. Doubtless, to an idealist, this would seem to be a more perfect reality. I am not an idealist. The logic of the poet — that is, the logic of language or the experience itself — develops the way a living organism grows: it spreads out towards what it loves, and is heliotropic, like a plant.

 

Thomas Merton