Quotes About Proof

The ultimate court of appeal is observation and experiment... not authority.

The ultimate proof of confidence for a small-business owner is, are they hiring employees?

I cannot understand how something as ubiquitous as war can simply be dismissed as pathological. It is not clear to me that it is an unspeakable evil. If it is, I need proof of it.

Wisdom is not finally tested by the schools, Wisdom cannot be pass'd from one having it to another not having it, Wisdom is of the soul, is not susceptible of proof, is its own proof.

What can be asserted without evidence can be dismissed without evidence.

Take nothing on its looks; take everything on evidence. There's no better rule.

Freedom always carries a burden of proof, always throws us back on ourselves.

We must never assume that which is incapable of proof.

Demonstration is also something necessary, because a demonstration cannot go otherwise than it does, ... And the cause of this lies with the primary premises/principles.

Upon the solution of this problem, or upon sufficient proof of the impossibility of synthetical knowledge a priori, depends the existence or downfall of metaphysics.

If you cannot attain salvation in this life, what proof is there that you can attain it in the life or lives to come?

I have plenty of proof of the love of God if I like to contemplate it, if I like to sit down and think about it and weigh things up. But how many of you have ever done that in the hour of trial, and found your escape that way?

Absence of evidence is not evidence of absence," he told me reproachfully.

What Gentzen had done was prove the obvious by assuming the doubtful.

In 1936, Gerhard Gentzen provided a proof of the consistency of arithmetic, but to do it he needed to use a controversial technique known as transfinite induction. This technique is not among the usual methods of proof, and it hardly seemed appropriate for guaranteeing the consistency of arithmetic. What Gentzen had done was prove the obvious by assuming the doubtful.

The proof of Euclidean geometry's consistency eluded mathematicians. By the end of the nineteenth century, the best that was achieved was a proof that Euclidean geometry was consistent as long as arithmetic was consistent.

in 1900, David Hilbert listed what he considered to be the twenty-three most important unsolved problems of mathematics. The second item on his list was a request for a proof of the consistency of arithmetic. Such a proof would ensure the consistency of a great deal of higher mathematics. What this proof had to guarantee was, in essence, that one could never prove one equals two. Few mathematicians regarded this as a matter of much import.

What Gentzen had done was prove the obvious by assuming the doubtful. 7A

But what happened, it was almost as if I were a theologian proving that there was no God. Not just fearing it, but knowing it for a fact. [...] It's a feeling I can't convey to you. It was something that I believed deeply, implicitly, and it's not true, and I'm the one who demonstrated it.

By the end of the nineteenth century, the best that was achieved was a proof that Euclidean geometry was consistent as long as arithmetic was consistent.

A proof that mathematics is inconsistent, and that all its wondrous beauty was just an illusion, would, it seemed to me, be one of the worst things you could ever learn.

There's nothing I hate more than someone who speaks in the draft room with absolute conviction, but they have nothing to back it up.

I see myself as a spiritual person, but I don't think anyone should claim proof of a god. No one can prove it. That's why I don't claim to know whether there are one, many or no gods.

There are over 2,000 direct clones of the Groupon business model. However, there's an equal amount of proof that the barriers to success are enormous. In spite of all those competitors, only a handful are remotely relevant.