Willard Van Orman Quine Quotes

You can't criticize geometry. It's never wrong.

I mean the word proof not in the sense of the lawyers, who set two half proofs equal to a whole one, but in the sense of a mathematician, where half proof = 0, and it is demanded for proof that every doubt becomes impossible.

I believe only in the mathematics.

Arithmetic is where the content lies, and not logic; but logic prompts certainty, and not arithmetic.

There aint no substitute for the truth, either it is or it isnt. You see the truth it needs no proof, either it is or it isnt. And you know the truth by the way you feel.

Proof is an idol before whom the pure mathematician tortures himself.

I am not a mathematician, but I was aware that for centuries, mathematics was considered the queen of the sciences because it claimed certainty. It was grounded on some fundamental certainties - axioms - that led to others.

No authority is higher than reality.

One cannot really argue with a mathematical theorem.

Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform.

And for mathematical science, he that doubts their certainty hath need of a dose of hellebore.

In practical life we are compelled to follow what is most probable ; in speculative thought we are compelled to follow truth. A man would perish of hunger and thirst, if he refused to eat or drink, till he had obtained positive proof that food and drink would be good for him. But in philosophic reflection this is not so. On the contrary, we must take care not to admit as true anything, which is only probable. For when one falsity has been let in, infinite others follow.

Mathematics is, I believe, the chief source of the belief in eternal and exact truth, as well as a sensible intelligible world.

I want to represent possibilities. I want to represent magic, right, that you're in a universe, and two plus two equals four.

The truth, it needs no proof. Either it is or it isn't.

I am obliged to interpolate some remarks on a very difficult subject: proof and its importance in mathematics. All physicists, and a good many quite respectable mathematicians, are contemptuous about proof. I have heard Professor Eddington, for example, maintain that proof, as pure mathematicians understand it, is really quite uninteresting and unimportant, and that no one who is really certain that he has found something good should waste his time looking for proof.

[I]f in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics, in so far as disposed through it we are able to reach certainty in other sciences and truth by the exclusion of error.

Numbers are the most certain things we have.

In mathematics there are no true controversies.

Truth is fine. Absolutely.

Truth is that which cannot be proved false.

We cannot ... prove geometrical truths by arithmetic.

As Bertrand Russell once wrote, two plus two is four even in the interior of the sun.

When speculation has done its worst, two and two still make four.

All you have to do is write one true sentence. Write the truest sentence that you know.