David Berlinski Quotes

We cannot ... prove geometrical truths by arithmetic.

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.

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.

Validity is the touchstone of inference, and truth of judgment: the fact that vichyssoise is cold ratifies the judgment that vichyssoise is, indeed, cold, and the judgment that vichyssoise is cold expresses the fact that vichyssoise is cold.

It was easier to know it than to explain why I know it. If you were asked to prove that two and two made four, you might find some difficulty, and yet you are quite sure of the fact. ~ Sherlock Holmes

Mathematics is the only good metaphysics.

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

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

I believe only in the mathematics.

There is no such thing as absolute proof. There is only evidence.

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

Facts are not truths; they are not conclusions; they are not even premises, but in the nature and parts of premises.

The truth shall set you free. When you hear the truth, it sets you free. So mathematics is truth. It adds up. There's no error. Only time there's an error is when man miscalculates his own problems or his own equations.

The man who has learned that three plus one are four doesn't have to go through a proof of that assertion with coins, or dice, or chess pieces, or pencils. He knows it, and that's that. He cannot conceive a different sum. There are mathematicians who say that three plus one is a tautology for four, a different way of saying "four" ... If three plus one can be two, or fourteen, then reason is madness.

Arithmetic has a very great and elevating effect, compelling the soul to reason about abstract number, and rebelling against the introduction of visible or tngible objects into the argument.

Now this principle of induction cannot be a purely logical truth like a tautology or an analytic statement. . . .

All reasoning ends in an appeal to self-evidence.

Mathematics in general is fundamentally the science of self-evident things.

God forbid that Truth should be confined to Mathematical Demonstration!

Logic is the foundation of the certainty of all the knowledge we acquire.

We do not know a truth without knowing its cause.

Mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics.

There's math, and everything else is debatable!

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

A train of thought is never false. The falsehood lies deep in the necessities of existence.