Aristotle Quotes

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

If you have ever studied geometry, you remember that by a course of reasoning Euclid proves that all the angles in a triangle are equal to two right angles. Euclid has shown you how to work it out. Now, if you undertake to disprove that proposition, and to show that it is erroneous, would you prove it to be false by calling Euclid a liar?

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.

Mathematics is, as it were, a sensuous logic, and relates to philosophy as do the arts, music, and plastic art to poetry.

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.

For the things of this world cannot be made known without a knowledge of mathematics.

… mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

And therefore in geometry (which is the only science that it hath pleased God hitherto to bestow on mankind), men begin at settling the significations of their words; which settling of significations, they call definitions, and place them in the beginning of their reckoning.

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

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

There are no sects in geometry.

Geometry will draw the soul toward truth and create the spirit of philosophy.

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.

One geometry cannot be more true than another; it can only be more convenient.

Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry.

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

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.

317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is so, because mathematical reality is built that way.

Man is a rational animal—so at least I have been told. … Aristotle, so far as I know, was the first man to proclaim explicitly that man is a rational animal. His reason for this view was … that some people can do sums. … It is in virtue of the intellect that man is a rational animal. The intellect is shown in various ways, but most emphatically by mastery of arithmetic. The Greek system of numerals was very bad, so that the multiplication table was quite difficult, and complicated calculations could only be made by very clever people.

"She can't do Subtraction." said the White Queen. "Can you do Division? Divide a loaf by a knife-what's the answer to that?" "I suppose-" Alice was beginning, but the Red Queen answered for her. "Bread-and-butter, of course."

Why do you keep maintaining your ideas are right if you can't prove them?

Euclid Alone Has Looked on Beauty Bare.

In mathematics there are no true controversies.

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.