Charles Sanders Peirce Quotes

Mathematics is purely hypothetical: it produces nothing but conditional propositions.

Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then suchand such another proposition is true of that thing.... Thus 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.

Mathematics has the completely false reputation of yielding infallible conclusions. Its infallibility is nothing but identity. Two times two is not four, but it is just two times two, and that is what we call four for short. But four is nothing new at all. And thus it goes on and on in its conclusions, except that in the higher formulas the identity fades out of sight.

Mathematics is entirely free in its development, and its concepts are only linked by the necessity of being consistent, and are co-ordinated with concepts introduced previously by means of precise definitions.

You can go through your whole life telling yourself that life is logical, life is prosaic, life is sane. Above all sane. And I think it is. I've had a lot of time to think about that. And what I keep coming back to is [her] dying declaration: 'So you understand that when we increase the number of variables, the axioms themselves never change.'

As an exercise of the reasoning faculties, pure mathematics is an admirable exercise, because it consists of reasoning alone and does not encumber the student with any exercise of judgment.

It is the merest truism, evident at once to unsophisticated observation, that mathematics is a human invention.

Only Numbers. Pure math. You have to accustom yourself to thinking that way.

In the pure mathematics we contemplate absolute truths which existed in the divine mind before the morning stars sang together, and which will continue to exist there when the last of their radiant host shall have fallen from heaven.

Mathematics is a more powerful instrument of knowledge than any other that has been bequeathed to us by human agency.

Mathematical Reasoning is not only exact; it has its own criteria of reality.

One of the high points of my life was when I suddenly realized that this dream I had in my late adolescence of combining pure mathematics, very pure mathematics with very hard things which had been long a nuisance to scientists and to engineers, that this combination was possible and I put together this new geometry of nature, the fractal geometry of nature.

Algebra is the intellectual instrument which has been created for rendering clear the quantitative aspects of the world.

We are not very pleased when we are forced to accept a mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context.

Mathematics is a language plus reasoning. It's like a language plus logic. Mathematics is a tool for reasoning.

Geometry is one and eternal shining in the mind of God. That share in it accorded to men is one of the reasons that Man is the image of God.

Science must not impose any philosophy, any more than the telephone must tell us what to say.

Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.

The subtleties of mathematics defecate the grossness of our apprehension, and supply the elements of a sounder and severer logic.

Nature does not count nor do integers occur in nature. Man made them all, integers and all the rest, Kronecker to the contrary notwithstanding.

Mathematics is not only real, but it is the only reality.

To my mathematical brain, the numbers alone make thinking about aliens perfectly rational.

Science itself is a humanist in the sense that it doesn't discriminate between human beings, but it is also morally neutral. It is no better or worse than the ethos with and for which it is used.

Mathematics is the only good metaphysics.

We need to have real science, and real science doesn't happen under the hand of lobbyists with a conflict of interest. So get the revolving door done and over with and get the big money out of politics.