I believe that two and two are four and that four and four are eight.
A tautology's truth is certain, a proposition's possible, a contradiction's impossible.
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.
A mathematical equation stands forever.
You can't criticize geometry. It's never wrong.
It is possible--indeed possible even according to the old conception of logic--to give in advance a description of all 'true' logical propositions. Hence there can never be surprises in logic.
And for mathematical science, he that doubts their certainty hath need of a dose of hellebore.
Even in the valley of the shadow of death, two and two do not make six.
You can't argue with physics, mate.
The method of not erring is sought by all the world. The logicians profess to guide it, the geometricians alone attain it, and apart from science, and the imitations of it, there are no true demonstrations.
One cannot really argue with a mathematical theorem.
As Bertrand Russell once wrote, two plus two is four even in the interior of the sun.
Irrefragability, thy name is mathematics.
Almost all thinking people agree that you should not have probability 1 (or 0) for any event, other than one demonstrable by logic, like 2 x 2 = 4.
