Among the minor, yet striking characteristics of mathematics, may be mentioned the fleshless and skeletal build of its propositions; the peculiar difficulty, complication, and stress of its reasonings; the perfect exactitude of its results; their broad universality; their practical infallibility.
Charles Sanders PeirceIt is a common observation that a science first begins to be exact when it is quantitatively treated. What are called the exact sciences are no others than the mathematical ones.
Charles Sanders PeirceThe one [the logician] studies the science of drawing conclusions, the other [the mathematician] the science which draws necessary conclusions.
Charles Sanders PeirceA sign, or representamen, is something which stands to somebody for something in some respect or capacity. It addresses somebody,that is, creates in the mind of that person an equivalent sign, or perhaps a more developed sign. That sign which it creates I call the interpretant of the first sign. The sign stands for something, its object. It stands for that object, not in all respects, but in reference to a sort of idea, which I have sometimes called the ground of the representamen.
Charles Sanders Peirce