It Is... Easy To Be Certain. One

A 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.

Theoretically, I Grant You, There Is No Possibility Of Error In Necessary Reasoning. But To Speak Thus "theoretically," Is To Uselanguage In A Pickwickian Sense. In Practice, And In Fact, Mathematics Is Not Exempt From That Liability To Error That Affects Everything That Man Does.

Another Characteristic Of Mathematical Thought Is That It Can Have No Success Where It Cannot Generalize.

It Has Never Been In My Power To Study Anything, Mathematics, Ethics, Metaphysics, Gravitation, Thermodynamics, Optics, Chemistry, Comparative Anatomy, Astronomy, Psychology, Phonetics, Economics, The History Of Science, Whist, Men And Women, Wine, Metrology, Except As A Study Of Semeiotic .

Mathematics Is Purely Hypothetical: It Produces Nothing But Conditional Propositions.