First then, we find that when we regard ideas from a nominalistic, individualistic, sensualistic way, the simplest facts of mind become utterly meani… - Charles Sanders Peirce

Are you sure twice two are four? Not at all. A certain percentage of the human race are insane and subject to illusions. It may be you are one of them, and that your idea that twice two is four is a lunatic notion, and your seeming recollection that other people think so, the baseless fabric of a vision.

Few persons care to study logic, because everybody conceives himself to be proficient enough in the art of reasoning already. But I observe that this satisfaction is limited to one's own ratiocination and does not extend to that of other men. We come to the full possession of our power of drawing inferences the last of all our faculties, for it is not so much a natural gift as a long and difficult art.

The ordinary logic has a great deal to say about genera and species, or in our nineteeth century dialect, about classes. Now a class is a set of objects comprising all that stand to one another in a special relation of similarity. But where ordinary logic talks of classes the logic of relatives talks of systems. A system is a set of objects comprising all that stands to one another in a group of connected relations. Induction according to ordinary logic rises from the contemplation of a sample of a class to that of a whole class; but according to the logic of relatives it rises from the comtemplation of a fragment of a system to the envisagement of the complete system.