Harles Peirces fundamental distinctions based on the number 3

Peirce presents several fundamental distinctions based on the number three; three components in the definition of belief, three levels of clearness of apprehension, three modes of being, and three things in any sign. Compare and contrast these four distinctions with one another and analyze their relationships to one another, if any. Do these four distinctions in any way correspond to or reflect each other? Or are they entirely independent of one another? Explain.

The preferred primary source is the book, Philosophical Writings of Peirce, by Justus Buchler.