  As with many of Peirce’s classificatory divisions, his classification of the sciences is a taxonomy whose tree is trinary. For example he classifies all the sciences into those of discovery, review, and practicality.  Sciences of discovery he divides into mathematics, philosophy, and what he calls “idioscopy” (by which he seems to mean the class of all the particular or special sciences like physics, psychology, and so forth).  Mathematics he divides into mathematics of logic, of discrete series, and of continua and pseudo-continua. Philosophy he divides into phenomenology, normative science, and metaphysics. Normative science he divides into aesthetics, ethics, and logic. And so on and on.  Very occasionally there is found a binary division: for example, he divides idioscopy into the physical sciences and the psychical (or human) sciences. But, hardly surprisingly given his penchant for triads, most of his divisions are into threes.