“…Peirce constructs his entire systems architectonic (including his vast semeiotic) upon his three categories, admittedly "conceptions so very broad and consequently indefinite that they are hard to seize and may be easily overlooked" [CP 6.32]. In his view science is essentially trichotomic: 'First science' in science of discovery, mathematics, has three divisions (finite collections, infinite collections, true continua); 'second science', cenoscopic philosophy 4 , involves three sciences (trichotomic phenomenology, the three normative sciences of theoretical esthetics, practics, and logic as semeiotic, and lastly a scientific metaphysics); 'third science' includes all the physical and psychical special sciences, themselves arranged trichotomically (as descriptive, classificatory or nomonological) All the above trichotomies represent tricategorial relations and not mere triadic groupings. Retrospectively, a trichotomic structure can be seen at the very beginning of science in the mathematics of logic as a kind of mathematical valency theory in consideration of "the simplest mathematics" viewed in light of Peirce reduction thesis 5 .…”