Septivium - 7 = 3 & 4
  1. Grammar
  2. Logic
  3. Rhetoric
  4. Mathematics
  5. Geometry
  6. Music
  7. Astronomy

This was the original list, but seeing what is coming up now, lets start with the master Logician himself, Peirce, and his Taxonomy of the disciplines to start. We can debate if he is or is not more fuzzy and pantheistic or rigorously logical.

in Wikipedia

  1. Mathematics
    1. Logic
    2. Discrete (Formal logic, Type Theory)
    3. Continuum (See Zalemea and others)
  2. Philosophy (Cenoscopy)
    1. Knowledge
      1. Phenomenology
      2. Normative Science
        1. Esthetics
        2. Ethics
        3. Logic
      3. Metaphysics
        1. Ontology
        2. Religion (Spiritual Community, Wholeness)
        3. Physical (Quantum Matter and Energy)
    2. Theory (I gather this is started in later papers and there might not be a lot of detail on it)
  3. Idoscopy, or the Special Sciences -- all experimental work is here, I think this should include inner (psychology, spiritual) as well as outer (instramental and direct observational methods). Arguably, they all involve observation, but in the former, the observation is private and shared second hand in language.
      1. Physical
        1. Nomological
        2. Classificatory
        3. Descriptive
      2. Psychical
        1. Nom. Psychics: Psychology
        2. Cl Psy: Ethnology
        3. Desc P: History

This is all preliminary to answering a bird app challenge

  1. Semiotics -- Not actuall in Peirce's list because it is prior to all of them. Signs and sign action (semiosis) is necessary for everything.
  2. Mathematics -- Most generally as type and category theory, and foundational for everything else. Note this is first in three forms in the taxonomy
  3. Monadology -- Identity in all forms and expressions
  4. Theory -- Philosophy and all grounding/binding processes
  5. Systems -- Complexity, emergence and Integrity -- Wholeness
  6. Arts
  7. Gratitude