Sets of three do seem to crop up quite frequently in Objectivism, for instance:
- Three metaphysical axioms (existence, identity, consciousness).
- Three evaluative branches of philosophy (ethics, politics, æsthetics).
- Three epistemological stages for grasping concepts (implicit, identification, conceptualising).
- Three elements of reason (percepts, concepts, logic).
- Three classic laws of logic (identity, non-contradiction, excluded middle).
- Three steps toward validation (possible, probable, certain).
- Three ethical questions building the Objectivist code of values (What is the ultimate value? What is the primary virtue? Who should benefit?).
- Three basic values (reason, purpose, self-esteem).
- Three governmental functions (police, military, courts).
- Three core æsthetic principles (selection, clarity, integration).
Threes also occur when setting Objectivism itself apart from other, usually two, erroneous philosophical paths, described throughout Peikoff’s The DIM Hypothesis.
As Objectivism is hierarchical (as postulated in the previous post, cascading down through three branches; metaphysics, epistemology, axiology), a pattern of nested triangulations seems to present itself.
Of course I may be over rationalising, and a quick search of OPRA shows that other numbers do occur, yet not as significantly as the reoccurring sets of threes.
Last month's ‘spiralling trichotomy’, although attractive as an image, is too ridged and too linear: it lacks nested three-way branching. I've been playing around with all sorts of shapes, seeking to convey this more fittingly (from Sierpiński tetrahedra to Apollonian gaskets), trying out apt physical structures on which to incorporate an outline of Objectivism in a more fruitful, integrated way than the stricture of a linear book.
More things shaping-up for next month…