Either is choosing: the combined scope of two recognitions. Where Together takes the shared refinement — what is recognized under both — Either takes the full range: what is recognized under one, the other, or both.
Either arises in Movement I: Logical Origination alongside Together as the dual way of combining distinctions. Once distinctions exist, they can be combined in two directions: inward (what do they share?) and outward (what do they cover?). Coherence demands both. Together gives the inward answer; Either gives the outward answer. Every pair of recognitions has both a greatest common refinement and a least common extension, and the interplay between these two gives the logical core its structure.
Choosing through Either is commutative (choosing between A and B is the same as choosing between B and A), associative, and idempotent (choosing between a recognition and itself produces itself). Either and Together interact through the distribution laws that any coherent field of recognitions must satisfy.
The presence of both Together and Either — both ways of combining — is what makes conditional relating (Implies) and denial (Negate) possible. Without Either, the logical core would lack the expressive range to formalize what it means for one recognition to conditionally relate to another.
Mathematical correspondence
Either corresponds to the join (least upper bound) operation in a lattice — set-theoretic union. Together is the greatest lower bound and Either is the least upper bound.
Related
- Together — the dual: shared refinement rather than combined scope
- Distinguish — produces the recognitions that Either combines
- Implies — conditional relating, whose construction depends on Either