logic, arrangement, reason, justice, truth
理 centers on the underlying order that makes sense of things: the logic, reason, or principle behind an arrangement, and the justice or truth that follows from that order.
reason; grounds; pretext; excuse; motive
unreasonable; unnatural; unjustifiable
understanding; comprehension; appreciation
control; management (e.g. of a business)
cooking; cookery; cuisine; food; dish
processing; dealing with; treatment; disposition; disposal
state of mind; mentality; psychology
ideal; ideals
theory
sorting; arrangement; organization; putting in order; adjustment; regulation
repair; mending; fixing; servicing
laws of nature; physical laws
prime minister (as the head of a cabinet government); premier
representation; agency; proxy
director; trustee
reason; principle; logic
logic
physiology
cooking; food preparation
rationality
principle; theory; fundamental truth
ethics; morals
reasoning; inference; deduction
(Platonic) ideal (of how things ought to be, e.g. human rights); foundational principle; idea; conception (e.g. of the university); doctrine; ideology
理 combines 王 (jade) with 里, which likely contributes the sound. The original idea relates to the natural veins or patterns in jade, extended to mean the underlying principle or order of things.
The left side 王 (jade) and right side 里 (village) together suggest the orderly layout of a village, like the natural veins in jade. 理 is the logic and reason that arranges things justly.
For リ, imagine a ruler (理) using logic to measure the veins in jade: ruler -> リ, and the ruler brings order and reason.