A taxonomy for the Daydreamer agent

The Shape of a Paradox

A paradox is not one thing. Each kind is built from a different mix of ingredients — self-reference, opposition, infinity, vagueness, aggregation — and how easily a single larger idea dissolves it. Plot those on shared axes and every family takes on a recognizable shape. These are also the ingredients a machine can be taught to detect.

How to read one

Six axes, each running from the center (absent) to the rim (definitive). A family's profile is the area it fills — compact shapes are the tractable paradoxes; far-flung spikes are the deep ones.

↺Self-reference — does it loop back on itself? (Liar, time loops)
¬Opposition — a thing asserted with its own antonym (the contradiction seed)
∞Infinity — an unbounded or limit process drives it
∿Vagueness — a fuzzy predicate slid along a continuum
ΣAggregation — rational parts summing to an irrational whole
◈Resolvability — one larger frame dissolves it. High = a surprising truth; low = the framework must change.

The families, grouped by what they turn out to be

Quine's truth-status is the color and the grouping. Read down each band and watch the shapes hold a family resemblance — then compare bands to see the profile shift.

The shapes sort with the color. The veridical band — probability, aggregation, physical — is compact and reaches far on resolvability: one correct calculation or theory absorbs it. These are surprising truths, not broken arguments.

The antinomy band spikes on self-reference and opposition while sitting low on resolvability. No larger frame contains it, so the framework itself must move. That low-resolvability, high-self-reference corner is where a paradox stops being a puzzle and becomes a crisis.