gardenfors-triviality-revision-counterfactuals
IN premise — summaries/2026/08/24/wiki-Belief_revision.md
Created 2026-08-24T17:11:07+00:00
Gärdenfors' triviality theorem proves that no non-trivial belief revision operator can simultaneously satisfy all AGM postulates and the Ramsey test (a > b ∈ K iff b ∈ K * a) when counterfactual conditionals are part of the object language.
Summary
If a system needs to handle "what would happen if X" kind of hypotheticals while also updating its beliefs rationally when new facts arrive, it hits a hard wall: satisfying both requirements at the same time forces the revision process into a degenerate state where it stops being useful. In practice, this means any agent or reasoning module that works with counterfactual conditionals must consciously choose which side of that trade-off to sacrifice, rather than assuming both can be had for free.