>[!abstract] >While $(A = B \land B = C) \implies (A = C)$ is true in a formal sense, $(A \approx B \land B \approx C) \implies (A \approx C)$ is not. The cumulative approximations may nearly cancel each other out, or they may compound — there is no way to tell just from those statements. >[!quote] >While following logical threads to their conclusions is a useful exercise, each logical step often involves some degree of rounding or unknown-unknowns. A -> B and B -> C means A -> C in a formal sense, but A -almostcertainly-> B and B -almostcertainly-> C does not mean A -almostcertainly-> C. Rationalists, by tending to overly formalist approaches, tend to lose the thread of the messiness of the real world and follow these lossy implications as though they are lossless. (rachofsunshine, 2025). ## References - rachofsunshine. (2025, February 01). In *Hacker News*. https://news.ycombinator.com/item?id=42902575