File 03 — Beliefs
The Chain of Argument
Seven links you're each 90% sure of add up to a coin flip.
Sagan's seventh tool: every link in a chain of argument must hold — not just most of them. Set how many steps your argument has and how sure you are of each, and watch the arithmetic almost nobody feels coming: independent confidences multiply, so seven strong 90% links carry a 48% conclusion. Tap a link you're only half-sure of and the whole chain drops to it. The honest catch is built in — multiplying assumes the links are independent, so the tool reports a range, from the full product up to the single weakest link, and leaves the judgment of where the truth sits to you. Grounded in Sagan's baloney detection kit and the Tversky–Kahneman conjunction fallacy.
What it feels like
90%
as sure as a typical link
What the conclusion carries
48% – 90%
independent … to weakest-link
0.90 ^ 7 = 0.48
Every link feels 90% solid, so the conclusion feels almost as sure. It isn't. Independent confidences multiply, and 7 of them compound down to 48%. Tap a link you're actually less sure of and watch the floor fall out. The honest range runs from 48% (independent links) up to 90% (links that are really one claim).