9/2/2026
The fallacy, in English
"If it rained, the ground would be wet. The ground is wet. So it rained." This feels right — and is wrong. The ground could be wet for some other reason. This is one of the oldest and most persistent fallacies in ordinary reasoning: affirming the consequent.
The diagram
Universe = {a, b}
R (RainsOn) = {a} (it rains on a, but only on a)
W (Wet) = {a, b} (both are wet)
Try it
Formula (g) says `RainsOn(a)→Wet(a)` — select it and click *True?*: it's true, since *a* is rained-on and is wet. Formula (c), `Wet(a)`, is also true. It's tempting to conclude `RainsOn(a)` from those two — exactly the affirming-the-consequent move. What is under consideration here is the inference:
RainsOn(a)→Wet(a), Wet(a) ∴ RainsOn(a)
Both the premises are true and the conclusion is true, and that tempts us into thinking that the inference is valid. It is not. The inference is fallacious.
Look at formula (h), `RainsOn(b)→Wet(b)`: also true (since Wet(b) is true regardless of RainsOn(b)) — and formula (d), `Wet(b)`, is also true. But `RainsOn(b)` is *false*. Select `RainsOn(b)` and click Deny — Deny is the *correct* move here, and the game will confirm it by walking straight to the atomic formula and showing you it's false. Then try **Endorse** on `RainsOn(b)` instead, just to watch the game correctly call that a loss — the fallacy, made concrete. Now we have shown that
RainsOn(b)→Wet(b), Wet(b) ∴ RainsOn(b)
has both premises true and a conclusion which is false. That means that the inference is invalid. Believing that inferences of that type to be valid is a fallacy, the fallacy of affirming the consequent.