A field guide to the ways reasoning breaks
Broken structure
Also called Inverse error
From if A then B, and A is false, wrongly concluding B is false. A may not be the only route to B.
If she trained she would win; she did not train, so she will not win.
Ask whether the conclusion has any other possible cause.
The invalid mirror of affirming the consequent: the second premise negates the 'if' half of a conditional, and from that the 'then' half is denied. Also called inverse error. Alan Turing planted one deliberately in his 1950 paper on machine intelligence as an example of tempting but broken reasoning.
If the merger goes through, the stock will jump; the merger fell through, so the stock won't move — said the day before earnings.
If we advertise, sales will grow; we're not advertising this quarter, so sales can't grow.
If the code has a bug, the tests fail; the tests pass, so the code is fine — ignoring that the tests only cover half the paths.
If interest rates rise, the housing market cools; rates didn't rise, so the market must be heating up.