Affirming the Consequent

You must have heard similar arguments.

1. If the lamp is broken, then the room will be dark.
2. The House is dark.
   So:
3. The lamp must be broken.

Or another:

1. Binge drinking leads to liver cirrhosis.
2. He has liver cirrhosis.
   So:
3. He must be a binge drinker.

Affirming the consequent is a logical fallacy that starts from a true statement and jumps to the conclusion that the converse form would be true by ignoring alternative explanations. In other words, the truth of the premises can not guarantee the truth of the conclusion. Take the first example: there may be other reasons why the room is dark. It can be a power failure or someone just switched off the light.

‘the lamp is broken’ and ‘binge drinking’ are the antecedents of the arguments. The consequent in the first example is ‘the room will be dark’, and for the second example, it is ‘ liver cirrhosis.’

Smoke without fire

Then there is this proverb, “There’s no smoke without fire”. Like so many other proverbs, this one is also a fallacy.

If fire, then smoke
smoke
So:
fire

Well, there could be a smoke machine, or someone mistook fog as smoke!

Reference

Affirming the consequent: Wiki