2

I have no idea why (2) is an invalid argument.

(1)

If A, then B

Not B

Therefore not A

(2)

If A, then B

Not A

Therefore not B

2

I have no idea why (2) is an invalid argument.

(1)

If A, then B

Not B

Therefore not A

(2)

If A, then B

Not A

Therefore not B

3

Let's try with some examples.

- If Alex is walking in the forest, Alex wears shoes.
- If Alex is walking on the street, Alex wears shoes.
- Alex is not walking in the forest.

if (2) were valid, then it would follow that Alex is not wearing shoes. But clearly we haven't shown that Alex is not wearing shoes, because there are other conditions under which he wears shoes.

(1), however, can remain valid, if

- If Alex is walking in the forest, Alex wears shoes.
- If Alex is walking on the street, Alex wears shoes.
- Alex is not wearing shoes.

In this case, we can infer both that Alex is not walking in the forest and that Alex is not walking on the street.

Now let's make it a bit more formal. **Valid** in logic means that if the premises happened to be true, then the conclusion must also be true.

By the counter example above, we have shown that the pattern you refer to as (2) can have a false conclusion with true premises. This pattern is the fallacy called "denying the antecedent."

1

See the truth tabel for the conditional: as you can see "if A, then B" is T(rue) in both lines F-T and F-F. Thus, if A is F(alse), i.e. Not A is T, we have no guarantee that B is also F.

– Mauro ALLEGRANZA – 2017-10-19T08:02:09.7001>