## Validity and Soundness

1

The following is an argument which I thought was sound but I have been told I am wrong.

1. Some men are married

Therefore

1. Some men are not married

I think this argument is sound because the premise is true, the conclusion follows on from the premise and therefore is valid.

I have been told the argument is invalid but I cannot see why.

5

Let's look at the translations (into first-order logic):

(1) ∃x : Man(x) ∧ Married(x).

(2) ∃x : Man(x) ∧ ¬Married(x).

The first is true in universes where there is at least one married man; the second is true in universes where there is at least one bachelor. To show that the argument from (1) to (2) is not valid, consider the counterexample: a universe with only one object, a married man. This is a counterexample because there is no bachelor in such a world. That shows the invalidity.

Now let me say a word about why I think you were thinking that this argument is sound or at least valid. Logically:

"there are φs" == "there is at least one x s.t. φ(x)"

e.g. "there are married men" == "there is at least one x s.t. x is a married man".

But colloquially, "some" is often used in a stronger sense to mean only some, so for example: