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

  1. Some men are married


  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.

1 Answer 1


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:

"sometimes I'm sad"

simply means that there are moments when the agent is sad, but it also seems to imply (in the literature they call this implicature) that there are times when she is not sad. To show that this is an implicature and not an implication, we can provide the following defeater:

"sometimes I'm sad; which makes sense, since I'm always sad."

It's kind of a silly example, but you get the idea. True implication cannot be defeated.


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