# Categorical syllogism question

I have trouble understanding this syllogism.

Given:

``````Some P are not G
No O are P
``````

My conclusion is : Some O are not G

In this online exercise I did my answer was incorrect and that website does not explain why it is wrong or what the correct answer is.

Consider an interpretation with domain the set of natural numbers N starting from 1.

Let :

Px = "x is Odd", Gx = "x is greater than 1", and Ox = "x is Even".

Some Odd is less-or-equal than 1 (Some P are not G).

No Even is Odd (No O are P).

Therefore : Some Even is less-or-equal than 1. <= wrong !

See Fallacy of exclusive premises : no categorical syllogism is valid when both of its premises are negative.

There are two negative premises, so the reasoning is invalid regardless of the intended conclusion. These two premises have no valid solution.

• What about this question. See this please. tinypic.com/r/35d9kj5/9. Why would second wenn drawing even be an option. Nowhere it says that scooters are trucks – Jerry K Oct 11 '16 at 23:32
• Jerry K: I think you're right. I think the second diagram says something like 'Some scooters are trucks', but nothing in the premises actually states that. – Mark Andrews Oct 13 '16 at 3:40
• Thanks Mark. It confuses me because as I learn how to solve these I often read "do not assume anything" and take into consideration only what you see in premises – Jerry K Oct 13 '16 at 4:05

Just adding a Venn diagram as a more intuitive counterexample. The only information given about O is that none are P, so "Every O is a G" is a possibility. As Mauro already pointed out, a categorical syllogism is not possible. • I assume that the new syllogism would be: Some P are not G, No O are P, thus All O are G. This new example would have two problems. First, a valid syllogism cannot have two negative premises. Second, a valid syllogism cannot have a negative premise and an affirmative conclusion. – Mark Andrews Oct 13 '16 at 3:48