1

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.

2

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.

2

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
2

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.

Counterexample

  • 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

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