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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.

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3 Answers 3

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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.

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

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  • 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, 2016 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, 2016 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, 2016 at 4:05
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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

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  • 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, 2016 at 3:48
  • The diagram is NOT a VENN diagram. What you drew is an Euler diagram. Only Euler diagrams allow circles within other full circles. Why are people getting this distinction wrong? Some Euler diagrams will look like Venn diagrams but Venn diagrams usually have three overlapping circles. The third circle would represent the conclusion while the two would be the premises. Euler was a mathematician while John VENN was a philosopher. The diagrams are not identical nor do the represent the same information. Euler diagrams require you to KNOW which circles go into others. What if the topic is new?
    – Logikal
    Aug 28, 2020 at 22:32

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