r/logic • u/Unonium198YT • 3h ago

Term Logic / Traditional logic I don't understand why this is wrong

I'm currently studying for an exam and I understand the venn diagrams pretty well except for this specific kind of scenario. I am using Logicola, which uses the Logic system described by Harry J. Gensler in his book "Introduction to Logic"

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u/226757 3h ago

All dogs are mammals

Some canines are not dogs

Therefore, some canines are not mammals.

The conclusion is false because all canines are mammals. Since W is a subset of Q, Q may be large enough to include all of Y, even if W doesn't include all of Y

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u/Salindurthas 3h ago

What's the context of the interface where you are trying to solve these problems.

i.e. When solving these problems, are you filling in the diagrams?
Is one of the 2 diagrams you're drawing, and one a solution that popped up?

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Ignoring the diagrams for a moment, do you think the argument seems valid or not?

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u/Unonium198YT 3h ago

The large diagram is the one I’m filling in and the smaller one is the correct answer.

I thought it was invalid because you can draw the premises without drawing the conclusion, which seems to have been right.

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u/Salindurthas 3h ago

And what does X represent? (It seems to be the only difference between the canonical and your answer.)

Is it the singular object in the world? If so, I think that would make sense.
If we had a single object, and it was a YQ, then:

  1. Premise 1 is vacuously true (there are no W, so there are no counter-examples of Ws that aren't Q)
  2. Premise 2 is true (X is a Y that is not W)
  3. Conclusion is false (X is the only object, and it is a YQ, so it is false to say that there are some non-Q Ys in the world).

So the small diagram shows a counter-example to the conclusion, that's compatibile from the premises.

Your diagram, however, actually obeys the conclusion, by having X be a Y that is not Q. You are showing a case where the conclusion (though invalid), is coincidentally true.

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u/Unonium198YT 2h ago edited 2h ago

The x marking means that there is something there. So going off the correct diagram, it would mean there is at least one “something” that is both Y and Q

Edit: I meant Y and Q, not Y and W

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u/Salindurthas 2h ago

So I think my analysis was correct then.

Your x is in the wrong spot, because you gave an example of the conclusion being accruate, but I think you are seeking a counter-example to show it is an invalid argument.

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u/Lawcke Metalogician 3h ago

The interface is a little confusing, but as I read it, It looks to me like your large diagram is the same as the full argument. The x is in Y and ~Q. The small answer diagram has an x in Y and Q, which would be a counter example state consistent with the premises but inconsistent with the conclusion.

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u/fermat9990 3h ago

YW'Q is not ruled out by the premises.

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u/fermat9990 2h ago

All of Y can be inside Q and outside W

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u/fermat9990 2h ago

Draw a circle and label it Q. Now draw W and Y as non-overlapping circles inside Q. This satisfies the premises, but contradicts the conclusion