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I have two fairly simple questions. I would just like someone to bounce this off as these questions involve validity and soundness. Funnily enough I feel more comfortable when this is done using Tarski's world and the analysis is more tangible if that makes sense. As soon as English is thrown into the equation my brain somehow hits a sieze.

So, the two questions are as a follows:

1) P: All nurses are friendly
2) P: All teachers are witty
3) P: Jacob is not a teacher and he is not a nurse
4) C: Jacob is unfriendly and not witty

My understanding of validity: An argument is valid iff it is impossible for there to be a situation in which all the premises are true and the conclusion false. So when I am testing for validity I assume my premises true and if I deduce a false conclusion my argument is not valid.

If I establish validity then I consider if my argument is sound in the real world. So I look to establish true for all my premises in the real world with a conclusion that follows as true. Obviously my argument can only be sound if it is valid.

If anything in my understanding of these arguments seem incorrect, I would appreciate feedback here.

So, back to my question: I assume all premises true in this regard and then ask myself if it is possible for Jacob to be unfriendly and not witty just because he is not a nurse and not a teacher.

Just because he is not a teacher and a nurse it does not seem valid to imply that he is not friendly of witty.

Thus, I deduce that the conclusion is false and consequently the argument invalid and therefore not sound.

Question 2:

1) P: All piano players are able to play "Rock around the Clock"
2) P: Rutendo is a piano player
3) C: Rutendo can play "Rock around the Clock"

Here I assume both premises true and deduce my conclusion to be true as it follows from my premises Rutendo would be able to play Rock around the Clock if he were in fact a piano player.

In the real world though, I cannot say that this is sound though as it isn't necessarily the case that all piano players can play "Rock around the clock". I for one am a piano player and I cannot play this. So ultimately my first premises would prove false and say even if Rutendo was a piano player the conclusion would resolve false as I do not believe this possible in the real world.

Thanks for taking the time to read through this. I just want to make sure I am on the right track here and understanding validity and soundness as it should be understood.

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Correct.   An argument is valid if its form ensures that the premises logically entail the conclusion.   An argument is sound if both its form is valid, and its premises are justified.

You have also correctly assessed the reason why the first argument is invalid, and why the second is valid but not sound.

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  • $\begingroup$ Thanks :) Appreciate the input. $\endgroup$ – Metamorphosis Nov 5 '15 at 9:04

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