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Suppose that the conclusion of a particular argument is ‘Grass is green and it is not the case that grass is green.’ Without knowing anything more about this argument – in particular, without knowing what its premises are – is it possible to tell whether it is valid or invalid? Explain your answer.

marked as duplicate by Jo Wehler, Bumble, James Kingsbery, virmaior Nov 10 '15 at 0:08

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  • The fact that there are two almost identical questions posted within a short time of each other makes me think that this is homework... – DTR Nov 9 '15 at 17:38
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First of all, I'm going to assume that you're working within classical propositional logic. Therefore, we can symbolize the expression 'Grass is green and it is not the case that grass is green' as:

(G & ~G).

Now, note that the formula (G & ~G) is unsatisfiable (i.e. it cannot be made true). To convince yourself of this, just draw the truth table for (G & ~G).

So, how does this relate to the answer to your question? Well, the standard definition of a valid argument is an argument in which there is no way to make all the premises true while making the conclusion false.

It seems that the conclusion of this argument is always going to be false. So, in order to check whether the argument is valid, we have to check whether or not there is a way to make the premises all true. If there is a way to make all the premises true, then the argument will be invalid because then the premises will be all true while the conclusion is false. If there is not such a way to do this, then the argument is valid.

Overall, it looks like you would need more information to decide whether or not the argument is valid. In particular, we would need to know whether or not we can satisfy all the premises of the argument at once. No, we cannot tell whether or not the argument is valid without knowing the premises.

  • oh... cos I thought the G & ~G in the real world is necessary true ..... – Cici Xiang Nov 10 '15 at 22:37
  • You're thinking of G v ~G. – Jay Nov 11 '15 at 3:44

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