identifying an argument

Question

If quotas are imposed on textile imports only if jobs are not lost, then the domestic textile industry will modernize only if the domestic textile industry is not destroyed. If quotas are imposed on textile imports, the domestic textile industry will modernize. The domestic textile industry will modernize only if jobs are not lost. Therefore, if quotas are imposed on textile imports, the domestic textile industry will not be destroyed.

- is it valid, invalid, strong, weak or not an argument

Answer 1

Strong and weak arguments involve probabilities. They are not strictly speaking "logical" or at least not in the traditional sense of the word. This question clearly implies some sort of syllogism is meant to be taking place so you can rule those out right from the beginning. I'm not sure exactly what your professor means by "not an argument" because strictly speaking invalid arguments are not really arguments, since they are invalid. But I think it is safe to assume that if "invalid argument" and "not an argument" are both possible options then, this is definitely an argument because it appears to have the structure of an argument. So it will either be invalid or valid. Therefore it is necessary for us to break down the argument into parts and see the conclusion (what follows "Therefore") must be true if the premises are true. If the answer is yes then the argument is valid. If not then it is invalid.

I'll start by taking the four statements involved and assigning them each a letter. This makes it easier to see the parts of the argument. I will then use symbolic logic to show what each statement is saying but then I'll put a translation of the symbols in case you are not familiar with them:

Q= "quotas are imposed on textile imports"

J = " jobs are lost"

M= "the domestic textile industry will modernize"

D = "the domestic textile industry is destroyed"

(~J ⊃ Q) ⊃ (~D ⊃ M) -- "If not J then Q THEN if not D then M"

Q ⊃ M -- "If Q then M"

~J ⊃ M -- "If not J then M"

∴ Q ⊃ ~D -- Therefore, If Q then not D

What you should do is try to see if there is a way to prove that Q ⊃ ~D from what is above. If there is you have a valid argument, if not then you have an invalid argument. Now the problem is that if the argument is invalid you don't really have a way to prove the negative (that is prove something isn't there), so at some point you just give up and conclude it is invalid. However, there is usually a reason why and I'll show you it here.

You'll notice that ~D is in the apodosis (that is the "then" part of an if-then statement). However, in the first premise "(~J ⊃ Q) ⊃ (~D ⊃ M)" you'll see that it is in a protasis (the "if" part of and if-then statement). The only way to get something in a protasis into and apodosis is to deny the prostasis's apodosis; This is called modus tollens. It would work like this:

(~D ⊃ M) -- "If not D, then M"

~M -- "Not M"

∴ D -- "therefore D" (the opposite of ~D "Not D")

But ~M ∴ D -- "Not M therefore D" is the same as ~M ⊃ D -- "If not M therefore D". So you have moved D from the protasis to the apodasis.

Therefore in order to get D into the apodasis at some point in the argument you would need to get to ~M, but there is no way to do that from what is given, and so you know the argument is invalid.