Sound and Unsound arguments?

Question

I've been taking this Philosophy courses at my college and I got stuck at these homework. It asks to identify in the given paragraph which arguments is sound or unsound, and if it is unsound, I have to correct it to make it sound. Now, I know all the basic concept and definition. In order for an argument to be sound, it need to be valid first, and all the premises have to be true also. However, I come across a lot of premises that are not fact, meaning they are not verifiable. If that's the case, how do I know that it's a sound or unsound argument ? Here are some arguments that I come across:

1. If I had ADD, I'd have a prescription for this drug. But I don't have a prescription, so it's clear I don't have ADD.

A = I had ADD
B = I have a prescription

The symbolic form is:
If A then B
~B
---------------
~A

2. I haven't studied at all. If I don't study all night, I'll fail the test. But I can't fail the test, so I must study all night.
A = I don't study all night
B = I'll fail the test.

If A then B
~B
------------
~A

Both of them are valid arguments. However, I can't tell if they are sound or unsound, since all the premises are not facts, they're just some assumptions and all. How can I tell if they're sound or not ? And if they're unsound, what would I should add in to the premises to make the the argument become sound ? Thank you.

Answer 1

These are strange examples to give as an exercise!

Normally you'd take some common folk knowledge on which we all agree ("Socrates is mortal", "all dogs are mammals" and the like). Also, the second example includes some (logically) nasty terms ("can't", "must") that are usually treated as modal operators. But those requires a more advanced treatment, called modal logic. I guess that you're taking an introductory logic course and you're being taught classical propositional logic.

Comments

As for your first example: your logical translation is correct. My best guess is that this exercise is meant to take the second premise of the modus tollens (~B) as indicating something which you know is true (hence the "first person"-perspective) and only evaluate if the first premise (the conditional) is true. But this evaluation is really a context-dependent affair and you are not given enough informations to evaluate the factual truth of these conditionals. Still, without being provided any further restrictions, the conditional "If I had ADD, I'd have a prescription for this drug" is arguably false - I can certainly think of a real situation in which I have ADD, but I don't have a prescription for an ADD drug. So, the argument seems unsound.

As for your second example: your logical translation could be problematic. "I haven't studied at all" is not the same as "I [haven't] study all night", so the first premise is not the same as the antecedent of the conditional in the second premise.

The actual argument seems to me to include the inverse of the conditional: from the premise "If I don't study all night, I'll fail the test" it concludes that "If I do study all night, I'll pass the test".

That is:

If A then B
-----------
If ~A then ~B

The inverse of a conditional is the contrapositive of the converse. The converse of "If A then B" is "If B then A"; the contrapositive of "If B then A" is "If ~A then ~B". While the contrapositive does necessarily follow , the converse does not. So inferring the inverse from a conditional alone is an invalid argument. Thus the argument is unsound.¹

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¹ Or not, I don't really care.