whozum said:
Okay, that is actually how I see it, I've only taken a semester of logic so I'm not indepth as to the actual names of each instance. Is there a more proper/better way to looka t it?
Heh, I was taking forever to figure out how to correct something, so I just deleted it. I'll put it back:
I guess you could look at it that way. For example,
If the moon is made of green cheese, then pigs can fly;
The moon is made of green cheese;
Therefore, pigs can fly.
To check for validity, you ignore the meaning of the premises and only look at the relationships between them; So you ask:
If the premises were true, what would that imply about the conclusion? You'll recognize this as an instance of Modus Ponens, so it's valid. But to check for soundness, you need to look at the meaning of the premises and determine whether or not they actually are true; So you ask: Is it true that if the moon is made of green cheese, then pigs can fly? Is it true that the moon is made of green cheese? The moon isn't made of green cheese, so this argument is unsound (but still valid).
What I was trying to correct is that when checking validity you don't actually ignore the "meaning" completely, and you aren't really only looking at the relationships between premises and conclusion. An argument can be valid for three reasons:
1) its premises are inconsistent (cannot all be true together),
2) its premises logically imply its conclusion, or
3) its conclusion is a tautology (always true).
(2) is where you can just look at relationships. (1) and (3) are special cases of (2). An inconsistent set of premises logically implies any conclusion, and a tautology is logically implied by any set of premises (including the empty set of premises). In (1) and (3), the relationships don't matter. So you really need to consider all 3 cases. I don't know if that makes sense to you- I couldn't find a better way to explain it. But that is a proper way of looking at it. As an example, let P denote "Pigs can fly" and H denote "'Hurkyl' is a girl's name". Consider the arguments:
1) P, ~P therefore H.
2) (P -> H), P therefore H
3) H therefore (P v ~P)
\begin{array}{|c|c|c|c|c|}\hline P&\neg P&H&P \rightarrow H&P \vee \neg P \\ \hline T&F&T&T&T\\ \hline T&F&F&F&T\\ \hline F&T&T&T&T\\ \hline F&T&F&T&T\\ \hline \end{array}
Find the rows where all premises are true. If the conclusion is true in
every row where all premises are true, then the argument is valid.
1) There are no rows where both P and ~P are true (i.e. the premises are inconsistent), so this argument is valid.
2) The premises are both true in the first row. The conclusion is also true in the first row, so this argument is valid.
3) The premise is true in the first and third rows. The conclusion is also true in the first and third rows (it's a tautology- true in every row!), so this argument is valid.
Notice that in (1) and (3), it's not the relationship between premises and conclusion that determine the argument's validity; It's the meaning of the premises and conclusions themselves.
Now to test for soundness, you just ask if the argument is valid and all premises are true in the real world.
1) Valid, but "Pigs can fly" is false, so this argument is unsound. An argument with inconsistent premises is always valid and (it's pretty safe to say) unsound. It doesn't tell you anything about the relationship between premises and conclusion.
2) Valid, but "Pigs can fly" is false, so this argument is unsound.
3) Valid, and "'Hurkyl' is a girl's name" is true, so this argument is sound. Notice that if "'Hurkyl' is a girl's name" were false, the argument would still be valid but would be unsound. An argument with a tautological conclusion is always valid, and its soundess depends solely on the truth of the premises; It doesn't tell you anything about the relationship between premises and conclusion.
So arguments of type (2) are the only interesting or persuasive ones, as far as truth about the real world goes.
Maybe this is more than you care to know; I just didn't want to leave you with the wrong information.
