Wednesday, September 12, 2007

Logical Validity

On Monday, you had a quiz where you were asked to add the premise needed to make this argument valid:

P1. The parents didn't want their twins separated.
P2. ________________________________
Therefore, separating the twins would be wrong.

It's important to note that you have seen this kind of argument before.
First, from the Rachels chapter on logic there was this example:

1. Jimmy Carter is from Georgia.
2. All people from Georgia are famous.
Therefore, Jimmy Carter is famous.

Suppose the question were what premise is needed to make this argument valid:
1. Jimmy Carter is from Georgia.
Therefore, Jimmy Carter is famous.

Something like premise (2) above is what you'd need to add. Another that would work is "If someone is from Georgia, then that person is famous."

You've also seen another example from the sample argument worksheet and this argument form from the logic handout:

Universal Generalization

P1. A is P.

P2. All things P are also Q. (Or, if something is P, then it is also Q).

C. Therefore, A is Q.


The Jimmy Carter argument is of that form:
A = "Jimmy Carter", p = "is from Georgia", q= "is famous".
It asserts a connection between p and q, between being from Georgia and being famous. The premise claims that if someone is from Georgia, then that person is famous.

The argument from the quiz is of that form too; it assumes a connection between "p" -- parents wanting something (an action) to be done -- and "q" -- that action's not being wrong. It asserts:

P1. The parents didn't want their twins separated.
P2.
If the parents want something to be done, then it is wrong to not do it. or
All things that parents want to be done are wrong not to do.
________________________________
Therefore, separating the twins would be wrong.

Here's another version of the argument that uses "kept together" instead of "separated":

P3. The parents want their children kept together.
P4. If parents want something done to their children, then it is morally obligatory that it be done. (Or, all things that parents want done to their children are morally obligatory to do).
Therefore, it is morally obligatory that their children be kept together.