Review-- This Stuff Is Important

Since we'll be using these terms and concepts for the remainder of the semester, I figured I'd collect all of the main points in one post. So, a review of yesterday's class:

Truth is a description we give to propositions-- not to arguments. We decide if a proposition is true by looking at the world and seeing if it matches the proposition.

Validity is a description we give to arguments as a whole. Or to be even more specific, we look to see if the argument follows a valid argument form-- a pattern we've already identified as valid. An argument is valid if, when the premises are accepted as true, the conclusion must also be true (regardless of whether the premises actually are true or false).

Soundness is a further description we give to arguments. An argument is sound when it is valid, and the premises are true. (Note: This, of course, guarantees that the conclusion is also true).

So, the usual procedure is that we check for validity by pretending the premises are true, then checking what that does for the conclusion. If we have a valid argument, we look for the actual truth of the premises, by examining the world. If that also checks out, we can say we have a sound argument. And that's the bestest kind of argument in the whole world. (As long as it's not a stupid argument, which I explained in class.)

The three most important valid argument forms are:

Syllogism
All A are B
x is A
x is B

Modus Ponens
If p, then q
p
q

Modus Tollens
If p, then q
~q
~p

One final point. We talked about how to read a conditional proposition-- an if-then statement. For a proposition of the form:

If p, then q

we say that p is a sufficient condition for q, and that q is a necessary condition for p. But like I said yesterday, this is not a causal relationship between the two parts, or a temporal relationship (that is, it's not about which one comes first), but a purely logical relationship. To wit:

If the match is struck, then the match will catch fire.

According to this sentence, striking the match is a sufficient condition for the match to catch fire. Why? Because when the match is struck, nothing else needs to be done. All the conditions for a fire have been met.

But note also that the match catching fire is a necessary condition for the match being struck. This might not sync up well with your immediate intuition, but it is true. Why? Because when the match is struck, there is no way the fire can be avoided. Or, put another way, without a fire we can automatically tell that the match was never struck. The logical conditions for the match being struck were not fulfilled.

Wrap your head around that, and you'll be all set.