>As I stated in the post below, I just finished a logic class.

It had a very cool tool to help you learn how to apply logic. It works best when paired with Hurley’s Concise Introduction to Logic. (I have the 9th edition.)

I’ve added links where I think they’ll be useful, but all links were provided to the class by Mrs. Roth, the instructor!

Now, the example I used was S>~I S*I // G Let me give you the stuff to translate this out, since part of what tickled me pink about this class is that we spent a lot of time translating English– well known for the wiggle room available– into math, which is… not. ~ in front of a letter means that it is not so, that it is false. * means that both are true– it’s “and” v means “or”. At least one of the two is true. > is kind of like starting the phrase with “if” and putting “then between the two. If the first one is true, the second one also is; the first can be false and still have the second be true, but the second can’t be false with the first one true. = (it’s got three lines in the formal symbols, but eh) means “if and only if”– no matter what, if the first one is true, the second one has to be. If the second one is true, the first has to be. Ditto for false. // symbolizes that you are going from the argument to the conclusion. Whatever is after // is the answer that’s offered, and you have to figure out if it’s right or not. () or {} or [] are used to group the arguments.

When things get complex, you can’t just say A*D*R, or AvD*R. That’s too much wiggle.

~~ is a double negative– basically, it doesn’t effect anything except for symbolizing, but it’s got its own rule called “double negative”. You can add or remove these at any time without effect.

So, *S>~I S*I // G* would translate as *If S is true, then I is false. S and I are true. Thus, G.*

The letters stand for phrases in the argument– as Anon mentioned, the argument makes no sense, because G has nothing to do with S or I in the argument. (Is that you, Darth? The writing seems familiar somehow, but not like my guildmates.)

Although we didn’t cover this in class, I’d venture that it it’s an informal fallacy, such as missing the point or Red Herring. However, I’m trying to focus on, well, formal logic.

That means it’s either valid/sound or invalid/unsound. Truth really doesn’t come into it much.

It’s bloody obvious that you can’t have both S causing ~I and S*I both being true, someone has to be wrong. Now, the first rules we learned, among the rules of inference, were: Modus Ponens: if P>Q, and you know P is true, then you know Q is true. This makes sense, since it’s basically restating “If P, then Q.”

Modus Tollens: if you know P>Q, and you know that Q isn’t true, then you know that Q isn’t true, either. This is a bit harder– and the “MP or MT” messed me up a LOT– but it also makes sense, since if P “causes” Q, and Q didn’t happen, P must not have, either.

Hypothetical Syllogism: If P>Q, and Q>R, then Q>R. This one is practically the ideal of logic that I grew up with– “we know that if P is true, then Q is true. We know that if Q is true, then R is true. So *of course* we know that if P is true, then R is true!”

Disjunctive Syllogism: if QvP, and ~P, then Q. Also, pretty basic– if you have steak or fish, and it’s not fish, it’s steak.

Constructive Dilemma: Given (P>Q)*(R>S) and PvR then you can say QvS. I think this is related to the following rule of simplification: Simplification: If you know A*B, then you can simplify to A. If you use the rule you learn later, called Commutativity (where you can switch any arguments around a v or a *) you can make it B*A, and simplify it to B. It’s pretty easy to see why this works. “I know today is Tuesday, and I get ice-cream on Tuesday. I know today is Tuesday.” Now, I said above that I think this is related to CD, and that’s because if both P and R are true, and both Q and S result, then it would be almost like– not actually true, but almost like– P could result in Q and S, since if you know that P *or* R is the case, then Q *or* S is also true.

Conjunction: Knowing P, and knowing Q, you can say P*Q. It’s just the opposite of simplification– you know they’re both true, so you can join them up. Addition: this one is a weasel. If you know that P is true, then you could also say that PvQ, since v only means that at least *one* of them is true. If you’ve got the hang of logic, despite me, you’ve probably figured out that Addition is the way that you can end up with a result that isn’t even kind of related.

Now, back to the problem: S>~I S*I // G Well, we have to prove everything out, so we take S*I and simplify it down to S. (Save this, then go get the rest of the parts.) Then we go back to S*I again and switch it around with Commutativity, so that it’s I*S. Then we simplify I*S down to just I, same as we did with S*I.

Once we have I, we use the double negative rule– adding a ~~ without any real change being made to the equation– so that it says ~~I. Since we now can prove that ~I is false– that’s what ~~I translates as, remember– then we can take the disjunctive syllogism and prove that S is also false, so ~S. You then go back to S and use addition– that weasel I mentioned?– and say that SvG is true.

Since you’ve said that either S or G is true, and right there in the paragraph above you proved that S isn’t true, you know that G must be true. And that’s how you can end up with a *valid* logical formula that is just silly.

I don’t know why, but this just tickles me pink….