Oog.

[logomancer]

Just came back from Discrete Math. Brown was in rare form today, as he explained to us the mechanics of conditional statements. My biggest beef with the class is this: It claims to be a class to teach reasoning skills, but the concepts he presents sometimes are not logical. For example, we learned about the conditional statement, "p implies q". p is what we called a hypothesis and q is a conclusion. However, Brown tells us that if p is false and q is true, then the conditional statement is true. Which puts me off because if one's hypothesis is false, how can one derive a conclusion that is true? And even if that's the case, how does that prove that the conditional statement is true? It's confusing.

The rest of the class was somewhat easier to follow. Nothing compared to Chemistry, where Prof. Amateis played with liquid nitrogen today, freezing a banana and breaking it (although it didn't shatter -- it wasn't cold enough). She also splashed some LN₂ on the floor, which freaked out the first row ("Oh, and by the way, class, be sure to wear closed-toe shoes in your labs.") Very cool.

Anyway, I need folders, dinner, and Spiel.

Comments

Oh, shut up, Data

[mikailborg.livejournal.com]

I probably have this wrong, but imagine this:

p = "Ed is a horse" and q = "Ed has four legs". (p implies q) works out to: "Ed is a horse" implies "Ed has four legs". So far, so good.

Now, what if Ed is a dog? p is false, yet q is true. However, the conditional statement is still true, because it is not claiming he is a horse. It's just claiming that if he were, he'd have four legs.

Another example: p = "All science-fiction fans go to Virginia Tech" and q = "Virginia Tech is crowded". p isn't true, and q is (by the accounts I've heard), yet the statement only claims that Tech would be crowded is all science-fiction fans were there, and is therefore true.

How it works

[matthiasrat.livejournal.com]

The statement (if p then q) is always true if p ends up being false, regardless of what q is. Why?

Notice that the statementes begins IF p...

So, everything that follows in the statement depends on p being true. If q is false and p true, then the statement is quite obviously false, because when p is true, q has to be true.

But, what happens when p is false? Then q does not matter. So the statement (if p then q) itself is still logically true, as the if condition was never actually triggered (because p is false).

Why is the statement true though? Because it is NOT false. When p is false, then the truth of q is irrelevant and can do nothing to contradict the conditional. Thus, the statement is NOT false. Thus, it must be true.

I hope that was clear.

[yubbie.livejournal.com]

Because sometimes q is only true *because* p is false.

[slitherrr.livejournal.com]

here's another thing. assume p -> q. like those guys up there said a million times, if p is true, then the entire statement p -> q is true. q is not necessarily true, and is not necessarily false. it's just that p -> q as a statement is still valid, because it has not been proven to be false.

for example: assuming the statement "'Ed is a dog" implies "Ed has four legs'" is true:
if Ed is, indeed, a dog, then he has four legs
if Ed is not a dog, then he may or may not have four legs, but since you haven't proven the implication false, it is still true, since you have not proven that there exists an Ed that is a dog but does not have four legs.

my main point is, you're saying "if one's hypothesis is false, how can one derive a conclusion that is true?", and you're way off base. your hypothesis, that Ed is a dog, isn't saying that your conclusion, that Ed has four legs, is correct if Ed isn't a dog. it's just saying that, as a statement, "Ed is a dog implies Ed has four legs" is still valid, and makes no comment whatsoever on whether or not Ed the non-dog, indeed, has four legs.