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

Re: Oh, shut up, Data

[mikailborg.livejournal.com]

Well, with further thought, I was beginning to wonder if I missed something, because "p implies q" can't be true for all values of p and q. If (p implies q) is true for selected values of p and q, p need not necessarily be true for q to be. Conversely, even if p and q are true, it does not always follow that p implies q - there may be no causal connection. "I have 10 fingers" and "I like pizza" are both true, but neither implies the other.

Maybe the professor accidentally skipped over a paragraph or two of lecture notes today.

Re: Oh, shut up, Data

[zerblinitzky.livejournal.com]

It's really quite simple. I was amazed at how many people thought that it wasn't simple and were confused for days after Shockley explained it.
Here's how simple it is:

If p then q.

That's it. That's the whole thing. If p is true, then q has to be true. If p is false, then all bets are off and q could go either way.

Don't try to rationalize it by using words. Words have no place in logic. It's just a function.

You were right, it isn't always true. Here's a truth table:


See, it's true whenever p isn't, and it's true whenever both p and q are true. It's false, however, when p is true but q isn't, because that means that clearly p doesn't imply q (if p can be true without q).

Re: Oh, shut up, Data

[robertliguori.livejournal.com]

[b]
If p is false, then all bets are off and q could go either way.
[/b]

That's the thing. If this were trying to accurately model the universe, than p->q would only have a truth value for 1,0, because it requires extra random evaluations to discover if p->q is true in the verbal sense, instead of q depending on, perchance, r.

Re: Oh, shut up, Data

[zerblinitzky.livejournal.com]

If this were trying to accurately model the universe

Allow me to paraphrase Shockley, from when I took the course:
"The most dangerous assumption you can make is that logic has any bearing on actual events. A proof is only as useful or as true as the propositions that go into it."

This isn't trying to accurately model the universe, not in the way that you're thinking. Forget the "verbal sense", the verbal sense is ambiguous and imprecise, which is why this notation was made in the first place.