My position is:
Logic is always the best problem-solving tool. To put it clearer:
1. If a question has an answer, answering the question logically will be more likely to get the right answer than answering it any other way.
2. If you have to make a decision, making the decision logically will work better than making it any other way. By "work better", I mean whatever it is you want from that decision, you'll be more likely to get it by using logic.
When some people hear "logic", they think of a sci-fi robot saying "I compute probability of success at 93.5014%!". But logic also includes wearing a jacket because it's cold out, or not playing loud music because your flatmate's trying to study, or believing trolls probably don't live in your closet.
Logic is basically just believing something if there's a good reason to believe it, and not believing something if there's a good reason not to believe it. Lots of very smart people have found ways to put this into mathematical language and define what "good reason" and "belief" and so on mean, but that's the basic principle. So to rephrase the box above:
1. If you want to know whether or not something's true, you should look at the evidence for and against it.
2. If you want to make a decision, you should look at the evidence, use the evidence to find which way is better, and then do whichever way is probably better.
I'd spend several paragraphs supporting this, but I don't think anyone really disagrees. If you do, say why you disagree below and I'll see if I agree with your objection. But I'm kind of at a loss for this whole first discussion because it's hard for me to imagine someone seriously thinking logic sometimes doesn't work. I guess I'll finish by thinking up a few situations where people might think logic doesn't work, and responding to them.
Objection 1: Logic can't tell me what art to like, what music to like, what girl to date, etc! No, it can't. Neither can anything else. "What art should Yvain like?" is, in my opinion, a meaningless question. Yvain can like any art he damn well pleases, and there's no "should" about it. But logic can have a bearing on these sorts of questions by helping make things clear. For example, if you're allergic to cigarette smoke, logic can tell you that you'll probably be less happy dating a girl who smokes than a girl who doesn't, all else being equal.
Objection 2: Logic is too hard to use for everyday life. I don't want to have to write a three page proof about why I eat toast instead of donuts this morning. Okay, fine. In that case, logic should be able to tell you that using logic too often will make you unhappy, and in that case, from the point of view of someone who wants to be happy, using logic too often would be illogical.
Objection 3: People aren't logical. No, they're not. It's too bad, isn't it? If they were, they'd probably be better off. I'm not asking you to treat other people as logical, just suggesting you'd be better off if you were more logical yourself. You can then do the logical thing and deal with people exactly as they are.
Objection 4: It's impossible for a human to ever be 100% logical. Yes, it is. It's also impossible for a football player to get a goal on 100% of kicks. That doesn't mean football players shouldn't try to get better at football, and it doesn't mean people shouldn't try to get better at logic.
Objection 5: Sometimes you have to just take things on authority Absolutely, and this is logical. I don't understand fluid dynamics, and if an airplane engineer tells me the most important equation for fluid dynamics is pr=tn^2, I'll believe him. Not because I have no evidence, but because my evidence is that a guy who thinks this is true can make airplanes fly, and get a degree in airplane engineering from a prestigious university, et cetera. If, later on, I become an airplane engineer myself and run experiments that show the equation is different, I'll have more evidence that the guy is wrong than I do that he's right, and I'll change my opinion. None of this, however, suggests that I should believe the authority of a random person on the street who says "Planes fly because of gremlins!"
Please post your thoughts, opinions, objections, and clarifications! I want everyone in Shireroth agreeing on this issue by
(Yvain checks his watch) the end of time.