Reason vs. Faith
Sometimes the best way to understand a concept is to contrast it with others. There are some aspects of reason that fit this description. Specifically, it's useful to contrast it with the concept of faith.
Objectivists have a very clear and specific concept of faith. Faith is accepting an idea as true without reason, or against reason. The first half of this is accepting an idea in spite of the fact that there is no justified reason to believe it. Obviously someone can try to rationalize anything, so we're not talking about just giving an excuse for a belief. We're talking about actual evidence that leads to that particular belief. Let's take some examples.
A few years ago, the Heaven's Gate cult decided that a group of aliens were hiding behind a comet, coming to free them from the turmoils of life on earth. All they needed to do to hitch a ride was to prove that they were sincere in their belief. Ritual suicide was the method. This is a wonderful example of faith. The first question, when someone suggests that you kill yourself to go to heaven, should be "What evidence do you have for such a theory?". Faith was required. Sure, the leader probably had told them about hearing voices in his head or whatever else, but these aren't really reasons. He couldn't provide any evidence. They only had his word, and that had to be weighed against all kinds of other possible explanations.
And that's the important part. Reason allows us to analyze the data and form the best possible conclusion from it. When someone takes any random piece of data and latches on to it, ignoring everything else, that also counts as faith. They're not forming their conclusions based on the evidence available. They're basing it on what they want to believe.
Obviously religions are a good example of faith, since many actually preach the virtue of faith. If you say you can't understand why God would let innocent people die, or children get abused, or anything else, they say you're not supposed to understand. You're supposed to just believe. Just take it on faith. Believe without reason, without evidence, and without understanding.
The other half of faith is believing in something despite contrary evidence for it. One old common belief was that central planning was an effective method of producing wealth. As the evidence piled up against it, people continued to believe. They want to believe, and they just refused to acknowledge the evidence. Country after country collapsed into famine and horrible poverty, and the belief went on. The Soviet Union had to collapse before people started having doubts, and there are plenty of hard-core believers still around. This is faith.
Contrast this with reason. Reason requires evidence to form a conclusion. It doesn't ignore or evade known facts. It is a process by which you try to formulate a conclusion based on all of the facts. It absolutely never accepts anything without reason for it.
Now this understanding of reason and faith are polar opposites. How about a middle ground between the two? What if you have some supporting evidence for a theory, but there are enough unknowns to make you seriously doubt if the conclusion is correct? The first point to make here is that this is acknowledging that you don't have enough evidence is a product of reason. Forming conclusions is not just weighing the known factors. We all learn in life that you can also evaluate the quality of the information, and how complete it is. In other words, there are reasons to not believe the evidence, and those reasons are based on your understanding of how thorough the information needs to be.
Let's take an example. You find out a woman was murdered in New York City last night. You find out someone you've never liked was also in NYC last night. Conclusion: he killed her! Well, you probably don't believe that's enough information to make that judgment. The first reason is that millions of other people could fit that description, so the evidence is equally supportive of concluding someone else did it. You'd also have no evidence of motive, which would explain why the murder happened. You may need better information on whether the person had the opportunity as well.
The point is that although you may have some weak data to suggest a conclusion, you know that there are a lot more factors that need to be understood before you can really be sure of it. So these reasons against the conclusion are based on your knowledge of what it requires to make a valid conclusion in this context. A more straightforward reason to reject it would be if the guy had an alibi. But there are all kinds of indirect reasons. What if he was known to be a moral person who you trusted? It may not directly contradict the conclusion, but you'd want a stronger case.
Now again, what if the evidence is weak? Well, if the conclusion is the best you can come up with, but still lacks sufficient backing, it would be wrong to accept the conclusion wholeheartedly. In other words, reason would say that you can tentatively accept the conclusion, for lack of a better one, but you should treat this "knowledge" as tentative. If you accept it as strongly as you accept any other piece of knowledge, it would be unjustified.
So even in this case, faith and reason are never combined. If you accept the weak conclusion as if it were absolutely true beyond any doubt, you'd be acting on faith, not reason. Your belief wouldn't be justified by reason. If you accept it tentatively, you're not accepting it on faith, but reason. And only to the extent that reason supports it.
Reason and faith are completely incompatible. Faith is the destroyer of reason. It takes particular ideas and divorces them from reality and from reason. If you accept something on faith, you are essentially saying that you will take it off of the table with regards to reason, and treat it how you feel like treating it. Wherever faith goes, reason is pushed out.
But it's worse than that. If you accept an idea on faith, it can conflict with the ideas you've accepted with reason. To make sense of it all, and to integrate the different ideas, you have to reconcile those beliefs. That means either throwing out the ideas based on faith and sticking to reason, or more likely throwing out reason and sticking with the faith.
Imagine you are analyzing an idea with reason and it conflicts with your faith. If you ignore the contradiction and accept it anyway, you'll be undermining your reasoning process. Reason requires a logical exploration of the data, weeding out any contradictions it finds. If you allow the contradiction anyway, you'll have to suspend your reasoning ability. And that means you'll be accepting the new idea, not on reason as it very well might be justified by, but on faith. Faith grows, and reason gives ground.
If, on the other hand you don't ignore the contradiction, but accept it as valid, you'll use your reasoning method on incorrect facts. Simple case is Creationism. If you accept that the universe was created a few thousand years ago, as the bible says, then you have to start interpreting actual facts in this light. When you see the dinosaur bones, you'll have to imagine that god put them in the earth to trick everyone (he is mysterious, isn't he?).
So if faith and reason conflict, one must give way to the other. One must grow at the expense of the other. They are in mortal combat for your soul.
Now what if they don't exactly conflict? What if you believe random things like the center of Jupiter is made of chocolate pudding? Does that cause reason to retreat? Well, if ever the two came into conflict, they would. It does have two direct side effects.
First, anything taken on faith is treated by your mind as a buffer zone against reason. If you were to analyze it with reason, the ideas would die a quick death. So to maintain them, you have to avoid using reason with them. This creates a sort of minefield in your head, where you have to twist and turn your reasoning skills to avoid all of the sensitive spots. That's doesn't work well in regards to efficiency.
Second, every idea taken on faith cannot be integrated with the rest of your knowledge. To simply maintain all of the random ideas you can fill your head with, you'd have to devote a lot of mental energy. And then you have the problem that those ideas may conflict with one another. The end result is that your mind is cluttered with useless garbage, and you have to compare every new idea with the thousand arbitrary ideas you've accepted on faith.
Hopefully this gives you some insight into why faith is bad, and consequently the advantages of reason.