I suppose the whole entire point of me investigating Objectivism was to find a guide to living. I didn't start looking into it because it was a defense of capitalism or atheism or any such thing, but because at first it seemed like the only group of ideas actually meant for practical use in the real world. Even though I have been aware of it for about three years, I have only begun to understand it recently. In the last three years I have made many mistakes intellectually. For the most part, I never really bothered to deal with Objectivism by means of integrating it with the rest of my knowledge.
My general approach was for the most part 1) Find a conclusion 2) Argue for it until I find a conclusion with better arguments. This has caused a great amount of chaos mentally. At this moment I think that this is because I never understood Objectivism, and therefor was never able to argue for it. I have seen so many people make this mistake and it is very troubling. In the context of the internet, I have seen many people who start out as "Objectivists" who then turn into people who say things like "anything goes as long its is within the non-aggression principle", and then they turn into people who say "ethics is magic just like the state and god".
Fundamentally, the source of this is a particular kind of rationalism, which puts importance on argumentation, not knowledge. That knowledge only exists if it can be expressed well. Now while someone who claims to know something should be held to that standard, it is a reversal of cause and effect to say "I think Objectivism is true, I need to start looking for arguments for it". This can't be done, one needs to first spend the time to actually learn an idea and convince one self of it before they can start worrying about how they should be expressing themselves. They want to express themselves first, and be validated by the fact that no one has any retort, then be comforted by the fact that they have knowledge.
This leads to intellectual decay, as one stops thinking about the world, and keeps himself busy with the nuances of debate. An approach to learning based on argument leads exclusively to the upholding of deductive logic over inductive logic. This is extremely problematic because deductive logic isn't sufficient for all cognitive tasks (neither is inductive logic).
An argument based on induction requires a massive dedication of time and energy. This is illustrated by the fact that a good rationalist argument is about a thousand pages of covering one's ass. No one even bothers to prove an idea in fullness with inductive logic. Ayn Rand didn't, and even Peikoff, who organized and elaborated on her views didn't attempt to organize all the information required to validate her views. This isn't a bad thing either, people can only think for themselves, and do not need to be provided with ever aspect of an argument in order to see if it is true or not.
Rand's epistemology is based primarily on induction based on perception, with deduction playing important roles in certain contexts. What follows from this is a view of consciousness that has all aspects of it explained by how someone chooses to think. Do they context drop? Do they reverse hierarchy? Are they emotionalist? These sorts of questions can explain ultimately every aspect of someone's consciousness, including what they value.
Ayn Rand looks at the function of value in nature (what value does for people). The discover that not only do values exist because people are alive, that people are alive because they have values. This allows her to identify values as something cognitive. They are not primarily emotional (subjective, preferences). This allows us to trace all values back to methods of thinking. Values follow the same rules as concepts, because they are concepts, implicit or explicit, conscious or not. They aren't "preferences" that magically appear from no where, or that are left to be explained by Freud or Skinner. They are concepts that are developed by how one thinks. This means they can be analyzed logically.
This conclusion is only possible based on inductive logic. Nihilists are stuck with a given "preferences" with they are completely unable to explain, and have to say "they are just there, maybe it has something to do with how you were raised".
To sum up my points:
1) Many people believe in knowledge through argument.
2) These people in the end rely to heavily on deductive logic, floating abstractions, and arbitrary "givens".
3) This leads them to become incapable of understanding Objectivists ideas unless they put a huge amount of effort into them (like I have).
4) Many people who start with Objectivism, but do not integrate it, treat it as a floating abstraction, usually end up becoming anarchists, and then nihilists (As I have in the past).
As a side note: The idea that one needs to be able to completely prove (I might mean explain here) an idea to hold it as knowledge is bullshit anyways. For instance, there are many concepts and rule in mathematics that I know, use, and manipulate, that I could not prove. The same is with Objectivism. I don't know everything about it, and if put to the task, I could not prove every point of it, but when I apply its ideas, it works. Maybe I am wrong on this, but if you can apply the idea consistently, over time, and get results, it is knowledge.