In evaluating religions, I can't automatically and time-efficiently know the full scope of the contradictions, there is so much material in religions. Similarly, how can I know that objectivism is fully valid and that it is free of contradiction without needing to know every word in all of Rand's books illustrating and introducing and defining objectivism as it is and is not?
(new) I mean, the axioms and basic metaphysics, epistemology...etc; how can I be certain there are no errors or cases or contexts in which it failed to make sense. It sounds good, the logic good, but how can I be certain?
If any of you can make a compressed synopsis of objectivism with logical structure intact, it might help me. I have watched YouTube videos that go over the basics and one that applies it to the question of God and faith, and it sounds good, and there were other videos that attacked its axioms of rational self-interest, and I do not really understand the validity or necessary wisdom of the laissez faire capitalism. How can I be sure it works in all contexts and situations?
Validation of Objectivism:
Objectivism is the name of the philosophy of Ayn Rand. Its tenets are all those that Rand herself set out. Thus, to “know that objectivism is fully valid and that it is free of contradiction,” you must indeed read and think about all of the things Ayn Rand said about her philosophy.
You ask for a shortcut that would allow you to know that every tenet of Rand’s philosophy is true without having to actually know every tenet—this is impossible. You cannot know a proposition is true if you do not even know what the proposition is.
Does that mean that every person who considers themselves an Objectivist does or should understand every tenet of Objectivism? No. For most non-philosophers a basic understanding is sufficient. Does that mean that they do not know objectivism is “fully valid”? Yes, in that they have not validated every tenet of Objectivism. However, those tenets that they do know are true (because they have verified that they correspond to the facts of reality) are “fully valid.”
Of course, after discovering the truth of so many tenets of Rand’s philosophy, one begins to greatly respect her masterful mind. Thus one will naturally presume that those few tenets of Rand’s philosophy which one has not learned/validated yet are very likely to also be true. However, until one has actually validated them oneself, one cannot claim knowledge of their truth—no one, not even Rand, is infallible. Thus, for example, I would claim that I know 98% of Objectivism is “fully valid” because I have learned and verified those tenets, and I presume (but cannot claim to know) that the remaining 2% is also true.
You mention axioms in your question. I want to caution you against using an improper methodology in approaching objectivism. You cannot start with an axiom and deduce from it the tenets of Objectivism. Objective knowledge is obtained largely through the process of induction—you look at reality, discover facts, and integrate those facts together into generalizations. As you gain knowledge, you must continually strive to integrate that knowledge with all of your other knowledge. The axioms are part of your knowledge, and thus you must integrate any new knowledge with the axioms as well. If a new piece of information contradicts an axiom, then you know it cannot be true. Thus the axioms serve as important guides to help us integrate our knowledge, but are not the source of our knowledge. The source of knowledge is you looking at reality.
Most philosophies take the opposite approach—they start with basic (and generally arbitrary) propositions and deduce out the rest of the philosophy from there. If reality does not comport with their deduction, they hold, then reality must be flawed. However, Objectivism is a fact-based, reality-oriented philosophy.
Where to Start?
You are going to have to read if you want to learn about Objectivism. I think the best place to start is Ayn Rand’s two most famous fiction works, Atlas Shrugged and The Fountainhead. I think that you are more interested in non-fiction and short explanations, but I really believe that her fiction works are a much better introduction to the philosophy because they present the philosphy in realistic life situations which one can identify with and understand.
After that I would recommend Leonard Peikoff’s work Objectivism, the Philosophy of Ayn Rand for a broad overview of objectivism that hits all the major point of the philosophy. Next, non-fiction by Ayn Rand, such as The Virtue of Selfishness (1964), Capitalism: The Unknown Ideal (1966), For the New Intellectual (1961), Philosophy: Who Needs It (1982), Introduction to Objectivist Epistemology (1967), The Romantic Manifesto (1969) and many others. Along the way, refer to the Ayn Rand Lexicon for help understanding particular concepts used by Rand. The Ayn Rand Institute has lots of videos/audio about Objectivism as well, some by Rand herself, some by scholars explaining Objectivist ideas (although their views are extremely helpful, remember that only Rand’s view make up Objectivism , the rest is just commentary) (note that you may have to register to view some videos, but this is free). In particular, this video by Leonard Peikoff is a condensed introduction to her philosophy. This extremely short summary by Rand herself is the shortest you will likely find. Good luck on your journey of discovery.
A comment made a well-founded suggestion that I clarify that when I say we must integrate our knowledge we do so using reason. The comment also asked for an example of improperly trying to deduce a philosophy from axioms. Immanuel Kant comes to mind. I am no expert on Kant, but my understanding is that he quite arbitrarily decided that morality requires acting from duty, and from no other motivation. From that he tried to deduce an entire moral philosophy, starting with the "categorical imperative" and from that particular principles, such as honesty. To Kant "Reason, separate from all empirical experience, can determine the principle according to which all ends can be determined as moral. It is this fundamental principle of moral reason that is known as the categorical imperative." (excerpt from Wiki article, emphasis added)
Consider, on the other hand, the Objectivist ethics. All of the virtues (honesty, independence, productivity, etc.) are really different perspectives on the cardinal virtue of rationality. However, were these virtues discovered by deducing them a priori from rationality? No. Instead the principles are the product of looking at evidence in the world--at people and their actions, what is good for their lives and what is not, what principles have been tried throughout history and do they work, etc. The evidence is integrated by reason into generalizations, and these generalizations are integrated with all of our other knowledge, including the cardinal virtue of rationality and the basic axioms of existence, identity and consciousness.
Deduction has a role of course, it is just not the role of deriving an entire philosophy. We use deduction to check that our knowledge integrates correctly, to look for contradictions, etc. We can also use it to discover previously unknown consequences of a principle. We just don't discover the principles in a deductive void separate from all empirical evidence as Kant would like: we welcome evidence.