I got asked for my philosophy on one foot. I personally never found Objectivism on one foot that useful. I thought it's too hard to understand if you don't already know what the stuff means. Philosophy is hard enough to communicate in whole books. Some people read Atlas Shrugged and think Rand is a communist or altruist. Some people read Popper and think he's a positivist or inductivist. Huge mistakes are easily possible even with long philosophical statements. I think the best solution involves back and forth communication so that miscommunication mistakes can be fixed along the way and understanding can be built up incrementally. But this requires the right attitudes and methods for talking to be very effective. And that's hard. And if people don't already have the right methods to learn and communicate well, how do you explain it to them? There's a chicken and egg problem that I don't have a great answer to. But anyway, philosophy, really short, I tried, here you go:
There is only one known rational theory of how knowledge is created: evolution. It answers Paley's problem. No one has ever come up with any other answer. Yet most people do not recognize evolution as a key theory in epistemology, and do not recognize that learning is an evolutionary process. They have no refutation of evolution, nor any alternative, and persist with false epistemologies. This includes Objectivism – Ayn Rand choose not to learn much about evolution.
Evolution is about how knowledge can be created from non-knowledge, and also how knowledge is improved. This works by a process of replication with variation and selection. In epistemology, ideas and variants are criticized and the survivors continue on in the process. This process incrementally makes progress, just like biological evolution. Step by step, flaws get eliminated and the knowledge gets better adapted and refined. This correction of errors is crucial to how knowledge is created and improved.
Another advantage of evolutionary processes is that they are resilient to mistakes. Many individual steps can be done badly and a good result still achieved. Biological evolution works even though many animals with advantageous genes die before other animals with inferior genes; there's a large random luck factor which does not ruin the process. This is important because of human fallibility: mistakes are common. We cannot avoid making any mistakes and should instead emphasize using methods that can deal with mistakes well. (Methods which deal with mistakes well are rational; methods which do not are irrational because they entrench mistakes long term.)
A key issue in epistemology is how conflicts of ideas are handled. Trying to resolve these conflicts by authority or by looking at the source of ideas is irrational. It can make mistakes persist long term. A rational approach which can quickly catch and eliminate mistakes is to judge conflicting ideas by their content. How do you judge the content of an idea? You try to find something wrong with it. You should not focus on saying why ideas are good because if they have mistakes you won't find the mistakes that way. However, finding something good about an idea is useful for criticizing other ideas which lack that good feature – it reveals a flaw in those rivals. However, in cases where a good feature of an idea does not lead to any criticism of a rival, it provides no advantage over that rival. This critical approach to evaluating ideas follows the evolutionary method.
This has implications for morality and politics. How people handle conflicts and disagreements are defining issues for their morality and politics. Conflicts of ideas should not be approached by authority and disagreement should not be disregarded. This implies a voluntary system with consent as a major issue. Consent implies agreement; lack of consent implies disagreement. Voluntary action implies agreement; involuntary action implies disagreement.
Political philosophy usually focuses too much on who should rule (or which laws should rule), instead of how to incrementally evolve our political knowledge. It tries to set up the right laws in the first place, instead of a system that is good at improving its laws. Mistakes should be expected. Disagreement should be expected. Everything should be set up to deal with this well. That implies making it easy to change rulers and laws (without violence). Also disagreement and diversity should be tolerated within the law.
Moral philosophy usually makes the same mistake as political philosophy. It focuses too much on deciding-declaring what is moral and immoral. There should be more concern with fallibility, and setting things up for moral knowledge to incrementally evolve. We aren't going to get all the answers right today. We should judge moral ideas more by how much they allow evolution, progress and mistake-correction, rather than by trying to know whether a particular idea would be ideal forever. Don't try to prophesy the future and do start setting things up so we can adjust well in the unknown future.
Things will go wrong in epistemology, morality and politics. The focus should be on incrementally evolving things to be better over time and setting things up to be resilient to mistakes. It's better to have mistaken ideas today and good mistake-correction setup than to have superior ideas today which are hard to evolve and fragile to error.