Here is a short summary of my ideas, with an emphasis on political philosophy.
Objective reality exists, and humans can know about it. People create knowledge (learn) by reason. Reason works by evolution, which works by error correction – many candidate ideas/genes/replicators which contain randomness and error, and a selection process that eliminates bad ones. No alternatives to evolution are known. What makes a person rational is that they do a good job of keeping open ways for any mistakes in their ideas to get corrected. Major tools here are keeping an open mind and participating in critical discussion; these contrast with irrationality like being arrogant, over-confident, and disinterested in criticism and other ideas.
Political philosophy and economics do not stand in isolation. Everyone has and uses a philosophy, including when considering political philosophy and economics. The only question is whether they say what their philosophy is, accept the philosophy is affecting their conclusions, and keep trying to improve the philosophy and expose it to criticism, or if they claim a false philosophical neutrality and try to hide their substantive philosophical assumptions from critical discussion.
People own themselves and have a right to property. People should be free to pursue their self-interest and happiness. This will not create chaos and fighting because there are no conflicts of interest between rational men. There is an inherent harmony of mankind's interests, which laissez-faire capitalism facilitates. People benefit more from voluntary trade (which is win/win and creates value) than from fighting with each other (which is expensive and risky, and creates negative total value). When interaction mutual benefit isn't available, people should leave each other alone.
The proper purpose of government is to protect people against force (which includes physical violence, threat of violence, and fraud). Nothing else.
We do not live in a capitalist society today (2015 USA). In a capitalist society, for example, roads and parks would be privately owned, and there would be no anti-trust laws. And there would be no tax-funded welfare or pork barrel projects or other wealth redistribution. And no government bailouts or "economic stimulus" packages.
People are welcome to help others out, voluntarily. There are often good reasons to, though not always, and only for limited amounts of help that won't sacrifice the quality of one's own life.
If I want something that someone else has, I must buy it (with his voluntary agreement), persuade him to give it to me (with or without conditions, barter, etc), or leave him alone (go without it, or find a way to make my own, or hire someone else to build me one, etc).
Reason and force are incompatible opposites. Capitalism is compatible with reason, because freedom best allows for the correction of errors. When force is used, if the idea behind the force is mistaken, it's hard to fix that. It's hard to try out and learn about other ideas while under compulsion. It's hard to argue with a brute thug. In a system of force, the stronger forces his ideas on other whether they are good or bad. In a system of freedom, when people disagree, they can each keep trying life their way, they can resist errors that are merely suggested by others. With rational persuasion, people only change their mind if they think it's better, and change change their mind again if they think they see an error. A rational economic system is an extension of a rational epistemology.
See also Ayn Rand's short summary.