"The basic principles they now accept are called axioms. They are self-evident truths. A person owns himself and the fruits of his labor. She owns her property."
While I understand what you are getting at with this, all of it is imprecise or false.
"The basic principles they now accept are called axioms."
As I explained here http://nicksinard.com/2016/07/20/axiom-vs-priori/ when we refer to axioms we refer to synthetic a priori statements, but it can be misunderstood as a type of axiom that is in mathematics. Those types of axioms are just postulated and accepted as true. The "axioms" we are referring to are the type that cannot have their truth "undone;" in other words, they can only be denied with performative contradiction.
"They are self-evident truths."
If they were self-evident truths then everybody would realize them and anybody arguing against them would be lying, i.e. purposively misleading a person(s) from the truth; however, this is not the case. People sincerely and honestly believe the body-ownership principle, the homesteading principle, contractual exchange, and the non-aggression principle, following from the past three, are untrue. These a priori statements are, again, just statements whose truth can only be denied with a performative contradiction.
" A person owns himself and the fruits of his labor."
The first part is imprecise. One does not have property rights in one's "self" in the sense that it is separate from the body. One only can have property rights in scarce, contestable resources. One does have property rights in, i.e. has the justifiable exclusive control of, one's body (so long as one doesn't commit an aggressive action.
The second part concerning "the fruits of one's labor" is a faulty metaphor. It leads to intellectual disasters such as the justification of intellectual property. One does not own one's labor because (1) one can only have property rights in scarce, rivalrous resources and (2) labor is simply an action. Labor is not some metaphysical substance that can be mixed with a resource. Following from the fact that one does not own one's labor, one does not own " the fruit of one's labor." See also https://mises.org/blog/thoughts-intellectual-property-scarcity-labor-ownership-metaphors-and-lockean-homesteading and http://www.stephankinsella.com/paf-podcast/kol-037-lockes-big-mistake-how-the-labor-theory-of-property-ruined-political-theory/
I cover both points in http://nicksinard.com/2016/07/19/short-thought-intellectual-property/
"She owns her property."
A "property" is a quality and as such it makes little sense to call a scarce resource "property." It makes much more sense to say that one has a property right in a scarce resource. Towards the ending of this article http://nicksinard.com/2016/07/24/argumentation-ethics-libertarianism-culture/ I address this as well.
Overall, I like your work Sterlin. I do think you can be too metaphorical and imprecise at times for the purpose of sounding less "logical" and more "emotional", but in general you have some good insights.
Nick, i appreciate the insights and I agree with mostly what you are saying. Unfortunately, you tackled this mostly with your head instead of heart. This was not meant to be a rigorous logical piece meant to precisely articulate the LEM truths anarchism. It was purposely intended to be poetic and beautiful, while only touching on the logical aspects of the philosophy.