Libertarianism Discussion: Axiomatics

In my first post on this subject, I stated that:

1. Libertarianism is highly axiomatic: There’s a set of rules to be applied to evaluate what is proper, and the outcome given is the answer which is correct in terms of the moral principle of the theory. This leads to quite a few tortured ‘terms of art’ in libertarian thought since, due to it’s axiomatic nature, the libertarian rhetoric cannot survive counter-factual arguments.

To which Mr. Paul replied that:

Yes, Libertarianism *IS* a simple system. This is important for several reasons. One of these reasons is that ordinary people in a just society must know, without question, whether they are breaking a law at nearly all times. Even when grey areas are unavoidable, they almost must know where the grey area is, so that they can seek legal advice. To imprison or kill a person for a crime they do not understand and could not define seems to me the height of injustice. Note that Libertarianism is a political philosophy, not a moral one. It does not ask “What should I do?” but “What should all people be forced to do?”. Libertarians, though we have a consensus on most legal and political issues, have a wide variety of tastes and personal moral convictions, all of which are tolerable in a Libertarian society. Acting upon them is also tolerable, so long as they do not stray into the area which is axiomatically and legally impermissible. Which brings us to the non-initiation of force.

This is mostly non-responsive to what I wrote. When I claim right-libertarianism is “highly axiomatic”, I do so through the lens of both philosophy and of mathematics, so any reading of the term axiomatic to mean “simple” is, well, simplistic in the extreme.

The Basics of Axiomatic Systems

Any axiomatic system has a set of fundamental concepts which are imbued with meaning from involvement in contexts other than the one currently under consideration. Such outside associations prevent one from treating a concept as a simple building block of some particular system. To be a concept in an axiomatic system it must be free from external signification.

These (fundamental) concepts are interrelated via a set of axioms; the fundamental relations of the system. These axioms implicitly define the concepts, allowing them no meaning other than that supplied by the axioms themselves. (I mean to ‘implicitly define’ in an similar sense to the way that a set of three algebraic equations with three unknowns defines those unknowns.)

Since we must ignore any external associations which we make with the concepts, the axioms must be separated from any external verification, their truth simply being something given. Everything else in the system is then deduced from the axioms. Indeed, nothing else in the system way come from anything other than the axioms. Thus the system is closed under such processes of deduction.

Axiomatics in Philosophy

Though the notion of an axiomatic philosophy has been widely discredited since the days of Spinoza and Descartes, and even more recently has been discredited in mathematics itself (via Gödel), it is necessary for this discussion to sketch the philosophical applications of axiomatic principles.

In general, philosophies appear to have a limitless variety of fundamental concepts, and right-libertarianism is one of the very few that appear to have just one. Fortunately, we are not limited to considering only what a philosophy explicitly declares as a fundamental concept, even if we refrain from questioning any particular declaration a philosophy may make about itself. It is possible to see a system as axiomatic in multiple different ways; the fundamental concepts and axioms may fail to overlap between different axiomatizations within the single philosophy, which I what I see in right-libertarianism.

For the sake of simplicity I will take any philosophy as having only one fundamental concept; its theory – the sum total of what it puts forward as true. Any other concept it puts forward must be included in this one concept, and to be called a philosophy it must attempt to demonstrate the truth of its claims. It must also be able to describe the nature of its claims; its theory.

This does not, however, mean that the theory has to be included in the fundamental concepts of an axiomatization, though it does place it (as a concept) within the theory itself.

If we do take a philosophy to have only one fundamental concept, its theory, there would seem to be no possibility of axioms, for an axiom is a relation between concepts. However, as we have also seen, even our chosen single concept must be related to itself. The theory is the exposition; it does not have any content not supplied by its exposition, and its truth must be established independently of anything outside its exposition.

That is what I mean by “highly axiomatic” in relation to a supposed philosophy.

Formal Proof that Libertarianism is Wrong

Taking the above assertion, that a philosophy has only one fundamental concept, it’s theory and taking libertarianism, its exposition, as that one concept:

• libertarianism is a proposition (or can with little effort be formulated as either a proposition or question with identical semantic content).
• libertarianism itself cannot be proven by means of experience. It is an axiom, one of many possible, equally unprovable assertions of ways to determine truth, falsehood, or meaning.
• libertarianism requires still more axioms to establish the criteria of experiential proof as a prior condition, and they cannot be proven experientially or otherwise either without begging the question..
• Therefore, libertarianism is meaningless. I don’t know what you mean when you say that meaning can only be ascertained by the possibility of an experiential proof as that statement has no possibility of an experiential proof.
• I understand what you mean anyway. So not only is libertarianism meaningless, libertarianism is incorrect as well.