POSITIVE LIBERTY (Plato, Epictetus, Christian theology, Kant, and Marx). Positive liberty means free from internal restraints, such as greed, lust ignorance, etc. Here expresses the rationality of the true soul that is uncovered when internal restraints are removed. Strict laws should be in effect to prevent people from irrational acts: laws against gambling (greed); laws against homosexuality (unnatural acts); laws against adultery (lust). Most orthodox theology, East and West, is founded on positive liberty. "You shall know the truth and the truth shall make you free. The motto for positive liberty is one must do what one ought (according to the natural law). Positive liberty morally prescriptive; it has positive moral content.
NEGATIVE LIBERTY (Ockham, Hobbes, Lock, J.S. mill, Libertarian Party.) Negative liberty means freedom from external restraints, which are embodied in unnecessary laws, etc. As J. Bentham states: "Every law is an infraction of liberty." Laws are only conventional and convenient, and should be kept to the bare minimum involving murder, physical assault, theft, and fraud. No other laws are legitimate. One is allowed to indulge in the passions and eccentricities of the "soul" as long as this does not affect anyone else, except perhaps a partner, who has consented to "sin" along with you. In short, you may freely enslave yourself, but no one else.
The motto for negative liberty is one can do what one pleases (within a minimal legal framework). There is an empirical test for negative liberty, but none for positive liberty. One can count the number of external obstacles as a measure of negative liberty. It is also empty (negative) of moral content.