Generally, I like to talk about liberty the way that libertarians do. I primarily do that because liberty, as discussed by libertarians, actually makes private property ownership an injustice. Because few people ever bother to think about that, adopting libertarian notions of liberty in my interactions with people of that persuasion is a never-ending well of hilarity. "What do you mean unilaterally grabbing up pieces of the scarce world without the consent of others (whose previously-existing access you steal away) and then violently attacking people who don't go along with your fiat claims of ownership is aggression?" they say, "that's just homesteading followed by self-defense!" And on it goes.
The problem with the libertarian and right-wing notions of liberty is not just that they implode; it's that there is a more plausible notion of liberty offered up by the left-wing that is only really achievable through leftist political economy. Under this, liberty is achieved when individuals have their economic well-being so strongly secured that they can pursue their personal projects without worrying themselves about the potential of falling into utter destitution. True liberty requires, as FDR famously noted, freedom from want.
You can see an excellent case study of this superior take on liberty in Katie J.M. Baker's piece in the latest issue of Dissent. In it, Baker details the utter frustration faced by a famous "pick-up artist" (read misogynist loser) who tried and failed to ply his seduction techniques in Denmark. To explain his failures in Denmark, this pick-up artist "concludes that the typical fetching Nordic lady doesn't need a man 'because the government will take care of her and her cats, whether she is successful at dating or not.'"
Although a somewhat narrow example, its insights are profound and general. When individuals have their economic well-being secured, they do not have to put up with mistreatment from those whose private economic support their life might otherwise depend on. Freed from the specter of want, women do not have to tolerate abusive would-be spouses, workers do not have to tolerate abusive bosses, and people of color do not have to tolerate racial subjugation. When protected against the possibility of economic retaliation, people can speak more freely, associate more freely, and practice their faith more freely. In short, having their livelihoods publicly secured gives people much more genuine liberty to do what they'd like. And that's what really seems to matter when we talk about liberty, not some property rights formalism.
Of course, you don't have to take my word for this. Although libertarians oddly like to claim him as their own, even John Locke - famed philosopher of property rights - understood the liberty problems posed by economic coercion. He wrote this in his First Treatise:
"And a man can no more justly make use of another's necessity to force him to become his vassal by withholding that relief God required him to afford to the wants of his brother, than he that has more strength can seize upon a weaker, master him to his obedience, and, with a dagger at his throat, offer him death or slavery."
Some of the labels are a bit antique, but the point is clear as day. Locke realizes that employers can take advantage of the landless, the poor, those with few options and force them into a kind of slavery. He doesn't mean actual slavery of course; rather, he means subjugation, bringing someone under your control because they are in desperate need and will do whatever you say in order to get a paycheck.
Locke's method of blowing up the liberty-destroying coercion made possible by want is the leftist method. He demands that the needy be given relief from that need in order that they not be made to choose between "death or slavery." This is what leftists of all stripes demand, it is what Nordic states have delivered, and it is what the achievement of genuine liberty in the U.S. will require.