Well, I think there would be a level of interpersonal trust. That wouldn't go away.
But there is much in day-to-day life that we all trust to at least a Lowest Common Level that would no longer exist in a Libertarian world.
For example, did you visit an office building today? How do you know it won't fall in on you? Today you know because it was built to certain specifications set forth in regulation. You know the builders were certified and that the inspectors made sure no corners were cut (at least in a well functioning system as we generally have in the U.S.) In a Libertarian world that might be taken over by some sort of for profit certification body...or it might not. The onus would be on you to find out before you walk through the door and put your life in the hands of people you've never met.
The typical rejoinder to which is "enlightened self-interest!" That you can trust people to do the right thing because in the long term that works out for the best.
But it turns out we tried that on a massive scale with the best and brightest, and it got us the Great Recession. Even St. Greenspan had to admit it didn't work. There's a great section on that here:
But there is much in day-to-day life that we all trust to at least a Lowest Common Level that would no longer exist in a Libertarian world.
For example, did you visit an office building today? How do you know it won't fall in on you? Today you know because it was built to certain specifications set forth in regulation. You know the builders were certified and that the inspectors made sure no corners were cut (at least in a well functioning system as we generally have in the U.S.) In a Libertarian world that might be taken over by some sort of for profit certification body...or it might not. The onus would be on you to find out before you walk through the door and put your life in the hands of people you've never met.