[nybble41]

This is a good definition. It is very close to my own, though I would quibble about endorsing the propaganda term "legitimate". Certainly those who practice such violence want it treated as legitimate, and your phrase "no means of recourse besides violence of your own" gets to the core of the issue: that others allow them to get away with calling it legitimate, without offering resistance. However, these factors are not sufficient to justify violence when it is neither defensive nor proportional and reciprocal.

Also, you relegate "private ownership and transfer of property" to a minor and seemingly optional footnote while this is a necessary aspect of the definition of "violence". (Is theft not violence? If your answer is "no", how about starving someone by stealing all their food, or the land and capital equipment they need to grow it? Or the barter goods or money they needed to purchase it? Etc., etc.)

The problems with "the usual functions" (and the key difference between minarchists and anarchists such as myself) are: (a) These things can be, and have been at various times, provided privately without initiating violence, so it is not necessary to curtail freedom for them. (b) It's not enough to say "a military is necessary to reduce violence, and this falls under the heading of 'military', and thus is allowed". To justify it on the basis of minimizing overall violence this military must never employ more violence than necessary, or more than it demonstrably curtails elsewhere, including in its funding process or in enforcing any rules it imposes. The same goes for the police and the courts. The courts have the easiest path; they're not that far removed from private arbitration. The military is the hardest to justify, particularly a standing army in a country like the U.S. with only two neighbors sharing land borders or even on the same continent—both of whom are considered allies.