I think the more complete formulation is that the government has a monopoly on the legal use of violence. (Which I suppose isn't really true in all contexts: v

I think the more complete formulation is that the government has a monopoly on the legal use of violence. (Which I suppose isn't really true in all contexts: violence by private citizens can be legal when defending private property, for instance. But aside from small carve-outs for personal security, self-defense, and private property it generally holds.)