I don't like the idea very much myself. But, I suspect that the requirement of a concealed carry permit (CCW) from the state in which the park is located will reduce the number of gunslingers considerably. Moreover, a person who holds a concealed carry permit has to have attended a class on the legal issues of the use of deadly force and also has to show some minimum competence with a pistol. This should markedly reduce reckless behavior with guns.

In Arizona, anyone not a convicted felon or adjudged mentally incompetent can obtain a CCW. But, at least when I got mine, the permit holder had to pay for and attend two eight-hour days of class and show a minimum level of accuracy with, and safe handling of, the weapon before the permit was issued. You are also fingerprinted and the state runs a FBI check to be sure you are not a felon. I think that the effort required to get a CCW and the sobering lectures on criminal and civil liability surrounding use of a concealed weapon will ensure a reasonably high standard of responsible behavior. As far as I am aware, no holder of a CCW in Arizona has yet used their pistol in any criminal endeavor or unjustified shooting. I'm sure that will change but at present, CCW holders seem to be a pretty responsible group of citizens.
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May I walk in beauty.