Defense of Others

Tom was attacked by Mean Mike. Bob saw the attack and rushed over to help Tom. Bob grabbed Mean Mike and pulled him off of Tom.

Mean Mike did not consent to Bob's imposition on Mean Mike's property. Mean Mike did not aggress against Bob. In the context of the Non-Aggression Principle (NAP), what has happened? 

It's clear that Mean Mike has violated the NAP by violating Tom's property (his body). By violating Tom's property, Tom now has a claim to Mean Mike's property to compensate for the value Mean Mike has taken without consent. 

Bob initiated force against Mean Mike in defense of Tom. What does that mean? It isn't as clear. But the principles laid out in Libertarianism: the Manual to Humanity (LMH) give a guide:

"By violating the entitlement to the property of others, an aggressor implicitly agrees that property need not be respected. By violating his victim's property, thereby transferring value from the victim to himself, he creates a claim on his own property by which the victim may attempt to recoup the value taken from him. Because the aggressor has agreed, through his aggression, that property need not be respected, the victim is within his entitlement to use his property in defense of his property, or to recoup his property, even if this defense requires the use of force against the property of the aggressor."

Mean Mike has violated Tom's property. Therefore, Mean Mike has openly demonstrated that he believes property (which necessarily includes his own) need not be respected. He has, in effect, consented to the use of his own property by others. This is Bob's out. Because of Mean Mike's consent, Bob may impose himself on Mike's property.

But only to an extent.

Mean Mike's property is now Tom's property to an as-yet unknown degree because Mike's violation of Tom's property has created a claim on Mike's property. Because value is subjective, we don't know the extent of Tom's claim. So if Bob takes too much liberty with Mike's property, he risks violating the NAP against Tom if he infringes on Tom's claim to Mike's property. From LMH,

"Value is subjective. The value of property depends on the preferences and values of the beholder. All humans use the means available to them to achieve their goals. These goals are unique to the individual. Therefore, resources will be valued differently by different people at different times, or may even be valued differently by the same person at different times. Because of the subjectivity of value, only the victim is able to determine the value taken from him by an aggressor."

Bob's defense of Tom, in itself, does not constitute a moral transgression, a violation of the NAP. It does, however, put Bob at risk of violating the NAP if he infringes on Mean Mike's property to the point that it damages Tom's claim to Mike's property. It may be that, even if Bob did violate the NAP that Tom would forgive him in gratitude for his help in subduing Mean Mike, but defending the property of others is permissible under libertarian philosophy. 

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