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The thing that the market does not provide which a government does is a military.

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Demonstrate logically why a market would not provide militaries for property protection against invaders.

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Because when you are facing a horde of Mongols who ride out nowhere from a desert which is thought to be uncrossable, it is really hard to get your [censored] together in time to defend yourself. This happened across Asian circa 1250 to many free market economies located in the Caliphates of the day. You should read history more.

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You would agree, though, that the ability for a small group to fight a larger group is considerably better in this age. Take Switzerland (fast becoming the new anti-Somalia among ACists...). A small country that managed to avoid being overrun by the Wehrmacht during WWII. Why? Because they were armed to the teeth and the Germans knew that attacking would be very costly.