By the actual words in the Second Amendment....here:
You are assuming because of what Mason has said, but by looking at the actual text of the Second Amendment, it's clear two groups of people are being spoken about.
The first half....."a well regulated militia"
The second half....."the right of the people"
A "militia" is armed by its very definition, regulated by the government for the security of a free state.
They then secondly, separating between the two (militia and people), state the people also have the right to keep and bear arms, for it would be nonsensical to state this for the "militia".....it's just that simple.