Scalia's interpretation is historically unmoored. There was no controversy in 1791 about an individual's right to weapons for self-defense -- it was simply taken for granted. Hence, there was no need for a constitutional amendment to address that. What was fresh in the Founders' memory was the British raid on Concord to seize the weapons of the colonial militia. They didn't want the federal government, in the future, to be able to seize the weapons of the militia. In addition, in 1791, the newly constituted country was leery of a standing army. It couldn't afford one, and a standing army was considered a potential threat to liberty. The defense needs were to be delegated to the body of the citizenry. Therefore, the two clauses of the 2nd Amendment are inseparably linked.
The real question is what constitutes the militia. The contemporary writings of the Founders indicate that they thought it was practically everyone. Since the militia was thought to be universal, that translates into an individual right of ownership. And since the citizenry was in lieu of a standing army, it would follow that the individuals should be as well armed as such an army (that is, with the same types of weapons).