Isn’t capitalism an economic system based on the market?

The term capitalism is used here in the broader philosophical, political sense (social system), and not in the narrower economic sense (market economy).

Capitalism is not just an economic system (the free market) that can be grafted onto any political structure. Capitalism is an integrated social system that depends on a specific non-contradictory ethical, political, legal, economic, and cultural foundation.

The economy of capitalism — the free market — depends on a specific legal (objective law), political (individual rights), and moral (rational self-interest) foundation. It is these dependencies that make individuals free not only in their economic affairs but in their personal affairs as well.