Final answer:
The approach to gaining wealth through free trade and free markets is known as capitalism, free market, and mercantilism, but not socialism, which typically involves more government intervention and differing views on the distribution of wealth.
Step-by-step explanation:
The philosophical approach to gain wealth through free trade and free markets is known as all of the following except socialism. Capitalism, characterized by a free market economy where government intervention is minimal, is about letting markets operate freely, with prices determined by supply and demand. This philosophy is widely associated with the ideas of Adam Smith, who believed that an unregulated market naturally benefits both producers and consumers by finding the most efficient price through competition. In contrast, mercantilism is a system where wealth was traditionally measured by the accumulation of precious metals, and trade was heavily regulated by the government to ensure more exports than imports. Mercantilism emphasized tariffs, monopolies, and industry subsidies, promoting the idea that a nation's power is dependent on its wealth, often acquired through colonial possessions and restrictive trade practices. Therefore, socialism, which generally involves more government control over the economy and may feature social ownership of the means of production, does not align with the principles of free trade and free markets.