The Greeks didn't invent trade, or even maritime trade. It was common throughout the ancient world. And there has always been some form of capitalism operating, everywhere. There has never been a time when people didn't have a need for something and looked for a chance to make a profit. During the time the pre-Socratic philosophers were active, the Greeks were primarily farmers and artisans, with some inter-island trade, but certainly not as much as the Phoenicians who were contemporary with them. By the time the Athenian Empire and the Delian League dominated the eastern Mediterranean, the age of the pre-Socratics was coming to an end, and the Empire was relying heavily on slavery and imperialism. I don't think capitalism played any major role in the early development of natural philosophy. It certainly didn't in China or Arabia or Rome who were all great trading and merchant societies.

Bacon, who provided the philosophical foundation for modern science, was active in the 1200s. The Rennaissance re-introduced the learning of the ancients to Europe, but it wasn't until the 17th century that science really took off. I will concede this coincided with an explosion of
maritime trade, and the rise of what we would call today modern companies, banking, finance and a middle class. But it also coincided with the rise of imperialism and colonialism, too, as well as slavery in the New World.

Science certainly benefited by improved transport, communications and printing which all occurred around this time, but the effect was indirect. By the time of what we now recognize as the second stage of capitalism, Mercantilism, science was already on its way, although I doubt if there was a cause and effect relationship. People have been stretching their minds to make a profit from the beginning, all over the world. That is something you don't need a philosophical foundation for.

Capitalism may have provided much of the financing for scientific research in the 18th century and later, and it certainly helped by uniting the world together and beginning the overthrow of the great landowners and contributing to urban life. but by that time we were in the age of Newton.

Capitalism did not create science, but it certainly made conditions for its growth and spread more favorable. But we could just have easily had a capitalist economy without science. The Romans certainly did. There was little incentive for investment in basic research. All capitalism really needed was a strong maritime technology (center rudder, magnetic compass, and gunpowder. And all that came from the merchants of China.

It's important you understand exactly what I'm saying here. I'm not saying capitalism was irrelevant, or unimportant, but a lot of other things played a role, too. In my opinion, the growth of urban centers, universities and a middle class was the key factor, and that included not only merchants, but artisans and craftsmen too. Science really took off because it was no longer just the rich landowners who could afford to educate their children.