This idea usually takes on the meaning that those who act in their self-interest provide unintended consequences that betters society at large. If it wasn’t for Warren Samuel’s quote below reminding me how easily we are influenced through the “reiteration” and “invocation” of ideas, I would have forgotten how powerful a rhetorical device the “invisible hand” is for politicians and pundits.
The foundation of our society is not the predominance of falsity and pretense. The reiteration and invocation of terms like “free market” and “rule of law” as well as “invisible hand” distract attention from the key issues of policy and empower those with selective perception and selective specification. 
The debate on the significance and meaning of the metaphor that Adam Smith uses in the Wealth of Nations reminds me of the battle in exegesis over the authors’ meaning in Genesis I and II. The answer is we can never be sure of the authors’ intentions unless we ask them, and we all use our own heuristics to evaluate and interpret text.
We may prefer a literal over a figurative interpretation or place an emphasis on how context shapes meaning but often forget that our motivations cause us to favor one over the other. It is predictable when fundamentalists interpret Genesis I and II in a way that serves their interests, and we should expect the same when evaluating “left” versus “right” economists on the “invisible hand”.
I don’t have a stake in an economic camp and put an equal amount of time into an unbiased selection of sources. And a surprising result was that most economists, right or left, fall in line with the idea that it’s a metaphor. The only difference is that those on the “right” use it as a rhetorical device to show the magic of markets and those on the “left” are quick to point out that it doesn’t exist.
This sums the “invisible hand” up to be nothing more than an obfuscation that acts as a rhetorical device for social control. Persuasion is not always a bad thing if the ideology is good, but my cost-benefit analysis of capitalism is still lightyears away.
Much invisible-hand reasoning assumes the invisible hand to be a definition of reality, as well as part of the social belief system operating as psychic balm and social control. The invisible hand projected by such reasoning is believed to be in part about the economy but is also of the economy, part of the process of working things out. The rhetoric or belief system of the invisible hand is a self-projection of western civilization and the modern economy – an aspect of culture that resonates with, reflects, and reinforces other aspects. 
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 Kennedy, Gavin. “A Reply to Daniel Klein on Adam Smith and the Invisible Hand”. Econ Journal Watch 6(3): 374–388.
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