What is the difference between the idea that we can control our bodies in conformity with our will and magic? Aren't they suspiciously similar ideas?

Wonderful question!

There are some philosophers who are very committed to a form of determinism that rules out free agency and a thesis that seems quite contrary to common sense, namely that the self is an illusion or construct and not a real, substantial individual thing. For some of these philosophers, the idea that one might freely control one's body or one's agency is the equivalent of thinking we can do magic. I think Owen Flanagen believes that radical free will (in which a person could engage in libertarian free will) is like magic, and Daniel Dennett as well. But many of us are on the other side and believe that it is natural and plausible to think that we can act and have the power not to act in ways that are morally responsible or blameworthy. For a great book on this, check out Mawson's Free Will; A Guide for the Perplexed or Daniel Robinson's book On Praise and Blame.

Going on a bit further on the themes in you question magic and control I suppose the concept of the magical today is treated along the lines of miracles. A magical event (of the Harry Potter variety) is probably thought of as an event that someone brings about intentionally in a way that supersedes or goes beyond the non-magical, ordinary laws or course of nature. Magic, in this view, would involve a kind of extension of one's powers, so that under ordinary conditions it is not magic when I type this response, but it would be magic if I made these words appear to you in a dream (without using anything more than an incantation)! But you are right that what we think of as magic and control over our bodies does involve something in common: intentionality. In both cases, we intentionally bring about some state of affairs. In that sense, maybe they are "suspiciously similar ideas" though I suspect that there is nothing suspicious per se about acting intentionally.

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