What is a self? I will try to answer this question by developing an analogy with something much simpler, something which is nowhere near as puzzling as a self, but has some properties in common with selves. What I have in mind is the center of gravity of an object. This is a well-behaved concept in Newtonian physics. But a center of gravity is not an atom or a subatomic particle or any other physical item in the world. It has no mass; it has no color; it has no physical properties at all, except for spatio-temporal location. It is a fine example of what Hans Reichenbach would call an abstractum. It is a purely abstract object. It is, if you like , a theorist's fiction. It is not one of the real things in the universe in addition to the atoms. But it is a fiction that has nicely defined, well delineated and well behaved role within physics.
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