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premise one
physical substance is divisible (since its extended in space)
premise two
the mind is indivisible since its non-extended
premise three
identical things must have the same properties
Leibniz’ law of indiscernibility of identical
if two objects are in fact one and the same they have all the same properties
e.g. if Bruce Wayne and Batman are the same person then they share all the same properties
conclusion one
the mind therefore cannot be identical with any physical substance such as the body