Explain Descartes' divisibility argument for substance dualism.

As a substance dualist, Descartes defends the theory that there exist two ontologically distinct substances; the mental substance and the physical substance.
His divisibility argument is as follows:i. the mind does not have any parts; one mind performs all the different actionsii. therefore, the mind is indivisible iii. the body does have parts (e.g. hands, feet, legs)iv. therefore, the body is divisibleiv. therefore, the mind (mental substance) is distinct from the body (physical substance)
He relies on Leibniz's theory of the indiscernibility of identicals, which states that if two things are identical (i.e. are just one thing), then they share all their properties and so are indiscernible. Since the mental substance and the physical substance differ in properties (only the physical substance is divisible), Descartes establishes that there exist two independent substances.