What is the divisibility argument for substance dualism?

The divisibility argument is one of three of Descartes’ arguments for substance dualism: that is the view that the mind and body are separate.

The argument runs as follows: Bodies are divisible into spatial parts. Minds are not divisible into spatial parts. Therefore, the mind is a distinct substance from the body.

The argument relies on Leibniz’s principle of the indiscernibility of identicals. This says that if two things are identical they share all their properties. This is because one thing cannot have different properties from itself. Thus if two things have different properties, then they cannot be one and the same thing. According to Descartes, since the mind and body have different properties, then they cannot be the same thing.