Outline and explain the indivisibility argument for substance dualism.

Descartes formulated the indivisibility argument in order to support his theory of substance dualism. Substance dualism is the theory of mind which states that mind and body are two ontologically distinct substances. The body is extended and belongs within space and time while the mind is distinct, has no extension and does not exist within space and time.
The indivisibility argument rests on Leibniz’ principle of the indiscernibility of identicals which states that a substance A can only be identical to a substance B if and only if it shares at least all of the same properties. The body, Descartes claims, is divisible for example, one can remove a limb. However, the mind does not share this property and is indivisible. One cannot divide a thought for example. Therefore, the mind and body must be two distinct substances as they do not share at least all the same qualities.