Saturday Question: Descartes's Conceivability Argument

Usually we have Friday Questions, but this week I am posting two questions on Saturday instead. This first question comes from Amanda Donnan, who is a student in the first-year Human Nature module at Queen's University Belfast. (I have edited the question slightly.)

Descartes tries to prove that the body and the thinking mind are separate substances. He provides three central arguments for this claim, the doubt argument, the conceivability argument and the divisibility argument. Here I will discuss the conceivability argument.

The Conceivability Argument for dualism is given in Descartes’ Sixth Meditation. The argument is as follows:

1. I can conceive that I, a thinking thing, exist without my extended body existing.
   
2. Anything that I can conceive is logically possible.
   
3. If it is logically possible that X exist without Y, then X is not identical with Y.
   
4. I, a thinking thing, am not identical with my extended body.

This argument appears problematic: it is possible that thinking is essential to the mind or soul and extension is essential to bodies. However, it does not (obviously) follow that it is my sole essence to think, unless Descartes knows that thinking and extension cannot be essential properties of the same thing. In other words how can we know that the thinking thing does not have the property of extension?