The purpose of the Divisibility Argument is to prove that mental states are different from the brain states. My body, which includes my brain, is divisible. However, I cannot conceive of my mind as divisible. Therefore, my mind is distinct from any part of my body.
Descartes was the first who established the Divisibility Argument. He held that the two components which constitute man had an independent origin and are of a fundamentally different nature. The body is divisible, since it can be separated for example, my leg or my hand can be cut off; my brain can be cut on half. However, the idea of the divisible mind is inconceivable.

This argument relies on the Leibniz’s Law. It is a principle about identity, which says, “if an object or event X is identical with an object or event Y, then X and Y have all of the same properties.” So if X and Y have any different properties, then X can not be identical with Y. Divisibility Argument uses a different property to prove the distinctness of brain states and mental states: the property of being indivisible. In this case, the mind has a property and brain lacks it. The body can be divided, however, it cannot be done with the mind.

Mary has several objections to this argument. First, she believes that the mind is an entity, which is composed of several mental states: thoughts, beliefs, memories, desires, etc. Mary strongly disagrees with Descartes’ claim that the mind employs itself in its different properties: willing, desiring, understanding, and so on. Secondly, she clarifies the meaning of the word “conceive” in the Dave’s argument. The term “conceive” might mean either “imagine” or “understand.” Imagining literally involves “forming an image of” or “picturing” in one’s mind, whereas understanding is more “conceptual” and does not require the ability to picture something. In case, Dave interprets the word “conceive” as “imagine” in the second premise of the argument, this premise becomes untrue. The fact that he cannot imagine something to be the case does not make it true in everyone’s case. Different minds can imagine different things. However, if Dave implies “understand” as a meaning of “conceive” the second premise still remains doubtful. The fact that Dave cannot understand it does not exclude the possibility that someone else is capable to think of his mind as having parts.

The next major objection to the Divisibility Argument concerns first/third-person approach. Mary rejects Dave’s assumption that the true nature of the mind can be understood solely through introspection or from the first-person approach. She claims that things that cannot be conceived through the first-person approach, which is introspection, can be understood or investigated through the third-person approach, which is observation and science. Therefore, even if it is true that the mind cannot be conceived as divided from the first-person perspective, it is possible that it would be the opposite from the third-person perspective. The perfect example of that case is the multiple personality disorder. This is the clear case where the third-person perspective reveals the true nature of a mind as divided regardless of how it seems from the first-person perspective.
As a response to Mary’s objection, Dave agrees that the second premise in the argument does not have always a true value that makes the argument unsound. Therefore, he changes it to “I cannot conceive of my individual mental states as having parts.” In the case of the first/third-person approach, Dave relates to the multiple personality disorder as a case with several minds rather than one divided mind.

In my opinion, Dave does not satisfactorily respond to the Mary’s objections since he does not give a good reasoning for his point of view. However, I do believe that the mind is indivisible since there is no such thing as part of mind. Mind and matter have fundamentally different natures: matter, which is extended, divisible, passive, and law-like; and mind, which is unextended, indivisible, active, and free. I definitely agree with Descartes that the soul occupies the whole body in all its parts, so the reduction of the body in any way does not reduce the soul. Thoughts, feelings, desires and so on, are all properties of the mind but not its parts.