An Argument in Favor of the Soul?

I was considering an argument for the existence of the soul, initially put forward by Descartes and recently updated by people such as Alvin Plantinga (cf: “The Nature of Necessity”). It’s deceptively simple, yet very effective.

First, I will quickly define what I will call Leibniz’s Law (also called the Indiscernibility of Identicals) . For any 2 objects, let’s call them X and Y, if X and Y are identical, then everything that is true about X will be true about Y and everything that is true about Y will be true about X. For example, if we have 2 objects - Jimmie and the guy typing this paragraph - Jimmie’ and ‘the guy typing this paragraph’ are identical if and only if everything that’s true about one will also be true about the other.

Now take 2 objects - me (or my mind) and a material object (be it my brain or my body) - and let’s label them M (for either me or my mind) and B (for brain or body). Now consider the following:

(L) Leibniz’ Law

(1) It is logically possible that M exist without B
(2) B cannot exist without B.
(3) Therefore, M is not identical to B.

What this shows is that given Leibniz’s Law, there is at least one thing that is true about me that is not true about B. That one thing being “possibly existing apart from B”. Since there is one thing true of M that isn’t true of B, the 2 objects are not identical. So, I (or my mind) is not identical to a material object.

The truth of this hands on Leibniz’s Law or theorem (1). By saying that it’s logically possible for M to exist apart from B, I simply mean that it doesn’t break any logical laws and I don’t see how it’s impossible. Given those 2 things, I must concede that it’s possible that M exist without B. To deny the conclusion, it seems either it must be shown that it’s logically impossible for M to exist without B or that Leibniz’s Law is in fact false. I wouldn’t know how to begin to show the impossibility of M existing without B, and for the purposes of this post I‘m taking Leibniz‘s Law for granted.

Another version of this sort of argument is as follows:

(1) I have first person private access to my mind
(2) I do not have first person private access to my brain.
(3) Therefore, by Leibniz’s Law, my mind and my brain are not identical.

Just think about it.