One's mind and one's brain are not identical

Hi again,Again, very interesting argument, I am very interested in seeing how this pans out.As you noted in your defense of P1, the whole argument is built off of the acceptance of the Indiscernibility of Identicals. If this "law" (your wording) is therefore undermined then it will be found to be an invalid argument. It is therefore necessary on my part to argue against the Indiscernibility of Identicals primarily in this debate.Argument #1: Symmetrical SpheresThe most common objection to the Indiscernibility of Identicals comes from the very link you provided. Which I will present that argument here."Imagine a possible world that contains just two perfectly round symmetrical spheres. The spheres have the same diameter, they are an equal distance from each other, they are the only inhabitants of a completely symmetrical universe, they are both made of solid iron, etc. Intuitively, such spheres in such a world would have all and only the same properties; they are qualitatively identical. Yet, by stipulation, there is supposedly two of these spheres, not one. But if "they" are qualitatively identical, then by the Identity of Indiscernibles, "they" are numerically identical; "they" are one, not two. Thus, either (i) there cannot be a world where there are two qualitatively identical objects or else (ii) the Identity of Indiscernibles is false. Since it seems that we can imagine a world with two numerically distinct yet qualitatively identical objects, then (by disjunctive elimination) the Identity of Indiscernibles must be false."[1]In the link you provided it then goes through list of responses and problems with those as well, but ultimately I do not think this is a problem that can be answered for those who hold to the Indiscernibility of Identicals.Argument #2: Secret IdentityAgain, these arguments are nothing new on the matter but I will present them here and defend them because I do not believe the objections are strong enough. (i)Clark Kent is Superman's secret identity; that is, they're the same person (identical) but people don't know this fact. (ii)Lois Lane thinks that Clark Kent cannot fly. (iii)Lois Lane thinks that Superman can fly. (iv)Therefore Superman has a property that Clark Kent does not have, namely that Lois Lane thinks that he can fly. (v)Therefore, Superman is not identical to Clark Kent.[2]Your own listing of the law states the following:"The law states that if A is identical to B, then whatever is true for A is also true for B."This example would refute that notion because of the contradiction found in P1 and P5, namely that one lets us know that they are the identical (one being a secret identity), and the other revealing that they cannot be identical according to this law because of what Lois Lane believes. This is also linked in the source you provided for a reference in in your opening argument, where it states, "seeing if there is a property that one has that "the other" doesn't, will aid us in determining whether Clark Kent is in fact idenitcal to or distinct from Superman." As I have provided a relational property, and belief about these two identities I assert that according to this kind of logic it cannot be demonstrated they are identical.Concluding Statements:If one absolutely affirms Leibniz's law, which is the Law of Indiscernibility of Identity, then I agree that it is difficult to disagree with the logic. However, if my two arguments stand and remain unrefuted throughout this debate, then the foundation this argument is built on cannot support it's ultimate conclusion.Look forward to your response on the matter, and I hope to learn a thing or two throughout the course of this debate. :)Kind Regards,TrueScotsman[1] http://www.oberlin.edu...[2] http://en.wikipedia.org...