My argument rises from Alvin Plantingas view of epistemology. I believe that we have properly basic beliefs and that we are doing our epistemic duty in believing those as long as we lack a defeator for those beliefs. Of course my own view of epistemology is founded upon theism and this is why I said that if evolution is blind and random force without any end in sight we have no rational justification to trust our cognitive faculties. I don´t believe that evolution is blind and unguided process but that our cognitive faculties are designed to aim at true beliefs. And I also hold to the principle of credulity.
But I also must add that if one is naturalist (I am not sure of you) must face arguments like Boltzmann brain, and A. Plantingas Evolutionary argument against naturalism.

I am really clad to finally find a place where to cordially dialog with reasonable and thinking people:

1.Mathematical thoughts cannot be emergent properties of matter since they are not material things. And I don´t see how the applying of the law of identity is question begging so please open that up a bit.
2. Your analogy of fermion is pretty inadequate unless you think that mind is some sort of particle and thus presuppose materialism which is not good way to argue. And I claim that "I" (ego, self) am not my body, I am a soul and have a body.
3. Change of mind does not mean change in substance. I am not claiming that I am equivocal to my thoughts or beliefs. My soul (substance) have faculties like: Thought, beliefs, intentionality/volition, desires and feelings/perceptions. It does not follow that change of mind (thought are state of consciousness) is change in substance. The ship of Theseus I think is not wholly applicable to my argument for following reasons:
1. I think it is pretty obvious that the ship with which Theseus started his trip is not identical with the ship which arrived to his destination.
2. Then if a person is identical to his brain and body he/she is not identical (law of identity applied here) ego with his/hers old self. This leads to the question "Can we hold person responsible for their moral behavior since they are not literally the same being who committed the actions (lets take Joseph Mengele who died as non-identical to his old self).
3. If we say that Theseus´ ship is still Theseus´ (which, in context of ownership, seems obvious) then who owns the body that I have or what makes my body my body. I Think it is best explained that I (my soul/mind) is what makes my body mine. It makes best sense to say that I am not identical to my body but that I posses a property of having a body, I am a soul.

Your thinking, I believe has serious flaws. If your cognitive faculties are a result of evolution by natural selection and random genetic mutation you don´t have any reason to trust your cognitive faculties. For evolution "aims" to survival and not to produce true beliefs. Evolution is completely pragmatic process and its end is to produce behavior not beliefs. This does not commit you ontologically to non-existance of truth but it puts you in position in which you have defeator for all of your reasoning.

I am not sure if I am getting it right. Are you proposing that mind is emergent property of brain function. And I do believe that mind has and genuine influence on the body and vice versa. If mind is emergent property of matter it follows that epiphenominalism is true. If epiphenominalism is true then, if you are naturalist, you cannot trust your cognitive faculties (or at least you don´t have justification for trusting them) and if that is the case you cannot trust your reasoning what led you to the conclusion that epiphenominalism is true. Thus you have a defeator for epiphenominalism.

I agree with you that we don´t, at least to my knowledge, have any a priori reasons for thinking that soul is eternal or survives death. My point with this argument is merely to show that naturalism (reductive materialism) is not enough to explain all phenomena in the Universe. But the reason why immateriality of the soul is significant is that it allows for the possibility of libertarian free will and thus for moral responsibility. Since if we are mere material beings (and matter works according the laws of nature, either statistical laws like quantum physics or newtonian mechanics) we have no possibility for free will or action. That is a different topic but that is why I want to argue for immaterial soul and super naturalism apart from my theological convictions.

There are things that are true about my thought life ect. that are not true of my physical brain and body. Here are few examples:
According to the law of identity, if A=B then what is true of A is true of B and vice versa.
1. We can say that my thoughts that 1+1=3 or all humans are white, are not true. My thoughts thus have a property of being right or wrong but it is not the case with my brain. My mental state (m) (e.g.1+1=3) at a given time (t1) is not identical with my brain function (b) at given time (t1). So m at t1 is not identical with b at t1. This is because it is illogical to say, for example, that my brain function is right or wrong nor is it the case that my thought of a book is oval shaped as is the electric charge in my brain while I think about a book.
2. "I" (ego, my consciousness/person) am not divisible kind of thing. All spatially extended objects can be divided in percents (I don´t mean that we would have the means to divide lets say fermions, but that they can be divided into percents) but I cannot be. I don´t know what it means to say that after a brain surgery (10% of my brains would have been removed) I would be 10% less a person. This seem quite the obvious. 1. So all spatially extended objects are divisible. 2. I am not divisible. 3. I am not spatially extended object. 4. My brain and body are spatially extended objects. 5. Therefore I am not my brain and body.
3. If it would be the case that I am identical with my brain and body I would not be the same thing through the course of time. It is pretty uncontroversial that if I have a pile of 10 bricks and I would take one brick away and change it to another the pile that I know have is not identical with the original pile. Since our bodies are constantly changing, loosing parts and gaining new ones, our bodies and brains are not identical with the bodies and brains we had a week ago. But if we are identical with our brain and body then we are not the same human beings we were in past. If we do not endure through one hour to another due to our metabolic processes many things becomes absurd. One example is that it is obviously stupid to require a payment of loan from a person who have not taken the loan. But this is what banks are doing if we are identical with our brain and body.

These are some of the reasons for thinking that we have a soul/mind.

Ps. Sorry for my english, I am not native speaker.