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On what basis are you concluding that the soul is my memory bank and therefore part of the brain?"
For what You consider is the soul aspect, what exactly does your soul (aspect) draw from for the actions you perform, in lets say your community = your brain's memory bank.
That memory bank all summed up, is effectively The Kam, we could also say it is the spirit of Kam (spirit is another subject)
As with any story or movie, if you want to know what's going on, you need to go to the Beginning.
In the Beginning was LOL;
Gen 2:7 -
And Yehowah God formed man (Body) of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.
The breath of life (oxygen) made the body come alive and that is now summed up as, called, a living soul = includes ALL body parts.
Think of yourself as a human computer.
Now think, if I said to you that I want you to do this or that with all your soul -> from what exactly are the actions that you're going to do this, coming from = your memory, thoughts = memory bank = your brain.
Hence your entire body according to the above, while living is deemed as a Soul, the above quote is Clear on that, from what I'm seeing.
The verse doesn't say that after man come alive or during, he received a soul, as you appear to be suggesting.
I'll try and give another example of the Soul aspect that I'm talking about;
Luke 10:27 -
So he answered and said, “ ‘You shall love Yehowah your God with all your heart, with all your soul, with all your strength, and with all your mind,’ and ‘your neighbor as yourself.’ ”
How is your heart doing the loving????????????????????
Naturally I haven't brought up all verses with the likes of heart, soul, mind etc, etc, but the few that I have, when used singularity, what they are in fact doing, is interchanging them, meaning they are being deemed (or pretty much) as one in the same or coming from the one source which I would say the brain's memory.
So, if we go on your take, re the soul, then based on the above quote, you would have to do the same with the "heart", which you simply cannot do and the Gen's 2:7 suggests the same?
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"And if it is then Matthew 10:28 becomes a very tricky to explain verse. From your interpretation Matthew would be saying that the brain is not part of the body."
And do not fear those who kill the body but cannot kill the soul. But rather fear Him who is able to destroy both soul and body in hell.
You have to effectively think spiritual here?
It would appear that you have not grasped what I suggested is the soul aspect that you don't want killed -> all your hope and dreams etc.
Memory, storage bank = brain.
Your memory bank, brain, all part of your soul that Gen says man became.
Luke 8:11 - Now this is the parable: the seed is the word of God.
12 - Those by the way side are they that hear; then cometh the devil, and taketh away the word out of their hearts, lest they should believe and be saved.
13 - But the ones on the rock are those who, when they hear, receive the word with joy; and these have no root, who believe for a while and in time of temptation fall away.
15 - But the ones that fell on the good ground are those who, having heard the word with a noble and good heart, keep it and bear fruit with patience.
Verses 12,13 are the soul aspect that is stolen, killed so to speak, their hearts and hopes destroyed, killed so to speak.
However, those in 15, their literal body can be killed but the memory bank as in what they stood for, believed (soul aspect being referred to) could not be killed, they held onto it, in death, hence they will be resurrected, no second death.
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"But there is no Biblical evidence that the soul is the brain my friend."
I've never said it was, that is your misunderstanding. 
Man is a living soul and in that soul is Ya brain, you might say The You LOL.
