I am a trinity.

I have a mind, partly contained in my brain, though my mind is more than just my brain, for my mind lives on after my brain is dead..

I have a body, you can see it. Completely biodegrable, except the fillings in my teeth.

I have a spirit, that part which is neither of my other two parts, yet is my force of life.

I am a trinity.

This is not rocket surgery.

Eric's mind is fully Eric, yet only a part of Eric.

Eric's body is fully Eric, yet only a part of Eric.

Eric's spirit is fully Eric, yet only a part of Eric.

And if Eric is a trinity,

is God capable of being a Trinity?

Most certainly. 

Yes, He is,

Father, Son, and Holy Spirit