Are You Your Mind?
Well if you are not your personality, maybe you are the thing behind it doing the thinking. Unfortunately, the same logic explored in regards to your body applies. Not a single thought in your mind is the same as one you had when you were born. Your thought processes also change as you mature.
Also, consider this: is thinking even a prerequisite to living? It is possible to strike all thoughts from your mind. Monks and yogis practice this frequently in meditation. The yogi Sadguru (5) claims that he will often go days without thought. The Old English word for mind is gemynd (6), which means “memory or thought.” Therefore, in a moment where there is no thought, there is also no mind.
So in such a moment, do you lose identity? Of course not, there is still sameness or coherence in your existence from when thoughts ceased to when they resume. Therefore, you must have identity. But what is it?