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This is the context:

So, in principle, with a brain connectivity map we would have a vast trove of objective data about the brain, and with our own introspection, we have a vast trove of subjective data about consciousness. One might think it would then be possible to abstract out the relevant kinds of principles that connect the objective to the subjective. I don’t think this would mean that we would bridge the mind/brain gap, but we would have boiled down this conundrum to the simplest possible principles.

source: The enigma of human consciousness.New York Academy of Sciences.

What is the meaning of "abstract out" in this context?

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    distill from, extract only the parts necessary – user105719 Dec 26 '19 at 23:00
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It means that you (are able to) only take the relevant parts. "Abstract" here is a verb that means "to remove or extract".

From Collins,

If you abstract something from a place, you take it from there.

[formal]

  • ...a licence to abstract water from the River Axe.
  • The author has abstracted poems from earlier books.

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