Full Idea
Nagel argues (because of brain bisection experiments) that we should jettison our commonsense assumption that the unity of consciousness is an all-or-nothing affair.
Gist of Idea
Brain bisection suggests unity of mind isn't all-or-nothing
Source
report of Thomas Nagel (Brain Bisection and Unity of Consciousness [1971]) by Michael Lockwood - Mind, Brain and the Quantum p.84
Book Reference
Lockwood,Michael: 'Mind,Brain and the Quantum:The Compound 'I'' [Blackwell 1991], p.84
A Reaction
It seems wrong to call it 'commonsense'. It is an assumption that precedes any judgement, but if you rapidly grasp that your mind is in your brain, it becomes common sense that you can cut lumps out of your mind.