For system interrupts to work, memory is required, because after the interrupt call is successfully completed, the system must return to the state that it was in prior to the interrupt. "Why do we so often get confused when we're interrupted? Because then we have to keep our place in several processes at once. To keep things straight, our memory-control machinery needs intricate skills." Importantly, we are largely unaware of the intricate control structure required for this to work.
(NB: "Keeping track of multiple things" argument strikes me as having the same structure as Pylyshyn's arguments for FINSTs.)
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