Neurons in the primate parieto-frontal network represent the number of visual items in a collection, but it is unknown whether this system encodes empty sets as conveying null quantity. We recorded from the ventral intraparietal area (VIP) and the prefrontal cortex (PFC) of monkeys performing a matching task including empty sets and countable numerosities as stimuli. VIP neurons encoded empty sets predominantly as a distinct category from numerosities. In contrast, PFC neurons represented empty sets more similarly to numerosity one than to larger numerosities, exhibiting numerical distance and size effects. Moreover, prefrontal neurons represented empty sets abstractly and irrespective of stimulus variations. Compared to VIP, the activity of numerosity neurons in PFC correlated better with the behavioral outcome of empty-set trials. Our results suggest a hierarchy in the processing from VIP to PFC, along which empty sets are steadily detached from visual properties and gradually positioned in a numerical continuum. These findings elucidate how the brain transforms the absence of countable items, nothing, into an abstract quantitative category, zero.
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