Generalized quantifiers like "all cars" are semantically well understood, yet we know little about their neural representation. Our model of quantifier processing includes a numerosity device, operations that combine number elements and working memory. Semantic theory posits two types of quantifiers: first-order quantifiers identify a number state (e.g. "at least 3") and higher-order quantifiers additionally require maintaining a number state actively in working memory for comparison with another state (e.g. "less than half"). We used BOLD fMRI to test the hypothesis that all quantifiers recruit inferior parietal cortex associated with numerosity, while only higher-order quantifiers recruit prefrontal cortex associated with executive resources like working memory. Our findings showed that first-order and higher-order quantifiers both recruit right inferior parietal cortex, suggesting that a numerosity component contributes to quantifier comprehension. Moreover, only probes of higher-order quantifiers recruited right dorsolateral prefrontal cortex, suggesting involvement of executive resources like working memory. We also observed activation of thalamus and anterior cingulate that may be associated with selective attention. Our findings are consistent with a large-scale neural network centered in frontal and parietal cortex that supports comprehension of generalized quantifiers.