A set of frontoparietal brain regions - the multiple-demand (MD) system [1, 2] - has been linked to fluid intelligence in brain imaging [3, 4] and in studies of patients with brain damage [5-7]. For example, the amount of damage to frontal or parietal, but not temporal, cortices predicts fluid intelligence deficit [5]. However, frontal and parietal lobes are structurally [8] and functionally [9, 10] heterogeneous. They contain domain-general regions that respond across diverse tasks [11, 12], but also specialized regions that respond selectively during language processing [13]. Since language may be critical for complex thought [14-24, cf. 25-26], intelligence loss following damage to frontoparietal cortex could have important contributions from damage to language-selective regions. To evaluate the relative contributions of MD vs. language-selective regions, we employed large fMRI datasets to construct probabilistic maps of the two systems. We used these maps to weigh the volume of lesion (in each of 80 patients) falling within each system. MD-weighted, but not language-weighted, lesion volumes predicted fluid intelligence deficit (with the opposite pattern observed for verbal fluency), suggesting that fluid intelligence is specifically tied to the MD system, and undermining claims that language is at the core of complex thought.