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Thirty years of functional neuroimaging have been accumulating a wealth of evidence of the intricate relationship between structure and function. However, potential overlap, independence, granularity of and gaps between functions remain poorly understood at the global level. In this study, we extracted the latent structure of the current brain-cognition knowledge and revealed its organisational structure. This knowledge has been derived from the most comprehensive meta-analytic fMRI database (Neurosynth) that was used to compute a two-dimensional embedding space – the brain-cognition space – capturing the relationship between brain functions as we know it. The structure of the space allowed us to test the degree of logic in the relationship between functions statistically – a rationality index – and to predict the activation pattern of new and still undetermined functions. The organisation and predictive framework defined by the brain-cognition space will foster the investigation of novel functions and guide the exploration of the fabric of human cognition.