From Spearman's famous 1904 paper to Carroll's recent book on factor analytic results from a multitude of studies, there has been one consistent conclusion: 'g', or general intelligence, is the factor that defines the phenotype for intellectual functioning. It is no overstatement to say that g is undoubtedly the most important psychological construct discovered in this century. It predicts more and is implicated in a wider range of behaviour than any other psychological construct. The empirical support for g is extensive and overwhelming. It would seem that g is the perfect phenotypic definition of intelligence. I argue that it is not the perfect phenotype. If we are to understand intelligence, we need to define a new, more elaborate definition of intelligence taking g as the starting place. It must be remembered that g is a statistical abstraction. Current formulations of g are largely silent about the composition of g. I argue that g is actually made of further separable basic cognitive processes and does not represent a single underlying entity. These basic cognitive processes are integrated into a complex system in the brain that makes them difficult to identify. None the less, until these basic processes are identified and related to brain function there are a number of findings that cannot be explained and this will inhibit scientific progress.