Abstract: The tacit assumption that relative enlargement and differentiation of brains reflect a progressive evolutionary trend toward greater intelligence is a major impediment to the study of brain evolution. Theories that purport to establish a linear scale for this presumed correlation between brain size and intelligence are undermined by the absence of an unbiased allometric baseline for estimating differences in encephalization, by the incompatibility of allometric analyses at different taxonomic levels, by the nonlinearity of the “criterion of subtraction” used to partition the somatic and cognitive components of encephalization, and by the failure to independently demonstrate any cognitive basis for the regularity of brain~body allometry. Analyzing deviations from brain~body allometric trends in terms of “encephalization” obfuscates the complementarity between brain and body size and ignores selection on body size, which probably determines most deviations. By failing to analyze the effects of allometry at many levels of structure, comparative anatomists have mistaken methodological artifacts for progressive evolutionary trends. Many structural changes, which are assumed to demonstrate progression of brain structure from primitive to advanced forms, are the result of allometric processes. Increased brain size turns out to have some previously unappreciated functional disadvantages.