Howard Gardner's theory of Multiple Intelligences has had a huge influence on school education. But its credentials lack justification, as the first section of this paper shows via a detailed philosophical analysis of how the intelligences are identified. If we want to make sense of the theory, we need to turn from a philosophical to a historical perspective. This is provided in the second section, which explores how the theory came to take shape in the course of Gardner's intellectual development. The third section looks at changes in the theory since its inception in 1983 and at problems with its applications to education. The paper concludes with a response to Gardner's critical comments on the argument to this point.