There is an infinity of realized and potential creative things, creative ideas, and creative performances, and yet there is no such thing as creativity, at least not in the two ways most of us think about creativity. (1) There is no general essence of creativity, no indispensable factor or shared quality that is an intrinsic part of all creative ideas, performances, or products. Creativity and expertise are very different things, but what makes a painting, a scientific theory, or a dance performance creative varies across domains in the same way that what constitutes expertise varies in these different disciplines. (2) And just as learning what a haiku is will not increase one's expertise in cooking or cosmology, developing creative-thinking skills helpful in writing poetry will not make one a more creative chef or astronomer. Despite these constraints, it has been shown that creativity training can often result in more creative products, ideas, and performances, but primarily when trainers have put aside these two misguided and counter-productive ways to conceptualize creativity.