 To be sure, I do not come to this definition of circle by looking up to the heaven of Ideas; in fact, I may just be instructed about it by my geometry teacher. But what is not given to me by my geometry teacher is the understanding of the fact that what is expressed by the definition is indeed what I originally rather vaguely conceived by my concept abstracted from visible circles. This “flash” of understanding, when I realize that it is necessary for anything that truly matches the concept of a circle to be such as described in the definition, would be an instance of receiving illumination without any particular, miraculous  revelation.[24]