Regarding Logic as a branch of Philosophy, and defining Philosophy as the “science of a real existence,” and “the research of causes,” and assigning as its main business the investigation of the “why, (tä dÐoti),” while Mathematics display only the “that, (tä åtÈ),” Sir W. Hamilton has contended, not simply, that the superiority rests with the study of Logic, but that the study of Mathematics is at once dangerous and useless.∗