The Hippocratic Oath is a Philosophical and Initiatory text that is not exclusively addressed to doctors, but to anyone who would like to advance in the healing of themselves. Its aim is the creation of a new society in which Justice and the entirety of Moral Virtues will be applied, so that all people live fraternally among each other, as they will have managed to subdue the influence exerted on them by the materialistic way of life and will be more interested in the collective interest rather than the individual. Hippocrates' fundamental position is that a Person can be Healthy only when living in a Healthy Society, which will be suitably shaped through the Art of Medicine. In order to analyze the philosophical meanings of the Oath, an attempt is made for the first time to connect Hippocrates' Medical "Specialties" with Aristotle's "Categories" and Pythagoras' "Pairs of Opposites," so that we are allowed to enter the sanctuary of this Healthy Society of which we must strive to become its future members.