Philosophers today are inclined to propose virtues are either something subjective or something universal. However, Confucius and Aristotle,who made the most profound investigations into virtues, did not develop such theses. The deep-seated reason lies in their belief that there is always a possibility for a human being to become a man of practice, which cancels the need of proposing subjectivity thesis. The reason for their not raising the universality thesis of virtues is that they do not think that virtues are directly universal to all contemporarily existing minds. Rather, in their view, virtues involve a possible universality that may present in a virtuous mind. We can summarize Aristotle's view into the concept of possible universality of virtue understood in terms of the perfect state of mind, since he explains the perfect state of mind in terms of perfect state of activity, and makes his investigations with an eye to the interactions between people with similar states of virtues. The view of Confucius can be summarized into the concept of possible universality of virtue understood in terms of the history of mind, since his investigations are made from the point of view of the states of mind reached through virtuous practices, i.e., a historical process of human life in which one's pre-dispositions and feelings gradually reach some state of natural harmony and gains continual enrichment, and with an eye to the interactions between virtuous people and common people. From that similarly expressed view we can reasonably infer that virtues do possess the character called by today's philosophers as universality, but it is a possible universality whose possibility is based on practice and on the development of virtuous minds.