Plato claimed that all virtues are one – all are reducible to wisdom, and he basically answered the objection that we can know the good and still do evil by saying that true knowledge comes after a conversion process, in essence then, making his statement tautologically true. If you are truly wise, your soul has been converted to doing good and eschewing evil, acting wisely, justly, courageously, temperately, and piously.
But could it be more than a tautology?
Plato had a N=1 case right in front of him – Socrates, the wisest man and the best man, the most just, the most courageous, the most temperate man, and yes, even the most pious man (criticizing the immoral portraits of the gods given to us by the poets is hardly impious; rather the opposite), despite being charged with impiety by some powerful and unethical people in Athens.
Today the big Platonic question can be answered with some empirical definitions, some data collection, and some mathematical analysis.
First – define all the virtues empirically.
Second – Use random sampling to collect lots of data and force rank all of the people for all of the virtues. Check for normal distribution (highly likely they will be because the definitions are empirical [measurable]; we are not all equal in all virtues; and there would be lots of data points).
Third – use the Chi-Squared test for independence. The null hypothesis, Ho = all of the virtues are independent. H1, the alternative hypothesis, is that at least some are related (dependent). All could be related, as Plato claimed, all dependent on true wisdom, as the Chi Square tests would show.
Interesting aside: also measure happiness and see if any/all of the virtues can be correlated to happiness and whether happiness is a better independent or a dependent variable.