Why "lead a virtuous life?" To build stable and lasting joy that is not subject to the whims of Fortune or chance events. (I'm assuming you value this kind of joy.)
A few choice quotes below. These two are from the introduction to Seneca's Letters on Ethics (which I mentioned earlier up-thread):
• "In a word, Senecan joy comes from within, from a good person's own character and conduct: it arises from goodness itself and from right actions that one performs. This means that joy will not always be a matter of smiles, and laughter, for good actions may be difficult and unpleasant. A good person does these actions only when they are right, and only for that reason, but the doing itself is a good, and a reason to rejoice."
The above is also phrased as: "The reward for right action is having acted rightly."
• "Realizing that chance events lie beyond your control, the Stoic will find it unnecessary to experience grief, anger, fear, or even hope—all these are characteristics of a mind that waits in suspense, awestruck by things indifferent. We can have a life that truly involves joy (of the right sort) if we appreciate that the most precious thing of all ], and the only truly precious thing. lies within our control at all times."
And to quote from my favorite Stoic, Epictetus (this is from A.A. Long's exegesis on Epictetus):
• "Epictetus diagnoses unhappiness as subservience to persons, happenings, values, and bodily conditions, all of which involve the individual subject in surrendering autonomy and becoming a victim of debilitating emotions. Happiness, by contrast, is unimpededness, doing and experiencing only what you want to do and experience, serenity, absence of any sense that things might be better for you than you find them to be."
But the Stoics put a stake in the ground about what is virtuous. Doing so definitely has utility to society, but it has no more of a claim to being “correct” than a spider’s idea of a virtuous life: “eat flies and sometimes your offspring,” or whatever.
A few choice quotes below. These two are from the introduction to Seneca's Letters on Ethics (which I mentioned earlier up-thread):
• "In a word, Senecan joy comes from within, from a good person's own character and conduct: it arises from goodness itself and from right actions that one performs. This means that joy will not always be a matter of smiles, and laughter, for good actions may be difficult and unpleasant. A good person does these actions only when they are right, and only for that reason, but the doing itself is a good, and a reason to rejoice."
The above is also phrased as: "The reward for right action is having acted rightly."
• "Realizing that chance events lie beyond your control, the Stoic will find it unnecessary to experience grief, anger, fear, or even hope—all these are characteristics of a mind that waits in suspense, awestruck by things indifferent. We can have a life that truly involves joy (of the right sort) if we appreciate that the most precious thing of all ], and the only truly precious thing. lies within our control at all times."
And to quote from my favorite Stoic, Epictetus (this is from A.A. Long's exegesis on Epictetus):
• "Epictetus diagnoses unhappiness as subservience to persons, happenings, values, and bodily conditions, all of which involve the individual subject in surrendering autonomy and becoming a victim of debilitating emotions. Happiness, by contrast, is unimpededness, doing and experiencing only what you want to do and experience, serenity, absence of any sense that things might be better for you than you find them to be."