No - wisdom is not a cardinal virtue

- but prudence is.

How much knowledge is necessary for wisdom? A lot of modern followers of wisdom do not notice that the Stoics distinguished between wisdom understood as “knowledge about divine and human matters” (sophia in Greek, sapientia in Latin) and practical wisdom (phronesis, prudentia). The latter is knowledge about how to apply the first.

I suspect that overlooking this distinction is part of the reason why so many fall into the trap of thinking that the Stoics - in particular the Roman Stoics - were only interesed in practical wisdom.

Wisdom (sophia) is not one of the four cardinal virtues in Stoicism - since the cardinal virtues are all different manifestations of wisdom. The practical application of wisdom - when it's not courage, justice or temperance - is prudence (phronesis).

The mistaken idea that wisdom is one of the four cardinal virtues in Stoicism is very likely a result of the fact that modern English translations of the list of virtues in Marcus Aurelius' Meditations 5.12 translates "phronesin" with "wisdom" - which is very unfortunate from a Stoic point of view. George Long got it right in 1862 and Gregory Hays got it right in 2012 - as the only one among modern translators of Marcus into English: both use "prudence" to translate "phronesin".

Marcus is a little different from the rest of the Stoics. He distinguishes between eulogistia and phronesis and - and that distinction seems to run parallel with Senecas and Cicero's distinction between sapientia and prudentia.

And here is Cicero making obvious the difference between wisdom in the grand scale - knowledge of divine and human matters - and wisdom understood as the ability to apply that knowledge in how to live:

The foremost of all the virtues is the wisdom that the Greeks call sophia. (Good sense, which they call phronesis, we realize is something distinct, that is the knowledge of things that one should pursue and avoid.) But the wisdom that I declared to be the foremost is the knowledge of all things human and divine; and it includes the sociability and fellowship of gods and men with each other. If, as is certain, that is something of the greatest importance, then necessarily the duty that is based upon sociability is also of the greatest importance. Moreover, learning about and reflecting upon nature is somewhat truncated and incomplete if it results in no action. Such action is seen most clearly in the protection of men’s interests and therefore is concerned with the fellowship of the human race. For that reason this should be ranked above mere learning."

- Cicero, On Duties, 1.135