The philosopher, Michael Huemer, recently wrote a piece arguing against historical philosophy. In his words:  

We should think, for example, about what is the right thing to do, not what Kant said was the right thing to do; we should think about what is real, not what Plato said was real.

His primary target is academic philosophers studying history, but it's a fair point and one that we can restate it to applying and studying the philosophy of Stoicism today:

We should think about what the right thing to do is, not what Marcus Aurelius said was the right thing to do; we should think about the correct theory of mind, not what Epictetus said about how the mind works.

We can paraphrase another one of Huemer's points to make this challenger even sharper:

There are people today who are followers of Epictetus. They are Stoics. I think that’s crazy. If Epictetus lived today, there is no way that he would be a Stoic. If we brought him through time to the present day, he would swiftly start learning modern science, whereupon he would throw out his outdated worldview, and he’d probably laugh at the modern Stoics.

A serious challenge, but does it land? Yes and no.

Let's take the case of Epictetus. As an exercise, let's actually ask: "if he were alive today, what would he throw out from Stoicism?"

Ancient Stoicism had its own versions of physics, logic, and ethics. It's was a comprehensive worldview.

The physics and logics are certainly largely outdated. The fundamental elements are not water, fire, earth and air! We no longer think of the world in the teleological way that ancient Stoics did. Epictetus would likely, throw out most of Stoic physics. And I imagine he would do so happily. We've made a lot of important intellectual progress since ancient Rome. What would stay? Perhaps the Stoic ideas on determinism and free will. But I don't think the Stoics are the best place to go if you'd like to think about those issues.

We've also made impressive advances in formal logic (and probability) that Epictetus would be excited to learn about. Formal Stoic logic is incomplete, but the key epistemic idea: the importance of thinking objectively about the world using reason, that's an idea we need to keep. Epictetus constantly reminded his students to practice thinking well and I doubt he would change that if he found himself in the modern world.

What about the ethics? The Stoics focused on virtue ethics, a philosophical tradition that is alive and well today. This is something Epictetus would likely keep. And there are good arguments for doing so. Even here though there were cultural prejudices that Epictetus would need to shed.

From this brief exercise, we can see that some parts of traditional Stoicism would need to be updated. Arguably, modern Stoicism has already applied the update. Philosophers like Massimo Pigliucci, Lawrence Becker, Donald Robertson and more have contributed significantly to this project. The key Stoic ideas of modern Stoicism: the cognitive model of emotion and virtue ethics hold their own intellectual weight. It's Stoic psychology and ethics that have the most to offer.

Huemer may be too negative on historical philosophy, but he does get the philosophical attitude completely correct. Thinking well is a matter of asking, "is this true?" Not, "what did the Stoics say?" It's about asking, again and again, "are there good reasons to believe this?" Not, "what did Seneca believe?" In part, this is one reason why I ask questions like: "What did the Stoics get wrong" in the Stoa Conversations. Constantly questioning, embracing reality, and getting at what is true is the Stoic thing to do.

All this being said, the purpose of the reading Stoic writings isn't always to uncover the truth. Often, it's to motivate us to be better people.

Seneca's advice to Lucilius, Marcus Aurelius's notes to himself, and Epictetus's admonishments of his students are still relevant today.

The fact that they've withstood the test of time is evidence of their power.