Of course you know that Plato’s Republic is still taught in introductory philosophy courses (and some advanced ones as well). And I assume that you are also aware that the book is over 2300 years old. Together those two facts are an embarrassment. No other respectable discipline relies in texts that are so old. The ancient Greeks wrote about math and science and logic as well, but their writings in these areas are not presented to beginners as valuable instruction; students of those disciplines often learn about them only later when learning about the history of their discipline; and they are often referenced directly only by historians of the field. The only other field I can think of that relies directly on books of such age is religion/theology, and that is not good company to be in, given that we expect philosophy to a) explain the world and b) have rational foundations.
So why do we still teach and read The Republic, outside of the context of understanding the history of the field, or an understanding of ancient Greek literature? Let me investigate a few possibilities (from least likely to most likely).
I. The Republic is perfect
If The Republic is completely free from error then it would make sense that we would still reference it directly. Since it couldn’t be improved on why bother writing new books on the same issues? I find this explanation unlikely, since nothing else the Greeks did was completely free from error (it is rare that anybody is completely free from error). Thus it is reasonable to conclude that The Republic contains some mistakes, and could be improved on.
II. The Republic cannot be improved upon because we are bad at philosophy
Another possibility is that while The Republic contains errors no one has been able to write anything better on the same issues because we are just that bad at doing philosophy. It is hard to refute this claim, since philosophy often seems to get off track, to wander in circles, and to spawn groups of philosophers who produce nothing of value. But despite this I remain an optimist; even though there are many philosophers who didn’t accomplish anything of value it seems equally obvious that there are many who did. Although they may not have given us all the answers it seems possible to point to many of them as improving our knowledge on certain topics, including those discussed in The Republic, at least somewhat (for example, Rawls on justice).
III. The Republic cannot be improved upon because there are no philosophical truths
A possibility, similar to the previous one, is that we can’t improve upon The Republic because there are no truths about things like justice and the optimal structure of society, and that all philosophy is simply giving different opinions or different viewpoints. But even if this were the case it doesn’t explain why we still teach with The Republic. Especially if it were the case it would seem better to write a new book about justice and society that says that there is no truths about these matters, and then goes on to present the major viewpoints put forward on the issue, including those presented in The Republic. Since we don’t use such a book instead, or feel that it would be an acceptable substitute, I reject this possibility as a suitable explanation.
1V. Respect for tradition
It could be that philosophers simply have a very high regard for tradition, and so feel the need to keep the traditional texts alive, even if they have been surpassed by more recent works. To me this seems partly true, but it doesn’t explain everything. If this was the whole explanation we would expect The Republic to be taught only in a few upper division classes covering the history of philosophy. And that is not the case, not only is The Republic found in a number of other classes, but ancient philosophy tends to be one of the introductory courses, not an upper division class. Additionally, other disciplines have a respect for their traditions too (demonstrated by the fact that they teach history of … classes), but never use the primary texts themselves, but rather rely on commentaries and summaries of them.
V. Philosophers are idiots
Another possibility is that there are certain schools of philosophy (schools of thought, not universities) that are made up of idiots, or have idiotic ideas. By idiots in this context I mean that they misunderstand the purpose of philosophy, or think that arguments from authority are a good way to advance philosophy, or who think that there are no philosophical truths, or who think The Republic is perfect. Or, in other words, that there are people who seriously buy into one of the reasons to keep The Republic around that I discarded above. Certainly I believe that such people exist, but we should hope that the effort required to get a doctorate would filter out most of them. Still, it probably contributes somewhat to the problem; those pesky relativists are like roaches, you can never completely stamp them out.
VI. The questions are still relevant
A more optimistic possibility is that the questions raised by The Republic are still relevant, even though the answers aren’t. Certainly this is true, we still wrestle with the problems that Plato did his best to address. But even so we would expect that these questions would be turned into their own book, with perhaps a survey of attempted answers, and that this book would be the basis of the relevant introductory class. But see VIIb.
VII. Philosophy lacks an official method
The last possibility is that we still use The Republic since philosophy lacks an agreed upon method. And that because of this we simply expose students to the works of philosophy that have proven themselves to be important and hope that they will pick up the method of philosophy by exposure. Without an agreement upon how a philosophical investigation should be conducted no one can write a book that distills that method into form suitable for teaching and learning by itself. I think that this is the primary reason that we still teach The Republic in introductory courses, although I am sure some of the above factors contribute as well. To drive the point home let me compare logic to philosophy. If we taught students logic like we taught them philosophy they would be made to read the works of the great logicians, starting with Aristotle and working their way up to modern authors. No one would definitively tell them which authors were right and which were wrong, nor would they be taught how to construct and validate proofs, standard symbolic notation, ect. Instead we would expect them to just pick these things up by reading Aristotle, Hilbert, Tarski, Frege, Russell, ect. Not only would this confuse students, but it would create poor logicians as well. Instead of there being agreement as to how to structure a proof and as to which claims were right and which were wrong there would be widespread disagreement, and logic would progress slowly if at all. And this is exactly the problem we face in philosophy today. No one can agree on which arguments are right and which are wrong, and no questions stay answered for long. There isn’t even a standard way of approaching philosophical problems. The lack of a unified method for doing philosophy is a problem that underlies all the problems facing philosophy, one sign of which is that we still teach The Republic in introductory philosophy classes instead of in ancient Greek literature classes.
VIIb. Lack of replacement books
So the reason then that we still teach The Republic is that we have no replacement for it. Not because we haven’t been able to surpass Plato, but because there is no agreement upon what is right and what is wrong about The Republic in terms of its method. So, while we can give students commentaries summarizing its claims and the questions it addresses, we can’t give them a guide to the lessons about what philosophy is that they are supposed to take away from it. And so we keep making them read it.