In preparation for my Plato seminar tomorrow, I have been reading over book 6 and 7 of The Republic. I noticed that in the early passages of Book 7 Socrates admits to an assumption with unfortunate implications. Proceeding his initial exposition of the Cave parable, Socrates qualifies the conclusions drawn in the final section of Book 6:
If you identify the upward path and the view of things above with the ascent of the soul to the realm of understanding, then you will have caught my drift — my surmise — which is what you wanted to hear. Whether it is really true, perhaps god only knows. My own view, for what it’s worth, is that in the realm of what can be known the thing seen last, and seen with great difficulty, is the form or character of the good. But when it is seen, the conclusion must be that it turns out to be the cause of all that is right and good for everything. (517b)
Thus, the truth of Socrates’ first principle, the Good, is no more than an assumption. This assumption is a troubling one, given his preceding explanation of the divided line, particularly his distinction between thinking and understanding, as given by the contrasting examples of philosophic and scientific inquiry. To elucidate this contrast, Socrates first provides an example of thinking, where one “is compelled to work from assumptions, proceeding to an end-point, rather than back to an origin or first principle. (510b)” By way of analogy, Socrates characterizes the methods of the geometers:
When people are doing things like geometry and arithmetic, there are some things they take for granted in their respective disciplines. Odd and even, figures and the three types of angle. That sort of thing. Taking these as known, they make them into assumptions. They see no need to justify them either to themselves or to anyone else. They regard them as plain to anyone. Starting from these, they then go through the rest of their argument, and finally reach, by agreed steps, that which they set out to investigate. (510c)
This methodology moves from the realm of the doxa to the realm the forms, but since they “use assumptions as first principles” (511d) and treat their models as images rather than forms, they relegate their inquiry to the domain of belief and conjecture. Given that the faculties of reason are a tool of mathematics, however, the geometers reach the first part of the second section, that of thinking, the “halfway house between opinion and understanding. (511d)” This differs from the philosophic mode of inquiry, which “goes from an assumption to an origin or first principle which is free from assumptions. (510b)” The philosopher, then, does not proceed from the doxa, but from the dialectic alone:
Finally, by the other section of the line representing the objects of understanding you must take me to mean what reason itself grasps by the power of dialectic, when it uses assumptions not as first principles, but as true “bases” — points to take off from, entry-points — until it gets to what is free from assumptions, and arrives at the origin or first principle of everything. This it seizes hold of, then turns round and follows the things which follow from this first principle, and so makes its way down to an end-point. It makes no use at all of any object of the senses, but only of pure forms — working through them and towards them. And it ends in forms. (511bc)
Here we land in some trouble. Socrates states that for one to gain access to the realm of understanding, one must proceed from assumptions to that which lacks assumptions–a first principle–by the dialectic alone. Now, Plato began his dialectic with an inquiry into the nature of justice, and moved from justice to knowledge or understanding. It is his premises regarding these concepts that entail his first principle, and by assuming the truth of his first principle he seems to be affirming the consequent.
Socrates is running into the problem of the criterion. The power of the dialectic can only establish the validity of his argument, not its soundness. To establish the truth of his premises he faces a choice, he must either (a) descend into the realm of the doxa or (b) justify a circular form of reasoning. Given (a) Socrates is in no better a position than the geometers, and would thus be relegated to the halfway house between opinion and understanding. The alternative, on the other hand, is a more interesting matter. That is to say, if Socrates’ arguments are enthymematic, in that they presuppose his first principle, G, and if G entails his conclusions regarding knowledge, justice, and the like and these conclusions jointly entail his first principle, then the truth of G establishes the soundness of his arguments. Circular, but not viciously so. A problem remains, unfortunately, for the truth of G is only assumed, not established, and it seems the only method by which Socrates might establish this assumption is, again, either (a) by a descent into the realm of the doxa or (b) by an appeal to the agreement of his interlocutors. Unfortunately, given this strategy Socrates has simply passed the buck, for (a) lands him back in his halfway house and (b) simply widens the circle.
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