I Respond

If we consider the last two posts, we can see that they resemble a disputed question. However, unlike St. Thomas’s Summa Theologiae, and instead in the technical manner of a disputed question, there are arguments on both sides. Additionally, I did not include the typical “response of the master,” nor did I include responses to the arguments. I will explain these omissions shortly.

James Chastek, in the passage quoted here, asserted that it is difficult to make your opponent’s arguments without relating to them as something to be refuted. As we have seen from these examples, there is actually no big difficulty here, and historically this was done with the disputed question. In principle people could even write books this way, and they probably have, on occasion. One could write an entire book on the actual infinite with the structure, “Part I: An Actual Infinite is Possible,” and “Part 2: An Actual Infinite is Impossible.”

There are a lot of reasons why people don’t do this in general, and why for example I would not write blog posts like this in general. One factor is the practical issue that it is twice as much work. Another is the concrete goal of a book or a blog post.

Why did I not include the response of the master? In the medieval schools, the arguments on each side were formulated by the students, followed by the master’s response and his answers to the arguments. Thus, since the master did not compose the original arguments, he could make a new argument for his conclusion, outside of the original arguments. But since I was the one composing the arguments on each side, if I thought there was a very strong argument for one conclusion, I could simply include it there. Consequently a special response would simply repeat something contained in the series of arguments.

But there is more to it than this. A special response would also give away my personal opinion, which I preferred to avoid. If I could simply state the strong arguments in the series, nothing would be added by restating it as the “response of the master” except the bare fact that I agree with the one side rather than the other.

Consider how students will react to such a thing in real life. In terms of the argument, nothing is added to their understanding of reality by this response. Nonetheless, they receive additional evidence in favor of one conclusion, namely that the teacher agrees with one side. So they will have an additional reason to agree with that side, a real reason, but not one that adds to their understanding of the issues. Thus, to the degree that they believe that this response has contributed to their understanding, they are simply mistaken, and consequently believe that they understand things better than they do.

The issue of the responses to the arguments in somewhat different. If someone wrote the above book on the Actual Infinite, presumably Part I would also include responses to the main arguments in Part II, and Part II would include responses to the main arguments in Part I. This is in fact very important for understanding. Although arguments are never one-sided, they are frequently mostly one-sided, where most of the best arguments and evidence are indeed on one side. And in such cases, this usually becomes most clear when one considers the responses to the opposing arguments, and, consequently, where one begins to actually understand the matter at hand, and to recognize the truth of the matter.

So I did not include such responses because most likely they would reveal more clearly which side had the stronger argument, and which side I agreed with. But note that in principle these two things would be the same: the reasons which would show that I agreed with one side, would show that this was the better and more likely side. In practice of course there might be other ways that someone could guess my opinion, as for example from the style of the arguments and so on. (For the record, my opinion cannot be determined by which side went first; that was determined by the flip of a coin.)

Someone once posted on Twitter (I can no longer find the particular post) something along the lines of, “How can you be unbiased if I can tell which side you are on?” We can see here that in fact there is a valid answer to this: if I simply present all of the best arguments for both sides, together with their responses, then you can tell which side I am on by determining which side is probably right, and the fact that you can determine my side in that way does not suggest that I am biased. On the other hand, if you note that I have missed strong and important arguments on the side of the part that seems weaker in my presentation, that might be a reason for thinking that I am biased.

That said, the responses to the arguments in the previous posts, and consequently the “response of the master,” is left here as an exercise for the reader.

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