Devlin's Right Angle & The Precision Principle

Jul 10 2008
The Precision Principle

Like any good principle, the precision principle can be stated simply, is something everyone agrees with, and is flexible.

I've mentioned before that an example of a good principle is "free speech." This principle can be stated simply by a layperson like myself--"a person has the right to express herself however she chooses"--is something that we all agree with, and is broad enough to allow for stretching and shrinking its boundaries for different situations (the principle does not cover those who choose to yell "Fire!" in a crowded theater, for example).

Similarly, the precision principle is very simple: Instruction should be true. That is, what we communicate to students (however we do so) should be the truth, not a lie. And of course, everyone agrees with this, yet it is vague enough to allow for a great deal of flexibility in its interpretation.

As an example of this flexibility, consider this question: Which of the statements below is more precise, or more true?

A. This is a table.
B. This is an oak table.
C. This oak table is wobbly.
D. This table is brown.

Of course, the first problem we face in trying to make such a determination is that we don't know anything about the table in question. If it's not, in fact, an oak table, and it's not wobbly, then Choices B and C are out. If it is an oak table, but it's not wobbly, then C is out, and so on. Another problem may be the question itself. If we accept that all four statements are true, one would think it impossible for any one of them to be more true than another. We can certainly decide which is more precise, but substituting precise for true may erode our overall agreement inside this principle, given that many would not see true and precise as equivalent.

These are important problems, and attempting to tackle them is a part of that stretching and shrinking I mentioned earlier. But we can also set these problems aside for the moment. We can make the assumption that all four statements are true statements and that we are faced with the task of ranking them--somehow. In other words, we assume the role of judges deciding a case. We are all in agreement with the principle we are using to make our decisions, but we all interpret this principle somewhat differently. We must make some kind of decision, but this decision should not be arbitrary. Thus, our task is to not only make a specific judgment in this situation but also to formulate reasoned criteria for it where none have existed before.

One way judges devise criteria is by considering their implications. Suppose for example that we suggest that C is the best statement here with regard to truth or precision or whatever you want to call it. And suppose we reason that it is so because, out of all the choices, it contains the most information (table, oak, wobbly). Using this ("contains more information") as our criterion, we can trump statement C with a new statement (call it E): "This brown oak table is wobbly." Now we have four pieces of information (table, brown, oak, wobbly). And we can continue this process ad infinitum, producing "better" statements about the table and then whole sentences and then paragraphs. In the end, we could fill several books talking about the table. All of this gives us a clue as to the value of our criterion "contains more information." Following it alone leads us to impractical results for instruction (we can't spend infinity talking about one topic), so it must either be scrapped or supplemented in some way. Similarly, one could argue that A is the best statement, providing as a reason that it is the simplest of the choices. One can imagine, however, many situations in which this criterion--by itself--would steer us wrong.

So, how shall we rank instructional protocols with regard to precision or "truth"? What criteria can we formulate to guide us in making such decisions? We'll take that up next time.