November 05, 2005

Better to x than to not y

I read the following in this article on condensed Bibles in this weekend's NYT (emphasis added):

"But if the man in the street is not reading the Bible," Mr. Budd continued, "you have to ask, isn't it better to read a short version than not to read the long version?"

Obviously, what Mr. Budd means is: "isn't it better to read a short version of the Bible than not to read (any version of) the Bible at all?" But what he actually said isn't as clear as that, and the ambiguity of his statement seems to be what's at the core of the controversy over condensed Bibles reported in the article.

First, let's get rid of the interrogative format and focus on the gist of the claim couched in Mr. Budd's statement:

it's better to read a short version than not to read the long version (of the Bible)

This statement makes two distinctions among people: those who read a short version of the Bible (vs. those who don't) and those who don't read the long version (vs. those who do). Let's give these groups some names:

  • Short-version readers = SV
  • Short-version non-readers = ¬SV
  • Long-version non-readers = ¬LV
  • Long-version readers = LV

We can thus re-write the essence of Mr. Budd's statement as follows, where '>' means "is better than" (or "is greater than on the goodness scale"), and SV / ¬LV stands for being a member of the relevant group.

SV > ¬LV

In other words, being a short-version reader is better than being a long-version non-reader (all else being equal).

Putting aside the relatively uninteresting (and quite likely null) set of folks who read both versions (the intersection of SV and LV), the problem here is that SV is a proper subset of ¬LV: if you're a short-version reader, you're (likely) a long-version non-reader. So what Mr. Budd's statement means depends on how goodness is measured.

Here's what I mean. Suppose everyone starts out with 50 points on the goodness scale. Long-version non-readers (members of ¬LV) get -10 points, and short-version readers (members of SV) get +2 points. So if you're a member of both groups, you'll have 42 points (all else being equal), whereas if you're only a member of ¬LV you'll have 40 points. Assuming (a) that SV and LV don't intersect, so SV is really shorthand for SV&¬LV, and (b) that ¬LV refers to the complement within ¬LV of SV&¬LV, namely ¬SV&¬LV, then under this conception of things, the statement [SV > ¬LV] above is basically true, because 42 > 40.

However, suppose that long-version non-readers simply get all their goodness points erased -- that is, they have 0 points no matter what. Then [SV > ¬LV] is false, because SV = 0 (again, assuming SV and LV don't intersect) and ¬LV = 0. In other words, there's no substitute for reading the long version of the Bible, which is exactly what folks who don't approve of condensed Bibles seem to be saying.

Like I said, it's clear what Mr. Budd meant by what he said. But somehow, it's not clear that he said what he meant.

[ Comments? ]

Posted by Eric Bakovic at November 5, 2005 04:06 PM