Any and Or

Here's a fun quotation from my admin casebook:

Do you think the words "any" and "or" have as fixed a meaning as Chief Justice Rehnquist does? (And, by the way, do you think the just-preceding sentence would mean something different if it said: "Do you think the words "any" or "or" have as fixed a meaning as Chief Justice Rehnquist does?)

Peter L. Strauss et al., Gellhorn and Byse's Administrative Law 1007 (10th ed. 2003).

Naively. I'd say "no" and "yes," respectively, but I'm open to arguments that the second answer should also be "no."`

Now for the logical games. As a threshold matter, there's a missing quotation mark near the end, between the "?" and the ")". Presumably, it'll appear in the eleventh edition. One could object to the failure to encode embedded quotation marks; the appropriate fix is left as an exercise for the reader.

More seriously, let's try repunctuating the first sentence to a new, and somewhat more amusing version:

Do you think the words "any" and "or" have as fixed a meaning as "Chief Justice Rehnquist" does?"

My answer to this one, unfortunately, turns on the meaning of "as." On a broad reading, I'd say "yes," but if we demand strict equality, I'd say "no."

More subtly, there's a semantic problem lurking in here. For two words to have "a" meaning, as the first question asks, they must have the same meaning, implying that "any" and "or" are equivalent. Thus, this question's answer is vacuously false. There's a way out of this problem: treating "words" as a kind of quantifier (over the finite set {"any", "or"}), we can give it greater scope than the quantifier "a" (over the set of meanings). This scoping is at least possible, although it's the less natural one.

The second question, on the other hand, isn't even grammatical. It has a singular subject inside the noun clause ("the words "any" or "or"") but a plural verb ("have"). So it's not clear that this question has any answer at all.

This pair also seems as though it ought to be susceptible to Godelization, but I haven't quite worked out a version I'm satisfied with.

With which I am satisfied.