Here goes nothing (context):
This is a layman's response to John Derbyshire's comment regarding Romney's use of the phrase "a null set." For full disclosure, I am a mechanical engineer, and not a mathematician (or a lawyer). I was intrigued by your post, and decided to dig deeper. Per wikipedia's entry on null set, "in mathematics, a null set is a set that is negligible in some sense." (Wiki's emphasis). It goes on to say that in set theory there is only one empty (null) set, whereas in measure theory, any set of measure 0 is a null set.
By my understanding, iff (heh) Mitt Romney was discussing probability or statistics, than he was correct in his usage of "a null set." However, if Gov. Romney was thinking in purely mathematical terms, then Mr. Derbyshire's critique is correct. However, by my reading of NRO's excerpt of the debate, Gov. Romney was using "a null set" as a synonym for non sequitur. (Which can be either of the logical or absurd flavor). Since (roughly) "it doesn't follow" is not equal to "empty/none/zero/etc.," then it is my opinion that "a null set" is not a synonym for non sequitur, and therefore the entire subject is moot.
However, the real question should be Gov. Romney's usage of the phrase "non sequitur." It may be a valid usage if Gov. Romney considered the question a post hoc ergo propter hoc argument as opposed to a modus tollens argument. This is most certainly the case, since one additional reason someone might make the conclusion that invading Iraq was a mistake is because we didn't invade Iran first. Or maybe I'm trying to read too much into it. And yes, this is "Instalanche Bait".
Respectfully, Thomas Paine
Cross-posted at my blog, 21st Century Common Sense. :)
Updated June 8th, 2007 at 9:00 AM: ...crickets...heartache