The Meaning Of Words

David Henderson identifies an innumeracy expressed by Andrew Oxlade.

Oxlade writes "He declined to predict the exact trigger but said it was more likely to happen in the next five years rather than 10." However, as Henderson rightly points out, an event is always more likely to occur in a 10-year span than a 5-year span.

EconLog commentator "Radford Neal" (in scare quotes because I don't know whether or not that is his real name) defends the opposite position:
If 85 percent of Stanford grad students get it "wrong", that's pretty strong evidence that the answer is not actually wrong at all. And an explanation that they're using "system 1" (whatever that is), as most people do in the circumstances, is actually further evidence of this. The meaning of a statement/question is what most people will take it to mean. It seems most people take the statements in this example to mean something other than what the experimenter claims it means (a claim that is therefore clearly incorrect).
"Jameson" (ditto on scare quotes) criticizes the use of "mathematical precision" in language because he feels that it detracts from communication.

I was inclined to agree with both "Neal" and "Jameson" until I remembered an old Roderick T. Long blog post on a news report using the word decimated, in which he writes:
In recent years the term “decimate” has come to be widely misused to mean “devastate,” probably because the two words sound similar. But we have lots of words that mean “devastate.” We have only one word that means “decimate.” Why give it up?
As Long points out, we have words that mean things for a reason. That point also holds true for concepts. We might want to sometimes relax our rigidities to "get away with" mental shorthand, but why would we want to get away with anything at all? Likelihood is likelihood. Probability is probability.