Another mid-week re-run (more logic than mathematical). This very simple one (a good one for youngsters) comes in many forms but I'll pose it again as “The Broken Water Heater Problem” as follows:
Last week, I lost heat in my apartment when the water heater broke. I contacted someone in the building and showed them the water heater, and with a bunch of parts he had on-hand he was able to repair it and get it working. I paid him happily for his services.
Is this person more likely:
a) An accountant?
b) An accountant and a plumber?
Even if you’re not familiar with these type-questions, hopefully upon a moment of logical reflection the reader recognizes the answer should be a) that the person is “an accountant.”
The problem is, often people DON'T really give a moment of ‘logical reflection,’ instead jumping to the conclusion that it's more likely (more probable) that the individual must have plumbing skills, and thus must logically be “an accountant and a plumber.” But of course ANYone who is ‘an accountant and a plumber’ is automatically ‘an accountant’ (within 'logic' I believe this sort of classification error goes by a specific name, but am too lazy to try to look it up just now)— in Venn diagram terms, the circle of accountants includes wholly within it the circle of ‘accountants and plumbers,’ but, as I say so often, it is words that lead logic astray. In fact, words are so vague and imprecise and ambiguous it's a wonder, as Gödel noted, that we can successfully communicate at all! As we head into a highly charged political season, it gets me thinking (well, dismaying) how much of our communication is visceral, emotional, non-verbal, and primed by predispositions, rather than actually based upon information or word meanings.