On bad astronomy and words

John is an astronomer. A really awesome astronomer — he knows everything about stars, planets, zodiacs, and whatever else astronomers know (I’m not an astronomologist). If you need to calculate the distance to a star, figure out how to build a plane that works on Mars, or process telescope data to find habitable planets — he’s the guy you’d mean when you say “I know a guy”. Oh, and John lives in 2005, before Pluto was reclassified as not a planet.
He’s writing a book about the planets in the Solar System, comparing their statistics. In the chapter on planet sizes, he writes: “The smallest planet in the Solar System is about 2400 kilometers in diameter,” meaning Pluto.
Another astronomer, Jack, finds this book in 2010. He reads the sentence: “The smallest planet in the Solar System is about 2400 kilometers in diameter.” Jack knows Pluto isn’t a planet, so he believes the smallest planet in the Solar System is Mercury, with a diameter of about 4900 kilometers. He reads it and thinks: “The smallest planet in the Solar System is 4900 kilometers across. But John writes that the smallest planet in the Solar System is 2400 kilometers in diameter. That’s a huge discrepancy! He tried to measure a planet and got it wrong by almost a factor of two! Clearly John is a terrible astronomer if he can’t even get the size of a planet right.”

Yet John is actually an excellent astronomer. He only got one rather unimportant classification wrong. The reasoning “The smallest planet is Mercury, and John thinks the smallest planet is 2400 kilometers in diameter, therefore John thinks Mercury is 2400 kilometers in diameter” is not as logically valid an inference as it sounds.

…Okay, why is this seemingly trivial bit written here? As it turns out, for many people this reasoning isn’t nearly as obvious as it is to me. After hearing conclusions of this kind for the hundrendth time, on the hundred and first I’d rather just write a standard response on my blog and link to it from now on.