Talk:3210: Eliminating the Impossible

I’ve found that when looking for an item, I’ll search harder and more thoroughly in the places where the item is supposed to be, which is just frustrating and usually unsuccessful. Then I realized that if the item isn’t where it’s supposed to be, then it’s somewhere it isn’t supposed to be - so I start looking in those places. 170.64.111.76 20:51, 20 February 2026 (UTC)

It also assumes exclusion of the middle. MithicSpirit (talk) 20:59, 20 February 2026 (UTC)

I think you're kind of right, but it's a weird situation. Disjunction elimination does not require LEM. I can imagine that we have established some list of n "possibilities" p₀, p₁, ..., p_n. What does it mean that these are the only possibilities? Naturally, it means p₀ ∨ p₁ ∨ · · · ∨ p_n. Now, if we eliminate all but the k^th possibility, that means we have ¬p₀, ¬p₁, ..., ¬p_k-1, ¬p_k+1, ..., ¬p_n. By repeated use of disjunction elimination, this proves p_k intuitionistically, so the k^th possibility ("whatever remains") is provable ("must be the truth"). The problem with this approach is proving the original disjunction. How did we show to begin with that one of those n possibilities must hold? To do that intuitionistically requires actually proving one of those statements to begin with. And since only one of them is true, we must have already proved p_k, rendering this argument pointless. Still, it technically is valid. EebstertheGreat (talk) 14:20, 21 February 2026 (UTC)

I originally interpreted it as taking the collection of all (relevant?) propositions, excising the false ones, and deducing that anything that was not excised must be true. Effectively meaning that that if ¬p does not hold then p must hold, which is EM. I think your interpretation is incorrect because the comic does not require the collection of "whatever remains" to be nonempty, so we don't necessarily have the disjunction. MithicSpirit (talk) 20:43, 21 February 2026 (UTC)

These guys sure are some professors of logic (I'm not sure if they own any doghouses, is what I mean). Fephisto (talk) 21:07, 20 February 2026 (UTC)

As and when the Explanation gets written (I imagine that someone's right in the middle of that now), it must be noted that Sherlock Holmes's self-proclaimed "Deductive reasoning" is really Abductive reasoning. (I actually blame Sir Arthur, rather than Sherlock (or 'narrator' Watson), for that error... But then he also believed in fairies, so obviously he's less than perfectly rational.) 81.179.199.253 21:17, 20 February 2026 (UTC)

Well, nobody did do anything with it, in the last hour or so, so I scrawled something pretty basic for others to ruthlessly dismember and 'remember' in their own prefered fashion. 81.179.199.253 22:27, 20 February 2026 (UTC)

I think its pretty nice how this comics number is a countdown from 3. Xkdvd (talk) 22:57, 20 February 2026 (UTC)

By the way, meant to say earlier... just today (well, the day just before the midnight just gone), I spent a few moments trying to help someone find a single glove. They'd looked various places, and I went out to look in the car (twice, actually, because first I just checked the 'normal' places, footwells, door-pockets... then realised I hadn't actually checked the glove-compartment itself (which I don't think I've ever used to store gloves, of course, but I'd have looked silly if I hadn't gone back and checked it once it had occured to me) so out I went again) in order to not find the glove. Cue, later, the revelation that it had been in a bag (in the house) all along. And this was all mere hours before Randall published this comic. So, as we all used to say on the now defunct Fora, "GOOMHR!" 81.179.199.253 00:24, 21 February 2026 (UTC)

It's also possible to miss an item in a space you've searched. For instance, as a 12- or 13-year-old I once concluded that something (I forget what it was) must not be in my room, because I'd partitioned the rectangular box defined by the walls, floor and ceiling and searched each of the partitions. It turned out to be outside that box but still inside my room, because it was on the windowsill. Promethean (talk) 00:39, 21 February 2026 (UTC)

I actually did find it in the car though.--2604:3D09:84:4000:6FFB:F472:7679:FF75 02:34, 21 February 2026 (UTC)

Reminds me of this from Math Hysteria by Ian Stewart: 'As I have often stated, when you have eliminated the impossible, then whatever remains, however improbable ... remains improbable,' said Holmes, deflated. 'There's probably something altogether different going on, and you've missed it. But don't quote me on that,' he warned. Arcorann (talk) 09:23, 21 February 2026 (UTC)

I was going to get that actual book, before Christmas (after I'd decided what other book I was getting for someone else, when visiting a good bookshop with a nice selection of not-necessarily-new publications), as there's still just about space for it on my 'Pratchett-adjacent' bookshelves next to his (and specifically Jack Cohen's) other stuff. Which I'm a bit sorry now that I never got signed by them (both, where relevent) while I still could, the few times we had all crossed paths. 81.179.199.253 14:25, 21 February 2026 (UTC)

If it's not in the car, it's in the cdr. --2A02:3100:25A0:9400:6CEB:97FF:FE5B:8BDC 11:06, 21 February 2026 (UTC)

Yeth. 174.130.97.11 (talk) 14:10, 21 February 2026 (please sign your comments with ~~~~)

To be fair, it is SHERLOCK HOLMES making the comment. He literally means when you have actually eliminated all other possibilities. And he was pedantic enough to be thorough about it. Dúthomhas (talk) 21:27, 21 February 2026 (UTC)

Not at all; upon re-reading The Sign of the Four (his first use of the phrase) he most certainly has not eliminated all other possibilities in both his uses of the phrase. Hilariously, he then comments "I never guess" Nerd1729 (talk) 22:01, 21 February 2026 (UTC)