I posted it tongue-in-cheek, in fact I think that aphorism (which you probably know is Sherlock Holmes) is horrible. If you think you have eliminated the impossible, and what remains still seems highly improbable, think harder - there’s probably something you haven’t considered and your model is wrong.
Really? I’ve only ever heard “that doesn’t really make any sense but it must mean this”. What alternative possible meaning is there?
Huh? Right here in this thread, various posts are suggesting various things that might be meant by the phrase “X times less than”, including questioning that it might be some garbled reference to “X percent less?”
Not that I can see. OP was just clarifying what was WRITTEN, that it clearly did not say “25% less”, it said “25X less”. Only one interpretation of “25X less” has been proposed. All the rest is complaining that the expression just should not be used.
OP seemed to raise the possibility that some readers might think it means something like that. My point was, never mind what a reader might think, the bad phrasing suggests that even the writer doesn’t understand what he’s trying to say, or how to say it.
Meh, I just don’t agree. The expression is a bit awkward, but I think with a moment’s thought it can only possibly mean one thing. I think OP’s confusion arose principally from incredulity that a booster could increase protection 25-fold. Incredulity that was justified, because it was antibody titer rather than degree of protection that increases 25-fold, they are not at all the same thing. But that confusion has nothing to do with the “25 times less” expression.
Read literally, “25 times less” could only mean -2400% of the original. But no one has ever used the phrase in that manner. It’s always meant as 1/25 of the original.
In contrast, “25 times more” could genuinely mean 2500% of the original or 2600% of the original, and in many cases it’s impossible to distinguish the two from context.
So it’s a bit ironic, but it’s the “nonsensical” phase that’s unambiguous and can be safely used in practice, while the latter phrase cannot.
Better than using snark and thus adding negative information.
Ask Schroedinger’s cat
You may not like the usage (I certainly do not) but that is the way it’s used. Get used to it.
However, in this instance it is clearly wrong since it confuses antibody level with level of protection, as also pointed out above. The OP was absolutely correct in his doubts.
Natural language and mathematically precise language are not the same thing. I bet you also only say “and” at the decimal place when saying a number aloud so that it’s unambiguous when dictating it (like I do), but that’s not how normal people talk.
Given the general level of innumeracy and fear of fractions in the populace, it wouldn’t surprise me at all if “25 times less than” is better understood on average than “1/25th the”
I think it’s almost always possible, and it almost always means 2500%. The average person will mean 2500% and we math geeks won’t use that phrasing at all because it’s ambiguous.
Well, what comes naturally to me is mathematically precise language, so in my case, they are. 
Naturally? You were born that way, Lady Gaga? 
What you mean with that phraseology is that after many years of having the mathematically pedantic expression drilled into your head you reach for it automatically. Automatic is not the same as natural in language, at any level of discourse.
I’mma take refuge in the fact that nobody can check and say: Nope, born this way. 
I wonder when announcers say, “The fire has burned 25 square miles”, if they mean a 5x5 square, or a 25 x 25 square.
It’s unambiguously 25 [ square miles ], not [ 25 miles ] squared.
So the area of a 5x5 square.
Yes, but does the person who wrote the story realize that? I recall at least one instance where they did not.
This is the population that turned up their noses at A&W’s 1/3 pound burger for the same price as McDonald’s 1/4 pounder because the latter was “bigger” in their minds.
Your first paragraph is arguing against your second. If there exists any other referent at all, then the interpretation that you say would be meaningful would be exactly the same as the interpretation that you say is meaningless. It doesn’t matter what that other referent even is. And there’s always some other possible referent.
OP says it is a “simple math problem”, but it is actually an English language problem, not a math problem. All that is required is that people know what is meant. Whether or not it makes sense in the language of mathematics is irrelevant.