Why the secret, if at all? -- not good English (not in any interpretation that I can think of anyway).
Why the secret, if any? -- an unlikely thing to want to say. It would mean "Why is there a secret (relating to whatever's being discussed) -- if, in fact, there is a secret?"
Why is this a secret at all? -- means roughly the same as "Why is this a sec
Thanks, Mr. Wordy Given that you are a native speaker, everything that does not make sense to you for me will be incorrect. Thus there shouldn't be any more discussion on this. Yet, I wonder if the first one "why the secret, if at all", which you said is not good English, can be used to mean "why the secret, if (it is a secret) at all" (almost) = " why is this a secret at all ". It's probably
"Why the secret, if at all?" would normally be understood to mean something like "Why the secret, if it is a secret at all?", just because this is the nearest thing it could be trying to say. But for some reason the rules of English don't (in my opinion) allow "Why the secret, if at all?" as a correct sentence. At first, I thought the reason was that "at all" is an adverb, and so is looking