Never imagine yourself not to be otherwise than what it might appear to others that what you were or might have been was not otherwise than what you had been would have appeared to them to be otherwise.
The author and his commentators have been analyzing the sentence in terms of grammar; I thought I’d give it a go in symbolic logic. I’m probably totally off base, but it’s an interesting exercise, and since Lewis Caroll was a mathematician, I think I may have something here.
I(x) === to imagine x
B(x) === to be x
A(x) === for x to appear to others
Then, break the sentence down:
“never imagine yourself…” => ~I…
“not to be otherwise than …” => ~~B…
“what it might appear to others …” => A(…) | ~A(…)
“that what you were or might have been …” => Bx | ~Bx
“was not otherwise than …” => ~~…
“what you had been would have appeared to them to be otherwise.” => A(~Bx)
So the full formulation for the sentence is as follows:
~I(~~Bx) . A(Bx | ~Bx) | ~A(Bx | ~Bx) . ~~A(~Bx)
We can drop the middle term, since it is always true, and the double negatives, which gives us:
~I(Bx) . A(~Bx)
In other words, “Never imagine yourself to be what you do not appear to others to be”.
I suspect this is way too simplistic and just plain wrong :-) It’ll probably bug me for the next couple of days.