Translation:Under no circumstances can he know about my existence.
Under no circumstances have I met this rule before ;) Thank you Davu
P.S. A good article about different types of inversion in English: http://www.perfect-english-grammar.com/inversion.html
At the moment (20 Aug 2013) duo is offering 2 alternative English translations "In any case, he can know of my existence." and "He cannot know of my existence under any circumstance." Having read the above comments, I think the 2nd translation is OK, though not elegant, but the 1st is just wrong. It is a literal word for word translation which I think conveys an entirely incorrect meaning.
Isn't "In SOME circumstances he can know of my existence" correct? Wouldn't you want to replace "alguma" with "qualquer" if you wanted to express the idea that this person can know of my existence? And, even if you write "any", then that implies that there does not exist a time such that he does not know of my existence. So, the verb "pode" seems inappropriate. So, wouldn't "Em qualquer circunstância ele sabe da minha existência." be a better Portuguese sentence?
See Davu's comment above, it's perfectly right.
To have the meaning you propose, you would write "Em algumas circunstâncias" (plural algumas before the noun)
- Em circunstância alguma ele pode = he never can / he cannot under any circumstances
- Em algumas circunstâncias ele pode = in some circumstances he can
- Em qualquer circunstância/quaisquer circunstâncias ele pode = he always can, he can in any circumstances.
It's not there; See Davu's expalantion at the top of this comments page!
- alguma coisa = something
- coisa alguma = nothing
- Em circunstância alguma = under no circumstances (in no circumstance)
- Em alguma circunstância = under some circumstances
- Em qualquer circunstância = under any circumstances
This link might be helpful:
With the disclaimer that I'm not a native speaker, I've always read that when algum is placed after the noun, the construction is semantically equivalent to using nenhum.