Maybe it is time for Wizards to clarify just what was meant by this one phrase.
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it may be useful to delve a little further into what is meant in English by the indefinite article.
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I, rather clumsily, posted up-thread that I read this to mean "any threat." I did not mean that the word "any" should be substituted for the word "a", which leads to an entirely different reading
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With regard to the interpretation that "a threat" could mean "all threats" or "every threat," I'd like to remind everyone that the indefinite article can be semantically regarded to mean "one." Thus, "a character who doesn't notice one threat is surprised," should be equivalent to the present language
"Any" in English exhibits the same ambiguity as "a" - "fails to notice any threat" can mean "fails to notice at least one threat" or "fails to notice even one of the the threats". (In quantificational logic, the two readings are "For some x, x is a threat and x is not noticed" and "For all x, if x is a threat x is not noticed.")
"Fails to notice one thread" most naturally means "there is at least one threat not noticed" but can also be read, with a bit of strain, but not beyond all bounds, as "fails to notice even one threat". If the word
one is emphasised, eg when spoken or via italics, then there is no strain at all: "You dolt, you failed to notice
one threat" could easily convey the meaning that the dolt in question failed to notice even one threat.
Rewording it as "if a character does not notice any threat" would eliminate the ambiguity - in favour of the "no surprise unless miss all the threats" interpretation. Rewording it as "if there is any threat the character fails to notice" would also eliminate the ambiguity - in favour of the "surprised by even a single threat" interpretation.
I continue to think that there is a difference between relying on GM adjudication of a key term that picks up the fiction - eg "threat", "able to be seen", etc - and simple ambiguity (whether syntactic, as in this case, or around mechanical categories of concealment, as in the Stealth case), which just reflects bad drafting.