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The sentence is: “X is not legal in all contexts.”

Couldn’t the logical negation be interpreted as applied to either “legal” or “legal in all contexts”, the former would result in “X is illegal in all contexts”, where the latter would result in “X is illegal in some contexts”

Is there a name of this type of ambiguity?

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    Yes, it's ambiguous, and yes, there is a name for this type of ambiguity. It's what happens when you put a negative like not in the same sentence as a quantifier like all. Both of these are operators and bind a variable, but their scopes can get twisted. Is it Not (All Legal) or is it All (Not Legal)? Can't tell. The term is Quantifier-Negative Ambiguity.
    – John Lawler
    Mar 19 at 2:28
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    Does this answer your question? Is it wrong to use 'not" in sentences that have an “all…not” form ... 'there is a quantifier (all) and a negative (not) in the same proposition, and when that happens there occurs what is called a Quantifier-Negative Ambiguity,' [JL]
    – Edwin Ashworth
    Mar 19 at 14:03
  • It's predictably ambiguous.
    – John Lawler
    Mar 19 at 15:07

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In a comment, John Lawler wrote:

Yes, it's ambiguous, and yes, there is a name for this type of ambiguity. It's what happens when you put a negative like not in the same sentence as a quantifier like all. Both of these are operators and bind a variable, but their scopes can get twisted. Is it Not (All Legal) or is it All (Not Legal)? Can't tell.

The term is Quantifier-Negative Ambiguity.

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