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This is Snapple Real Fact #851. Is this sentence ambiguous between

  1. They installed the first ATM specifically for rollerbladers, and
  2. They installed the very first ATM, coincidentally for rollerbladers

I'm assuming they mean the former. Does the grammar imply solely the former as well? And would a comma - "the first ATM, for rollerbladers" - explicitly imply the latter, or would it still be ambiguous?

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The sentence is grammatically ambiguous, but common knowledge and reasoning resolves the ambiguity with little conscious involvement. The idea that an ATM would have been invented first only with the intention of serving rollerbladers is pretty far out, and would not be brought to mind. (Not to mention, ATMs predate rollerblades by many years.)

Adding a comma after ATM would suggest a parsing which makes the for rollerbladers nonessential to the core meaning, but the effect is not strong (IMO), and would probably be dismissed by most readers. To get that idea established, against the cognitive bias for the commonplace interpretation (of "first <​ATM for rollerbladers>"), would probably additionally require some further marking, such as ...first ATM, for rollerbladers! or ...first ATM, and it was for rollerbladers.

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It is an example of an ambiguous sentence. Read what Wikipedia has to say about semantic and syntactic ambiguity.

Syntactic ambiguity is a property of sentences which may be reasonably interpreted in more than one way, or reasonably interpreted to mean more than one thing. Ambiguity may or may not involve one word having two parts of speech or homonyms.

Syntactic ambiguity arises not from the range of meanings of single words, but from the relationship between the words and clauses of a sentence, and the sentence structure implied thereby. When a reader can reasonably interpret the same sentence as having more than one possible structure, the text is equivocal and meets the definition of syntactic ambiguity.

In legal disputes, courts may be asked to interpret the meaning of syntactic ambiguities in statutes or contracts. In some instances, arguments asserting highly unlikely interpretations have been deemed frivolous.

Read the examples as well. Some of them are hilarious.

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