Exactly! So glad we're on the same page.
Language is created by and intended for big brains with huge amounts of knowledge about each other and about the world. Relying on external knowledge makes it extremely compact and flexible, but also means your parser needs a similar level of knowledge to function.
We're really not. I'm saying you've incorrectly defined the English language. By that definition, no piece of text is English.
Human language has a pretty clear distinction between syntax and sementics. This is how we recognize that "colorless green ideas sleep furiously" are perfectly well formed, if meaningless. In contrast, "I is happy" is meaningful and unambiguous, but grammatically incorrect.
In terms of syntax, English (like most, if not all) languages is literally ambigous.
Consider the sentence structure:
Subject Verb Object Prepositional-Phrase.
This can be either:
(Subject Verb (Object Prepositional Phrase))
Or
(Subject Verb Object ) Prepositional Phrase.
For instance, consider the sentence "I saw a man with binoculars".
In any sense of the word, this example is structually ambigous.
My favorite funny phenomenon in this area is when a sentence has two unambiguously different parses that mean exactly the same thing.
Politicians lie.
Cast iron sinks.
Politicians lie in cast iron sinks.
It's not actually ambiguous, but I think it's a lovely illustration of the subtleties of the problem.
An actually ambiguous example: I saw a politician lying in a cast iron sink.
"I couldn't fit the trophy in my suitcase because it was too big."
"I couldn't fit the trophy in my suitcase because it was too small."