...nothing syntactically wrong with a sentence like "The cat the dog the man hit bit died."

Ah. Fluent reverse Polish. Or is it Yoda egg-nog on (too much) ?

I've tried to parse this... putting the brackets back in I get: died(the cat bit (the dog hit the man)) -- I'm assuming: (a) that each 'the' is part of the name of each object/subject; (b) that 'died' is a unary (intransitive); and (c) that 'bit' and 'hit' are binary operations (transitive).

So much for syntax... semantics-wise, assuming that the 'hit' and 'bit' operators return the object modified by the operation inflicted upon it by the subject...

...no wonder the man died. What on earth had he done to upset both the cat and the dog ? And what did the dog hit him with ?

Of course, being reverse polish the operators may themselves be reverse -- so the cat gets it because the man hit the dog ? What kind of twisted world is this ?