I understand the assumptions that have to be true about a property or set of properties in a Turing machine description for Rice's Theorem to apply.
But then what? If a set of Turing machines have an undecidable property, is the language itself necessarily undecidable? Or only if you can find a reduction from a known-undecidable machine is the language undecidable?
What does it really say about a language if it has an undecidable property? Are machines that recognize that language undecidable?