Rice's Theorem: implication of having an undecidable property
An undecidable property $\pi$ of Turing machines is the same as an undecidable language consisting of all encodings of Turing machines satisfying $\pi$. We identify the property with the language of encodings of Turing machines satisfying the property.

The fact that a language is undecidable just means that no Turing machine decides the language — this is the definition of undecidability. In particular, no machines recognize the language, assuming recognize means decide; a machine $T$ decides a language $L$ if $T$ terminates on all inputs, on inputs $x \in L$ returns $1$, and on inputs $x \notin L$ returns $0$. A machine cannot be undecidable, only a language can be undecidable.