The Halting Problem is not effectively decidable

CT can be understood to assign a precise epistemological significance to Church and Turing’s negative answer to the Entscheidungsproblem. For if it is acknowledged that \(\mathcal{F}_{\mathfrak{R}}\) (and hence also \(\mathcal{F}_{\Lambda}\) and \(\mathcal{F}_{\mathfrak{T}}\)) contain all effectively computable functions, it then follows that a problem \(X\) can be shown to be effectively undecidable – i.e. undecidable by any algorithm whatsoever, regardless of its efficiency – by showing that t