We would do well to remember (and apply) Godel to more than mathematics, as his incompleteness theorem applies to any formal system and may be helpful in understanding some of the limitations mentioned.
There's nothing special about consciousness, it's simply another loop of evolution. Since our consciousness doesn't actually *do* anything but preserve our biologic coherence (e.g. thinking about our intended actions and their perceived consequences to mitigate eradication) it borders on mysticism/theology to think it is distinct from any other process, biologic or otherwise.
A digital computer is not a universal computer. There is nothing universal about either pentadactility (our digits, the basis for our math) or binary circuitry (depending on how you define "digital computer"). Furthermore, it is confusing and meaningless to claim a distinction between "logic" and "ontology," to no apparent end but rhetorics.
Keep in kind that Turing's ideas were very much shaped by mechanical computing paradigms of his day. There's no evidence I've come across that he was particularly aware of quantum processes and how they differ from the machines he envisioned.