[ExI] Trilemma of Consciousness

[Adrian Tymes]

>>> Axiom 1: Let F(n) be the nth computable function with n being an
>>> admissible numbering of all possible computable functions.
>>> Axiom 2: Let K be the subset of F(n) such that all K share a semantic
>>> property k.
>>> Definition 1: Let k be called trivial if all F(n) have property k.
>>> Definition 2. Let k be called null if no F(n) has property k.
>>> Axiom 3: Let Dt be the decision problem as to whether a given F(n) belongs
>>> in K.
>>>
>>> Theorem: By axioms 1-3, definitions 1-2, and Rice's Theorem, Dt is
>>> decidable if, and only if, k is trivial or null.
>
> I made an error above in Axiom 1. It should read
>
> Axiom 1: Let F(n) be the nth partial computable function with n being an
> admissible numbering of all possible partial computable functions.

> Since my understanding of a semantic property of a function is one related
> to "meaning" that manifests in the behavior of the function. For example,
> "always halts on any input" would be a semantic property.

Fair enough.  But in that case, given
https://en.wikipedia.org/wiki/Rice%27s_theorem , your theorem would
seem to be true by definition, almost a circular proof:
* From the article, "Rice's theorem states that all non-trivial,
semantic properties of programs are undecidable."
* The union of what you call "trivial" and what you call "null" is
what the article calls "trivial".
* You appear to be using the same definition of "semantic property".
* Because these properties are undecidable (according to Rice's
Theorem), they are undecidable.