[ExI] Trilemma of Consciousness

[Stuart LaForge]

>>> Axiom 1: Let F(n) be the nth partial computable function with n being an
>>> admissible numbering of all possible partial 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.

>> 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.

Adrian Tymes wrote:

> 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.

Yes. Guilty as charged. I let Rice do all the heavy lifting, but I also
cited him right in the middle of my proof. What more do you want?

Stuart LaForge