> a system cannot be both sound a complete
Huh, what do you mean by this? There are many sound and complete systems – propositional logic, first-order logic, Presburger arithmetic, the list goes on. These are the basic properties you want from a logical or typing system. (Though, of course, you may compromise if you have other priorities.)
None of these systems are both sound and complete.
first-order logic is sound, but not complete (Ie. I can express a set of strings you can not recognize in first-order logic).
My take is that the GP was implicitly referring to Gödel’s Incompleteness Theorems with the implication being that a system that reasons completely about all the human topics and itself is not possible. Therefore, you’d need multiple such systems (plural) working in concert.
That doesn't make much sense.
If you take multiple systems and make them work in concert, you just get a bigger system.
> If you take multiple systems and make them work in concert, you just get a bigger system.
The conclusion may be wrong, but a "bigger system" can be larger than the sum of its constituents. So a system can have functions, give rise to complexity, neither of its subsystems feature. An example would be the thinking brain, which is made out of neurons/cells incapable of thought, which are made out of molecules incapable of reproduction, which are made from atoms incapable of catalyzing certain chemical reactions and so on.
This is just emergence, though? How is emergence related to completeness?
This happens over and over with the relatively new popularization of a theory: the theory is proposed to be the solution to every missing thing in the same rough conceptual vector.
It takes a lot more than just pointing in the general direction of complexity to propose the creation of a complete system, something which with present systems of understanding appears to be impossible.
> How is emergence related to completeness?
I didn't make that argument. I think, the original conclusion above isn't reasonable. However, "a concert" isn't "just" a bigger system either, which is my point.
It just depends on your definition of system, doesn’t it?
Sort of, the guardrail here IMO is you have an ontology processor that basically routes to a submodule, and if there isn't a submodule present it errors out. It is one large system, but it's bounded by an understanding of its own knowledge.
Concerts - again plural. And naturally you only bring in appropriate instruments.
Turtles all the way down?
A collection of systems is itself a system. The theorem would not recognize the distinction.
I believe, neither the expansion of Gödel's theorems to "everything", non-formalized systems, nor the conclusion of a resolution by harnessing multiple systems in concert, are sound reasoning. I think, it's a fallacious reductionism.
What is a non-formalized system?
I am very curious on this. In particular, if you are able to split systems into formalized and non formalized, then I thinks there are quite some praise and a central spot in all future history books for you!
I am not a native speaker, so please don't get hung up on particular expressions.
I meant, the colloquial philosophies and general ontology are not subject of Gödel's work. I think, the forgone expansion is similar to finding evidence for telepathy in the pop-sci descriptions of quantum entanglement. Gödel's theorems cover axiomatic, formal systems in mathematics. To apply it to whatever, you first have to formalize whatever. Otherwise, it's an intuition/speculation, not sound reasoning. At least, that's my understanding.
Further reading: https://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_th...
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Yep - when you use a multiplum of systems, then some systems can be regarded complete while other systems are sound.
This is in contrast to just one system that attempts to be sound and complete.