undefined | Better HN

0 pointskachnuv_ocasek6mo ago0 comments

> 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.)

0 comments

lemonwaterlime6mo ago

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.

eru6mo ago

That doesn't make much sense.

If you take multiple systems and make them work in concert, you just get a bigger system.

jijijijij6mo ago

> 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.

1 more reply

CuriouslyC6mo ago

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.

tossandthrow6mo ago

Concerts - again plural. And naturally you only bring in appropriate instruments.

1 more reply

Jeff_Brown6mo ago

A collection of systems is itself a system. The theorem would not recognize the distinction.

jijijijij6mo ago

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.

tossandthrow6mo ago

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!

1 more reply

tossandthrow6mo ago

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).

tossandthrow6mo ago

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.

j / k navigate · click thread line to collapse

0 comments

lemonwaterlime6mo ago

eru6mo ago

That doesn't make much sense.

If you take multiple systems and make them work in concert, you just get a bigger system.

jijijijij6mo ago

> If you take multiple systems and make them work in concert, you just get a bigger system.

1 more reply

CuriouslyC6mo ago

tossandthrow6mo ago

Concerts - again plural. And naturally you only bring in appropriate instruments.

1 more reply

Jeff_Brown6mo ago

A collection of systems is itself a system. The theorem would not recognize the distinction.

jijijijij6mo ago

tossandthrow6mo ago

What is a non-formalized system?

1 more reply

tossandthrow6mo ago

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).

tossandthrow6mo ago

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.

j / k navigate · click thread line to collapse