An entity (in mathematics or physical reality) for which all descriptions in terms of formal theories or algorithms are incomplete I call a #proteon. The corresponding adjective is #protean. An entity for which a description by means of a formal theory or algorithm exists, on the other hand, is a (formalizable) system. It is systematic.
(The term "proteon" was coined after the minor greek god Proteus who, according to the Odyssey, could change his shape.) #philosophy

There are always more true statements about reality than can be derived in any single formal theory. Reality is not completely formalizable. It is what I call a #proteon. The theories can always be extended, but the extended theories are incomplete as well. #philosophy #incompleteness #formalizability

@corbden With regard to the designed systems, current "AI" is based on algorithms. There are learning #algorithms that produce #AI systems which are algorithms. It can be shown that each such learning algorithm is special, i.e. has systematic blind spots. Artificial General Intelligence (#AGI) would need to go beyond algorithms (#Turing-machines). It would need to be a #proteon (not formalizable in principle). I think that is possible and in such entities these principles would emerge as well.