Complex living systems are distinguished by the realization of (M,R)-systems and their impredicativity, or what he calls a closed path of efficient causation; self-referential systems in which metabolism, repair and replication interact to generate and maintain themselves.
Complicating this, however, is the further impredicativity that it is such errors which also generate novelty contributing to greater human cognitive development; the smarter we get the more errors we create, the more errors we create the smarter we get.
It is argued that in and of itself impredicativity
does not constitute sufficient grounds for rejecting a putative identity criterion.
Potter claims that Frege adopted an impredicative conception of the numbers in order to advance beyond demonstrating their infinity by appeal to the realm of thoughts, and argues that this impredicativity leads to two "unattractive" choices: "if ...
Second, why should impredicativity be a problem for Frege?
(The author overlooked the fact that the translation avoided impredicativity
Their lore is too deep for us to examine here; look elsewhere for explanations of universes, impredicativity
, intensional equality, and other mysteries.
In another option, Behmann (1931) proposed two criteria for solving the paradoxes based on banning impredicativity
from nominal symbolic definitions; in the end the proposals did not work,(6) but structure did not cause the failure.
(As emerges from comparison with Thiel's paper, the difference can equally well be viewed as one regarding impredicativity
. In Frege: Philosophy of Language (531-34) Dummett sought to isolate a minimal understanding of the vicious circle principle on which it was "indisputable," one on which it condemns an "explanation" or "specification" of a domain that quantifies over that very domain.