As a result, not only did Principia introduce a wide range of philosophically rich notions (including propositional function, logical construction, and type theory), it also set the stage for the discovery of crucial metatheoretic results (including those of Kurt Gödel, Alonzo Church, Alan Turing and others).
Kleinberg argues that these indicators offer "a richer notion of importance, or prominence, [that] contains an intrinsic element of circularity: it arises from the fragile intuition that a node is important if it receives links from other important nodes" [55], p. 611.
Other authors concerned with explaining the behavior of non-linguistic and pre-linguistic creatures have proposed applying a richer notion of nonconceptual content that is not essentially pragmatic and that can be deployed in a style of explanation analogous to propositional attitude explanation.
Again, axioms of definable determinacy and large cardinal axioms imply this version of CH for richer notions of definability.
One can pass beyond the above hierarchy of sets of reals by considering richer notions of definability.
At this point, however, it is important to note that there are two ways in which richer notions of information can be introduced.
The real problem is that we do not employ a rich enough notion of what personal liberty means to see why assisted dying requires very sensitive handling.
Despite their initially crude appearance, Mr. Deutsch's paintings are grown-up, complex of space and surface, and rich in notions of human interaction or the lack thereof; voyeurism and solitude; and often an ambiguous ominousness.
The homogeneous, empty time Benjamin associated with the onward march of capitalism and positivism is halted, albeit briefly, and replaced by a more experientially rich and redemptive notion of non-linear time.
This is a rich and inspiring notion.
