impredicativity
self-reference

By this method impredicativity could be avoided.

He strongly opposed Cantorian set theory, objecting to its use of Impredicativity definitions.

A prototypical example is intuitionistic type theory, which retains ramification but discards impredicativity.

Lacking impredicativity (Mathematical logic)

Russell's no-class theory is the root of the problem: Gödel believes that impredicativity is not "absurd", as it appears throughout mathematics.

This is a greatly weakened form of the axiom of power set in classical set theory, to which Myhill, among others, objected on the grounds of its impredicativity.

As noted below, some commentators insist that impredicativity in commonsense versions is harmless, but as the examples show below there are versions which are not harmless.

The opposite of impredicativity is predicativity, which essentially entails building stratified (or ramified) theories where quantification over lower levels results in variables of some new type, distinguished from the lower types that the variable ranges over.

A different objection put forth by Henri Poincaré is that defining sets using the axiom schemas of specification and replacement, as well as the axiom of power set, introduces impredicativity, a type of circularity, into the definitions of mathematical objects.

The reason for this is because of the problem of impredicativity: "classes cannot be regarded as a species of individuals, on account of the contradiction about classes which are not members of themselves ... and because we can prove that the number of classes is greater than the number of individuals, [etc]".

Some think this might be a self-reference, as in Mark himself.

Second, he has characterized the paradox as one of self-reference.

Against all this I would propose a rule of limited self-reference.

Self-reference is a condition for the efficient functioning of systems.

This to be used for self-reference and professional development.

By self-reference we mean a statement or set of statements that refer to themselves.

Possibly, though, this novelist self-reference should be dropped, along with much else.

Direct self-reference to the greatest civil rights leader in American history might also seem over the top to some viewers.

A reference that names an imaginary source is in some sense also a self-reference.

The mean number of recall for the group-reference was higher than self-reference.

However, we can eliminate the explicit self-reference and still reach the same conclusion.

The play also has elements of self-reference, if not self-parody.

There is also a bit of self-reference that some people have trouble finding; the back cover gives a hint.

Other languages with truth can be defined that lack vicious self-reference.

Psychologists questioned if these individuals would show the typical self-reference effect in memory.

Generally, this question is met by people that have two opposing views on the processes behind self-reference.

As Episodes can be, incidentally, when it doesn't get carried away with self-reference.

Any theory will be wrong when applied to a system which contains the observer himself due to self-reference.

Some languages, such as the language of arithmetic, will have vicious self-reference.

What one sees onstage, however, is without sentimentality or self-reference.

Yes, the very video you're watching-'the 90s was all about self-reference.

These may go through multiple layers before the self-reference is found:

The insular cortex is also thought to be involved in the process of self-reference.

Sure enough, they set the scene yesterday on the margin between self-reference and self-reverence.

THE line between self-reference and self-reverence is hard to find.