10 ENGLISH BOOKS RELATING TO «IMPREDICATIVE»
Discover the use of
impredicative in the following bibliographical selection. Books relating to
impredicative and brief extracts from same to provide context of its use in English literature.
1
Mathematical Fallacies and Paradoxes
REPAIRING THE DAMAGE In fact, it was to avoid this sort of thing that Poincaré
introduced the concept of impredicative definitions. The definition of the set of all
normal sets is impredicative. Using Poincaré's rule, it would not be allowed into ...
2
Advances in Modeling Adaptive and Cognitive Systems
Rosen's central argument is that organisms will have impredicative models,
which he takes to mean say that they have models that are not Turing
computable, which is to say that they are not machines. We have demonstrated
using hypersets ...
Angelo Loula and João Queiroz
3
Set Theory and Its Logic, Revised Edition
sets and classes is what we get from the skeletal Zermelo system if, instead of
adding Zermelo's further axioms, we take another turning and add the deviant
axiom IN e *0\ I momentarily present the skeletal impredicative theory of sets and
...
Willard Van O QUINE, 2009
4
Mathematics: The Loss of Certainty
Another example of an impredicative definition is that of the maximum value of a
function in a given interval. The maximum value is the largest of the values which
the function takes on in that interval. Both of these concepts are fundamental in ...
5
Multi-Scale Integrated Analysis of Agroecosystems
Similarly when a property P is possessed by an object m whose definition
depends on P (here M is the set of objects which possess the property P), an
impredicative definition is circular, at least on its face, as what is defined
participates in its ...
6
Hermann Weyl's Raum-Zeit-Materie and a General Introduction ...
Examples (6.2.23)-(6.2.25) of impredicative definitions in a theory of (simple)
types were discussed above in subsection 6.2. In addition, it was shown how the
theory of ramified types prevents impredicative definition by forcing a defined ...
Hermann Weyl, Erhard Scholz, 2001
7
Foundations of Set Theory
Derivatively, we shall call impredicative also those conditions ip(x) themselves
which contain bound variables of higher level than that of x l) and also the
corresponding classes and the process of forming them, i.e. of proving their
existence.
A.A. Fraenkel, Y. Bar-Hillel, A. Levy, 1973
8
Typed Lambda Calculi and Applications: 7th International ...
A typical example of impredicative definition is Leibnitz definition of equality,
which defines “a is equal to b” by the formula rag ∀X.X(a) → X(b) (∗) Here X(x)
ranges over all possible properties. In particular it could be the property P(x) P(x)
...
9
Basic Questions on Truth
Secondly, we can regard the contradiction [x(x) <-> -x(x)] derivable from (Vy)[*(y)
<^> -My)] as a means to a reductio ad absurdum and for this reason reject these
impredicative definitions as false. In this case one may call impredicative ...
10
Logic: A History of its Central Concepts: LOGIC: HISTORY OF ...
Such a definition is called an impredicative definition. The relation with the notion
of impredicative type is immediate:42 an object defined by an impredicative
definition is of a higher order than the order of the elements of the class to which
this ...
Dov M. Gabbay, Francis Jeffry Pelletier, John Woods, 2012
