theory of types वाक्य
उदाहरण वाक्य
मोबाइल
- Later Russell examined the problem of whether propositional functions were predicative or not, and he proposed two theories to try to get at this question : the zig-zag theory and the ramified theory of types.
- At about the same time Ludwig Wittgenstein made short work of the theory of types in his 1922 work Tractatus Logico-Philosophicus in which he points out the following in parts 3.331 3.333:
- An adaptation of radical theory was called theory of types ( theory of residues ), advocated by Charles-Adolphe Wurtz, August Wilhelm von Hofmann and Charles Fr�d�ric Gerhardt and another one was water type as promoted by Alexander William Williamson.
- But because the stipulations of the ramified theory would prove ( to quote Quine ) " onerous ", Russell in his 1908 " Mathematical logic as based on the theory of types " also would propose his " axiom of reducibility ".
- According to R . Blutner and E . Hochnadel, socionics is not so much a theory of personalities per se, but much more a theory of type relations providing an analysis of the relationships that arise as a consequence of the interaction of people with different personalities ."
- The Epimenides paradox appears explicitly in " Mathematical Logic as Based on the Theory of Types ", by Bertrand Russell, in the " American Journal of Mathematics ", volume 30, number 3 ( July, 1908 ), pages 222 262, which opens with the following:
- Metaclasses are sometime organized by levels, in a similar way to the simple Theory of types where classes that are not metaclasses are assigned the first level, classes of classes in the first level are in the second level, classes of classes in the second level on the next and so on.
- Deep studies of admissible representations of " p "-adic reductive groups were undertaken by Howe and Moy and Bushnell and Kutzko, who developed a " theory of types " and classified the admissible dual ( i . e . the set of equivalence classes of irreducible admissible representations ) in many cases.
- Russell in his 1920 " Introduction to Mathematical Philosophy " devotes an entire chapter to " The axiom of Infinity and logical types " wherein he states his concerns : " Now the theory of types emphatically does not belong to the finished and certain part of our subject : much of this theory is still inchoate, confused, and obscure.
- As Stewart Shapiro explains in his " Thinking About Mathematics ", Russell's attempts to solve the paradoxes led to the ramified theory of types, which, though it is highly complex and relies on the doubtful axiom of reducibility, actually manages to solve both syntactic and semantic paradoxes at the expense of rendering the logicist project suspect and introducing much complexity in the PM system.
- There is also a correspondence between confinement in QCD the fact that the color field is only different from zero in the interior of hadrons and the behaviour of the usual magnetic field in the theory of type-II superconductors : there the magnetism is confined to the interiour of the Abrikosov flux-line lattice, i . e ., the London penetration depth " & lambda; " of that theory is analogous to the confinement radius " R c " of quantum chromodynamics.
- Work of Roger Howe in the 1970s and his papers with Allen Moy on representations of " p "-adic GL ( " n " ) opened a possibility of classifying irreducible admissible representations of reductive groups over local fields in terms of appropriately constructed Hecke algebras . ( Important contributions were also made by Joseph Bernstein and Andrey Zelevinsky . ) These ideas were taken much further in Colin Bushnell and Philip Kutzko's " theory of types ", allowing them to complete the classification in the general linear case.
- In his " Introduction " to his 1921 Post places the blame on Russell's notion of apparent variable : " Whereas the complete theory [ of Whitehead and Russell ( 1910, 1912, 1913 ) ] requires for the enunciation of its propositions real and apparent variables, which represent both individuals and propositional functions of different kinds, and as a result necessitates the cumbersome theory of types, this subtheory uses only real variables, and these real variables represent but one kind of entity, which the authors have chosen to call elementary propositions ".
- "' Ramified theory of types : function-orders and argument-types, predicative functions "': When Russell proclaimed " all " classes are useful fictions he solved the problem of the " unit " class, but the " overall " problem did not go away; rather, it arrived in a new form : " It will now be necessary to distinguish ( 1 ) terms, ( 2 ) classes, ( 3 ) classes of classes, and so on " ad infinitum "; we shall have to hold that no member of one set is a member of any other set, and that " x " ? " u " requires that " x " should be of a set of a degree lower by one than the set to which " u " belongs.
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