At the end of 2006 the SAS UNIT class, located at Sturges Fields and known for the sports academy students, but containing only 14 students, will be demolished and completely revamped, and will include new changing rooms for the Rugby league and Rugby teams and a new grandstand.
32.
The reason is that, in Russell's detailed analysis, if a unit class ?% becomes a entity in its own right, then it too can be an element in its own proposition; this causes the proposition to become " impredicative " and result in a " vicious circle ".
33.
Unlike the University of California's chain of campuses, where some faculty members feel put upon if they have to handle more than one class a term, CSU professors ordinarily teach four three-unit classes per term, year in and year out, with additional duties as student advisors and as members of academic committees.
34.
Rather, he states ( confusingly ) : " We saw in Chapter II that a cardinal [ natural ] number is to be defined as a class of classes, and in Chapter III that the number 1 is to be defined as the class of all unit classes, of all that have just one member, as we should say but for the vicious circle.
35.
After he discovered the paradox in Frege's " Begriffsschrift " he added Appendix A to his 1903 where through the analysis of the nature of the null and unit classes, he discovered the need for a " doctrine of types "; see more about the unit class, the problem of impredicative definitions and Russell's " vicious circle principle " below.
36.
After he discovered the paradox in Frege's " Begriffsschrift " he added Appendix A to his 1903 where through the analysis of the nature of the null and unit classes, he discovered the need for a " doctrine of types "; see more about the unit class, the problem of impredicative definitions and Russell's " vicious circle principle " below.
37.
"' Fatal impredicativity in the definition of the unit class "': The problem that bedeviled the logicists ( and set theorists too, but with a different resolution ) derives from the ? = NOT-? paradox Russell discovered in Frege's 1879 " Begriffsschrift " that Frege had allowed a function to derive its input " functional " ( value of its variable ) not only from an object ( thing, term ), but from the function's own output as well.
