The set-theoretic and individual-theoretic analyses of collections make the same mistake: their ontologies are far removed from language. Our basic notion, the collector, has a clear linguistic counterpart: the definite article. Our theory furnishes a theory of definite descriptions as a special case. We use 3-valued valued logic in order to come to grips with the existential presuppositions of the collections.

SummaryIf there is truth, there is formal truth and finally truth in the set universe \V. Confiding in formal truth and reflecting this confidence we are led beyond all set and class theories to the Absolute Indefinite und formal inexpressibility of the whole concept of formal truth – a logical path to Mahlyha Buddhism.

Quine's metalogical 'quasiquotation' is formally added to classical first-Order logic; the resulting system lq is stronger and more natural than all former systems of quotational logic. Lq contains object-Variables ranging over the universe u and expression-Variables ranging over the set e of all expressions of lq; e is a subset of u. Object-Quantifiers are referential, Expression-Quantifiers are substitutional; only the latter ones bind into quasiquotations. Lq contains its own syntactic metatheory and arithmetics. Natural proofs of godel's and tarski's theorems are (...) given for lq. (shrink)

Let k be the number of all pure sets, und let K be the number of all pure classes. The Platonist, assuming that the class \V of all pure sets cannot be enlarged by any formal means, will come to the conclusion that cardinalities between k und K are conceptually impossible. So the Continuum Hypothesis is true on class level. And if this feature of \V is reflected by all infinite sets \Va, the General Continuum Hypothesis is true on set (...) level. (shrink)

Let k be the number of all pure sets, und let K be the number of all pure classes. The Platonist, assuming that the class \V of all pure sets cannot be enlarged by any formal means, will come to the conclusion that cardinalities between k und K are conceptually impossible. So the Continuum Hypothesis is true on class level. And if this feature of \V is reflected by all infinite sets \Va, the General Continuum Hypothesis is true on set (...) level. (shrink)