On existence conditions for elements and classes
W. V. Quine · Journal of Symbolic Logic · 1942
In the middle of myMathematical logicI defined a certain class of formulae as “stratified,” and conjectured that exclusion from this class is a feature “shared, presumably, by all the untenable statements (p. 157). This ushered in a set of axioms of class-membership which Rosser has since shown to be inconsistent. Accordingly, inElement and numberI dropped the principle*200, in which had been assembled axioms to the effect, roughly, that “stratified functions of elements are elements.” In lieu of*200 I set forth alternatives in which no appeal is made to stratification. The system ofMathematical logicexclusive of*200 carries over as an unchanging framework; and this framework admits, we know, of a simple consistency proof. My concern in the present paper is to draw attention to certain relationships between this framework and earlier theories.