Non-Traditional Squares of Predication and Quantification

Abstract.

Three logical squares of predication or quantification, which one can even extend to logical hexagons, will be presented and analyzed. All three squares are based on ideas of the non-traditional theory of predication developed by Sinowjew and Wessel. The authors also designed a non-traditional theory of quantification. It will be shown that this theory is superfluous, since it is based on an obscure difference between two kinds of quantification and one pays a high price for differentiating in this way: losing the definability between the existence- and all-quantifier. Therefore, a combination of non-traditional predication and classical quantification is preferred here.