Non-Traditional Squares of Predication and Quantification
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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.
Mathematics Subject Classification (2000).Primary 03C80 Secondary 62A01
Keywords.Internal negation predication denying quantification logical squares
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