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The binary quantifiers perspective on logicality

P. 103-104.

Some principles of demarcation of the bounds of logic as formal ontology are discussed. Although Tarski’s philosophical generalization of his permutation invariance criterion - our logic is logic of cardinality - appeared to be justified by the theory of monadic quantification (logic of properties of classes of individuals), it is not correct for the theory of binary quantification (logic of properties of classes of pairs of individuals). The point is that heterogeneous quantifier prefixes considered as binary quantifiers distinguish equicardinal relations. Thus not only cardinalities, but also patterns of ordering of the universe have to be taken into account by logic with binary quantifiers.