Mathematics of totalities: An alternative to mathematics of sets

Studia Logica 47 (4):319 - 326 (1988)
Abstract
I dare say, a set is contranatural if some pair of its elements has a nonempty intersection. So, we consider only collections of disjoint nonempty elements and call them totalities. We propose the propositional logicTT, where a proposition letters some totality. The proposition is true if it letters the greatest totality. There are five connectives inTT: , , , , # and the last is called plexus. The truth of # means that any element of the totality has a nonempty intersection with any element of the totality . An imbeddingG of the classical predicate logicCPL inTT is defined. A formulaf ofCPL is a classical tautology if and only ifG(f) is always true inTT. So, mathematics may be expounded inTT, without quantifiers.
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