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Mathematics of Totalities: An Alternative to Mathematics of Sets
Studia Logica: An International Journal for Symbolic Logic
Vol. 47, No. 4 (1988), pp. 319-326
Published by: Springer
Stable URL: http://www.jstor.org/stable/20015386
Page Count: 8
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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 logic TT, where a proposition letters some totality. The proposition is true if it letters the greatest totality. There are five connectives in TT: ∧, ∨, ∩, ⅂, # and the last is called plexus. The truth of σ # π means that any element of the totality σ has a nonempty intersection with any element of the totality π. An imbedding G of the classical predicate logic CPL in TT is defined. A formula f of CPL is a classical tautology if and only if G(f) is always true in TT. So, mathematics may be expounded in TT, without quantifiers.
Studia Logica: An International Journal for Symbolic Logic © 1988 Springer