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Studia Logica

, Volume 47, Issue 4, pp 319–326 | Cite as

Mathematics of Totalities: an alternative to mathematics of sets

  • Herman Dishkant
Article
  • 20 Downloads

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 σ # π means that any element of the totality σ has a nonempty intersection with any element of the totality π. 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.

Keywords

Mathematical Logic Computational Linguistic Nonempty Intersection Proposition Letter Classical Predicate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    R. Descartes,Regulae ad directionem ingenii, 1628.Google Scholar
  2. [2]
    D. H. H. Ingalls,Matherials for the Study of Navya-Nyaya Logic, Cambridge, 1951.Google Scholar
  3. [3]
    H. Rasiowa andR. Sikorski,The Mathematics of Metamathematics, Warszawa, 1963.Google Scholar

Copyright information

© Polish Academy of Sciences 1988

Authors and Affiliations

  • Herman Dishkant
    • 1
  1. 1.Theoretical Problems DepartmentThe USSR Academy of SciencesMoscow

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