Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

Mathematics of Totalities: An Alternative to Mathematics of Sets

Herman Dishkant
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
  • Download ($43.95)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
Mathematics of Totalities: An Alternative to Mathematics of Sets
Preview not available

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 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.

Page Thumbnails

  • Thumbnail: Page 
[319]
    [319]
  • Thumbnail: Page 
320
    320
  • Thumbnail: Page 
321
    321
  • Thumbnail: Page 
322
    322
  • Thumbnail: Page 
323
    323
  • Thumbnail: Page 
324
    324
  • Thumbnail: Page 
325
    325
  • Thumbnail: Page 
326
    326