The geometry of negation
| Abstract | There are two natural ways of thinking about negation: (i) as a form of complementation and (ii) as an operation of reversal, or inversion (to deny that p is to say that things are "the other way around"). A variety of techniques exist to model conception (i), from Euler and Venn diagrams to Boolean algebras. Conception (ii), by contrast, has not been given comparable attention. In this note we outline a twofold geometric proposal, where the inversion metaphor is understoood as involving a rotation o a reflection, respectively. These two options are equivalent in classical two-valued logic but they differ significantly in many-valued logics. Here we show that they correspond to two basic sorts of negation operators— Posts and Kleenes—and we provide a simple group-theoretic argument demonstrating their generative power. | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | No categories specified (fix it) | |||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,672 |
| External links |
  Try with proxy. Try with proxy. |
| Through your library | Only published papers are available at libraries |
Similar books and articlesMichael Beeson, Robert Veroff & Larry Wos (2005). Double-Negation Elimination in Some Propositional Logics. Studia Logica 80 (2-3):195 - 234.
M. Spinks & R. Veroff (2008). Constructive Logic with Strong Negation is a Substructural Logic. II. Studia Logica 89 (3):401 - 425.
Matthew Spinks & Robert Veroff (2008). Constructive Logic with Strong Negation is a Substructural Logic. I. Studia Logica 88 (3):325 - 348.
Arnon Avron (2005). A Non-Deterministic View on Non-Classical Negations. Studia Logica 80 (2-3):159 - 194.
Lloyd Humberstone (2008). Contrariety and Subcontrariety: The Anatomy of Negation (with Special Reference to an Example of J.-Y. Béziau). Theoria 71 (3):241-262.
Ernesto Napoli (2006). Negation. Grazer Philosophische Studien 72 (1):233-252.
Marco Hollenberg (1997). An Equational Axiomatization of Dynamic Negation and Relational Composition. Journal of Logic, Language and Information 6 (4):381-401.
Marie la Palme Reyes, John Macnamara, Gonzalo E. Reyes & And Houman Zolfaghari (1994). The Non-Boolean Logic of Natural Language Negation. Philosophia Mathematica 2 (1):45-68.
Dimiter Vakarelov (2005). Nelson's Negation on the Base of Weaker Versions of Intuitionistic Negation. Studia Logica 80 (2-3):393 - 430.
Analytics
Monthly downloads |
Added to index2009-01-28Total downloads15 ( #78,614 of 549,065 )Recent downloads (6 months)1 ( #63,185 of 549,065 )How can I increase my downloads? |
My notes
Discussion
