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# THE HOMEPAGE OF "NOT"

(*N*-Opposition Theory),

a.k.a. "Oppositional Geometry"

# THERE IS AN ENTIRELY NEW WEBSITE:
CLICK HERE

### (OR CLICK ANY LINK TO GET TO THE NEW WEBSITE)

Stemming from works on the geometry of logical negation (rooted in a discussion of the foundations
of paraconsistent logics), “oppositional geometry” (OG, for short) is the name of what seems to be
a new branch of mathematics, similar to, but different from theories like diagrammatic logic, graph
theory or knot theory. Previously known as “N-opposition theory” (i.e. NOT), OG gives one of the
most general frameworks explaining what are things like the “logical square (or « square of
opposition”) (200 a.D.), the “logical hexagon” (1950), the « logical cube » (2004), the « logical
tetrahexahedron » (1968) and so on (all seen, inside OG, as constituted of « oppositional
bi-simplexes of dim. m« ).
NOT.FourActorsOfNOT
One of the backbones of OG, the theory of the “oppositional poly-simplexes
(of dimension m)”, which generalises the notion of bi-simplex implicit in Aristotle’s theory
of opposition, is itself generated by an “ask-answer” game-theoretical device, the “Aristotelian
pQ-semantics” and its “Aristotelian pQ-lattices”. By unfolding the mathematics of opposition
in form of a new kind of geometry, OG gives to mathematicians, logicians, philosophers, linguists,
ontologists, computer scientists and many others a general framework for modelling and handling
through « oppositional structures » any “opposition phenomena” (first static, but then also
dynamic). The concept of “opposition” being a very fundamental, elementary and pervasive one
(recall that, for instance, “negation” – a highly important concept for logics and mathematics
– is just one particular kind of opposition), OG is already finding applications in linguistics,
modal logic, many-valued logic, formal ontology, artificial intelligence and in the humanities
(semiotics, anthropology, sociology, gender studies, …). OG is strongly related to some kind of
twin theory, « Logical Geometry » (LG): the field of both correlated theories is growing and
this website (as well as its twin LG-website) aims at giving access to anyone interested to
the state of the art. In that respect, NOT-workshops (i.e. workshops joining scholars of OG,
LG and similar) aim at promoting the exchange, possibly interdisciplinary, between scholars
concerned in various ways with opposition phenomena and opposition structures. Any feedback,
information and/or collaboration is very welcome

Webmaster : homepage - e-mail.
Website created the 16th March 2009

Last update: 11th/10/2015. The figure is taken from: Moretti, A.,
*The Geometry of Logical Opposition*, ch. 8 (2009)