Oppositions and Opposites
- Fabien SchangAffiliated withLHSP Henri Poincaré (UMR7117), Université de Lorraine Email author
A formal theory of oppositions and opposites is proposed on the basis of a non-Fregean semantics, where opposites are negation-forming operators that shed some new light on the connection between opposition and negation. The paper proceeds as follows.
After recalling the historical background, oppositions and opposites are compared from a mathematical perspective: the first occurs as a relation, the second as a function. Then the main point of the paper appears with a calculus of oppositions, by means of a non-Fregean semantics that redefines the logical values of various sorts of sentences. A number of topics are then addressed in the light of this algebraic semantics, namely: how to construct value-functional operators for any logical opposition, beyond the classical case of contradiction; Blanché’s “closure problem”, i.e. how to find a complete structure connecting the sixteen binary sentences with one another.
All of this is meant to devise an abstract theory of opposition: it encompasses the relation of consequence as subalternation, while relying upon the use of a primary “proto-negation” that turns any relatum into an opposite. This results in sentential negations that proceed as intensional operators, while negation is broadly viewed as a difference-forming operator without special constraints on it.
KeywordsINRC Group Negation Opposite-forming operators Opposition Proto-negation
Mathematics Subject Classification03B35 03B05 03B65
- Oppositions and Opposites
- Book Title
- Around and Beyond the Square of Opposition
- pp 147-173
- Print ISBN
- Online ISBN
- Series Title
- Studies in Universal Logic
- Springer Basel
- Copyright Holder
- Springer Basel
- Additional Links
- INRC Group
- Opposite-forming operators
- Industry Sectors
- eBook Packages
- Editor Affiliations
- ID1. , Institute of Philosophy, Federal University of Rio de Janeiro
- ID2. , Institute of Philosophy, University of Bern
- Fabien Schang (1)
- Author Affiliations
- 1. LHSP Henri Poincaré (UMR7117), Université de Lorraine, Nancy, France
To view the rest of this content please follow the download PDF link above.