Questions and Answers about Oppositions

In Jean-Yves Beziau & Gillman Payette (eds.), The Square of Opposition: A General Framework for Cognition. Berne, Suisse: pp. 289-319 (2011)
Download Edit this record How to cite View on PhilPapers
Abstract
A general characterization of logical opposition is given in the present paper, where oppositions are defined by specific answers in an algebraic question-answer game. It is shown that opposition is essentially a semantic relation of truth values between syntactic opposites, before generalizing the theory of opposition from the initial Apuleian square to a variety of alter- native geometrical representations. In the light of this generalization, the famous problem of existential import is traced back to an ambiguous interpretation of assertoric sentences in Aristotle's traditional logic. Following Abelard’s distinction between two alternative readings of the O-vertex: Non omnis and Quidam non, a logical difference is made between negation and denial by means of a more fine- grained modal analysis. A consistent treatment of assertoric oppositions is thus made possible by an underlying abstract theory of logical opposition, where the central concept is negation. A parallel is finally drawn between opposition and consequence, laying the ground for future works on an abstract operator of opposition that would characterize logical negation just as does Tarski’s operator of consequence for logical truth.
Categories
(categorize this paper)
PhilPapers/Archive ID
SCHQAA-5
Upload history
Archival date: 2019-03-09
View other versions
Added to PP index
2019-03-09

Total views
70 ( #48,414 of 2,439,379 )

Recent downloads (6 months)
13 ( #42,605 of 2,439,379 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.