Does a Leaking O-Corner Save the Square?
- Pieter A. M. SeurenAffiliated withMax Planck Institute for Psycholinguistics Email author
It has been known at least since Abelard (12th century) that the classic Square of Opposition suffers from so-called undue existential import (UEI) in that this system of predicate logic collapses when the class denoted by the restrictor predicate is empty. It is usually thought that this mistake was made by Aristotle himself, but it has now become clear that this is not so: Aristotle did not have the Conversions but only one-way entailments, which ‘saves’ the Square. The error of UEI was introduced by his later commentators, especially Apuleius and Boethius. Abelard restored Aristotle’s original logic. After Abelard, some 14th- and 15th-century philosophers (mainly Buridan and Ockham) meant to save the Square by declaring the O-corner true when the restrictor class is empty. This ‘leaking O-corner analysis’, or LOCA, was taken up again around 1950 by some American philosopher-logicians, who now have a fairly large following. LOCA does indeed save the Square from logical disaster, but modern analysis shows that this makes it impossible to give a uniform semantic definition of the quantifiers, which thus become ambiguous—an intolerable state of affairs in logic. Klima (Ars Artium, Essays in Philosophical Semantics, Medieval and Modern, Institute of Philosophy, Hungarian Academy of Sciences, Budapest, 1988) and Parsons (in Zalta (ed.), The Stanford Encyclopedia of Philosophy, http://plato.standford.edu/entries/square/, 2006; Logica Univers. 2:3–11, 2008) have tried to circumvent this problem by introducing a ‘zero’ element into the ontology, standing for non-existing entities and yielding falsity when used for variable substitution. LOCA, both without and with the zero element, is critically discussed and rejected on internal logical and external ontological grounds.
KeywordsAbelard Aristotle Boethius Buridan Existential import Null element O-Corner Predicate negation Restricted quantification Square of Opposition
Mathematics Subject Classification03B65 03B50
- Does a Leaking O-Corner Save the Square?
- Book Title
- Around and Beyond the Square of Opposition
- pp 129-138
- Print ISBN
- Online ISBN
- Series Title
- Studies in Universal Logic
- Springer Basel
- Copyright Holder
- Springer Basel
- Additional Links
- Existential import
- Null element
- Predicate negation
- Restricted quantification
- Square of Opposition
- Industry Sectors
- eBook Packages
- Editor Affiliations
- ID1. , Institute of Philosophy, Federal University of Rio de Janeiro
- ID2. , Institute of Philosophy, University of Bern
- Author Affiliations
- 1. Max Planck Institute for Psycholinguistics, PO Box 310, 6500 AH, Nijmegen, The Netherlands
To view the rest of this content please follow the download PDF link above.