Logica Universalis 2 (1):127-141 (2008)

.  Each predicate of the Aristotelian square of opposition includes the word “is”. Through a twofold interpretation of this word the square includes both classical logic and non-classical logic. All theses embodied by the square of opposition are preserved by the new interpretation, except for contradictories, which are substituted by incommensurabilities. Indeed, the new interpretation of the square of opposition concerns the relationships among entire theories, each represented by means of a characteristic predicate. A generalization of the square of opposition is achieved by not adjoining, according to two Leibniz’ suggestions about human mind, one more choice about the kind of infinity; i.e., a choice which was unknown by Greek’s culture, but which played a decisive role for the birth and then the development of modern science. This essential innovation of modern scientific culture explains why in modern times the Aristotelian square of opposition was disregarded.
Keywords Square of opposition  non-classical logic  incommensurabilities  Leibniz  infinity  fundamental choices
Categories (categorize this paper)
DOI 10.1007/s11787-007-0032-9
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

The Traditional Square of Opposition.Terence Parsons - 2008 - Stanford Encyclopedia of Philosophy.
From the Closed World to the Infinite Universe.[author unknown] - 1958 - British Journal for the Philosophy of Science 9 (35):234-245.

Add more references

Citations of this work BETA

Leibniz and the Square: A Deontic Logic for the Vir Bonus.Chris Johns - 2014 - History and Philosophy of Logic 35 (4):369-376.

Add more citations

Similar books and articles


Added to PP index

Total views
72 ( #158,296 of 2,499,071 )

Recent downloads (6 months)
15 ( #53,274 of 2,499,071 )

How can I increase my downloads?


My notes