Aristotelian Predicate Calculus Restored
Pieter Seuren

This is about a surprising thing I discovered  recently with regard to
predicate calculus. For the past 100 years, Aristotelian Predicate
Calculus (APC) has been replaced by modern, Russellian predicate calculus,
for valid reasons. However, the faults of APC are easily restored in a way
that differs from Russell's and involves only minimal changes to the
Aristotelian Square, something that was,  apparently, never noticed
before. This result is significant, especially in the context of natural
language semantic intuitions. I will also show how the original
Aristotelian Square is automatically restored to its pristine form if the
standard negation is replaced with a more restricted negation that leaves
presuppositions untouched.