A Study of the Metatheory of Assertoric Syllogistic

Logica Universalis 17 (3):347-371 (2023)
  Copy   BIBTEX

Abstract

We show how a semantics based on Aristotle’s texts and ecthetic proofs can be reconstructed. All truth conditions are given by means of set inclusion. Perfect syllogisms reveal to be valid arguments that deserve a validity proof. It turns out of these proofs that transitivity of set inclusion is the necessary and sufficient condition for the validity and perfection of a syllogism. The proofs of validity for imperfect syllogisms are direct proofs without conversion in a calculus of natural deduction. Transitivity of set inclusion turns out to be a necessary condition for the validity of imperfect syllogisms. As a consequence, it can be established what the main metalogical difference between a perfect and an imperfect syllogism is. The validity of the laws of conversion is also obtained by direct proofs. Finally, it is shown that and explained why some imperfect syllogisms satisfy the definition of a perfect syllogism.

Author's Profile

Maristela Rocha
University of Salzburg (PhD)

Analytics

Added to PP
2023-08-23

Downloads
42 (#97,144)

6 months
26 (#96,748)

Historical graph of downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.
How can I increase my downloads?