Year: 2026
Type: article
Abstract: Aristotle’s Analytica Priora contains three systems of syllogistic proof, what are known as ‘figures’ 1–3. Aristotle states that all syllogistic inferences reduce to the first one but does not carry that through. It turns out that this reduction hides up to three nested instances of indirect proof. Syllogistic derivations are given as two-dimensional derivation trees—the only addition of substance to Aristotle’s proofs—with the result that nested indirect proofs can be resolved into a single such step, in perfect analogy to steps of normalization in natural deduction.
Source: Studia Logica
Authors: Melissa Antonelli, Jan von Plato
Institution: University of Helsinki
Language: English
Subfield: Philosophy
Field: Arts and Humanities
Domain: Social Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
Funder: Helsingin Yliopisto
OpenAlex ID: W7130345414