In the Manner of Saccheri
DOI:
https://doi.org/10.5007/1808-1711.2019v23n2p145Abstract
I will apply a technique employed by Giovanni Girolamo Saccheri in Logica demonstrative (1701) to concisely prove the invalidity of moods of the First Figure of the Theory of the Assertoric Syllogism without appealing to facts outside logic.
References
CHELLAS, B. F. Modal logic: an introduction. Cambridge: Cambridge University Press, 1980.
GARRIDO, M. Lógica Simbólica. 6ª. Reimpresión revisada. Madrid: Tecnos, 1983.
HALSTED, G. B. Girolamo Saccheri’s Euclides Vindicatus. Second edition. New York: Chelsea, 1986.
MOSTOWSKI, A. “On the rules of proof in the pure functional calculus of the first order”. The Journal of Symbolic Logic 16 (1951): 107-111.
PRIOR, A. N. Independence-proofs without models. Editado por Adriane Rini, Max Cresswell e Peter Ohrstrom. Disponível em: https://research.prior.aau.dk/nachlass/. Acesso em: 21/02/2019.
SMITH, R. Aristotle Prior Analytics. Indianapolis/Cambridge: Hackett, 1989.
STRIKER, G. Aristotle Prior Analytics Book 1. Oxford: Oxford University Press, 2009.
WEIDEMANN, H. “Aristotle on the reducibility of all valid syllogistic moods to the two universal moods of the first figure (APr A7, 29b1-25)”. History and Philosophy of Logic 25, 1 (2004):73-78.
Downloads
Published
Issue
Section
License
![Licença Creative Commons](http://i.creativecommons.org/l/by-nc-nd/3.0/88x31.png)
Principia http://www.periodicos.ufsc.br/index.php/principia/index is licenced under a Creative Commons - Atribuição-Uso Não-Comercial-Não a obras derivadas 3.0 Unported.
Base available in www.periodicos.ufsc.br.