David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
Learn more about PhilPapers
Bochumer Philosophisches Jahrbuch Fur Antike Und Mittelalter 13 (1):54-86 (2009)
The goal of this paper is an interpretation of Aristotle's modal syllogistics closely oriented on the text using the resources of modern modal predicate logic. Modern predicate logic was successfully able to interpret Aristotle's assertoric syllogistics uniformly , that is, with one formula for universal premises. A corresponding uniform interpretation of modal syllogistics by means of modal predicate logic is not possible. This thesis does not imply that a uniform view is abandoned. However, it replaces the simple unity of the assertoric by the complex unity of the modal. The complexity results from the fact that though one formula for universal premises is used as the basis, it must be moderated if the text requires . Aristotle introduces his modal syllogistics by expanding his assertoric syllogistics with an axiom that links two apodictic premises to yield a single apodictic sentence . He thus defines a regular modern modal logic. By means of the regular modal logic that is thus defined, he is able to reduce the purely apodictic syllogistics to assertoric syllogistics. However, he goes beyond this simple structure when he looks at complicated inferences. In order to be able to link not only premises of the same modality, but also premises with different modalities, he introduces a second axiom, the T-axiom, which infers from necessity to reality or - equivalently - from reality to possibility. Together, the two axioms, the axiom of regularity and the T-axiom, define a regular T-logic. It plays an important role in modern logic. In order to be able to account for modal syllogistics adequately as a whole, another modern axiom is also required, the so-called B-axiom. It is very difficult to decide whether Aristotle had the B-axiom. The two last named axioms are sufficient to achieve the required contextual moderation of the basic formula for universal propositions
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
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
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
W. J. Blok (1980). The Lattice of Modal Logics: An Algebraic Investigation. Journal of Symbolic Logic 45 (2):221-236.
Giangiacomo Gerla & Virginia Vaccaro (1984). Modal Logic and Model Theory. Studia Logica 43 (3):203 - 216.
Kazimierz Świrydowicz (1990). On Regular Modal Logics with Axiom □ ⊤ → □□ ⊤. Studia Logica 49 (2):171 - 174.
Henrik Lagerlund (2009). Avicenna and Ūsī on Modal Logic. History and Philosophy of Logic 30 (3):227-239.
Richard Patterson (1990). Conversion Principles and the Basis of Aristotle's Modal Logic. History and Philosophy of Logic 11 (2):151-172.
Melvin Fitting (2012). Barcan Both Ways. Journal of Applied Non-Classical Logics 9 (2-3):329-344.
Tapio Korte, Ari Maunu & Tuomo Aho (2009). Modal Logic From Kant to Possible Worlds Semantics. In Leila Haaparanta (ed.), The Development of Modern Logic. Oxford University Press
Edward M. Engelmann (2007). Aristotle's Syllogystic, Modern Deductive Logic, and Scientific Demonstration. American Catholic Philosophical Quarterly 81 (4):535-552.
Added to index2010-08-14
Total downloads18 ( #216,586 of 1,934,425 )
Recent downloads (6 months)1 ( #434,207 of 1,934,425 )
How can I increase my downloads?