David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Logica Universalis 3 (1):19-57 (2009)
Whereas geometrical oppositions (logical squares and hexagons) have been so far investigated in many fields of modal logic (both abstract and applied), the oppositional geometrical side of “deontic logic” (the logic of “obligatory”, “forbidden”, “permitted”, . . .) has rather been neglected. Besides the classical “deontic square” (the deontic counterpart of Aristotle’s “logical square”), some interesting attempts have nevertheless been made to deepen the geometrical investigation of the deontic oppositions: Kalinowski (La logique des normes, PUF, Paris, 1972) has proposed a “deontic hexagon” as being the geometrical representation of standard deontic logic, whereas Joerden (jointly with Hruschka, in Archiv für Rechtsund Sozialphilosophie 73:1, 1987), McNamara (Mind 105:419, 1996) and Wessels (Die gute Samariterin. Zur Struktur der Supererogation, Walter de Gruyter, Berlin, 2002) have proposed some new “deontic polygons” for dealing with conservative extensions of standard deontic logic internalising the concept of “supererogation”. Since 2004 a new formal science of the geometrical oppositions inside logic has appeared, that is “ n -opposition theory”, or “NOT”, which relies on the notion of “logical bi-simplex of dimension m ” ( m = n − 1). This theory has received a complete mathematical foundation in 2008, and since then several extensions. In this paper, by using it, we show that in standard deontic logic there are in fact many more oppositional deontic figures than Kalinowski’s unique “hexagon of norms” (more ones, and more complex ones, geometrically speaking: “deontic squares”, “deontic hexagons”, “deontic cubes”, . . ., “deontic tetraicosahedra”, . . .): the real geometry of the oppositions between deontic modalities is composed by the aforementioned structures (squares, hexagons, cubes, . . ., tetraicosahedra and hyper-tetraicosahedra), whose complete mathematical closure happens in fact to be a “deontic 5-dimensional hyper-tetraicosahedron” (an oppositional very regular solid).
|Keywords||logical square logical hexagon logical bi-simplexes modal logic deontic logic opposition theory oppositional geometry modal graphs|
|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
Brian F. Chellas (1980). Modal Logic: An Introduction. Cambridge University Press.
Régis Pellissier (2008). “Setting” N-Opposition. Logica Universalis 2 (2):235-263.
Dominique Luzeaux, Jean Sallantin & Christopher Dartnell (2008). Logical Extensions of Aristotle's Square. Logica Universalis 2 (1):167-187.
Sally Popkorn (1994). First Steps in Modal Logic. Cambridge University Press.
Citations of this work BETA
Alessio Moretti (2015). Was Lewis Carroll an Amazing Oppositional Geometer? History and Philosophy of Logic 35 (4):383-409.
Hans Smessaert & Lorenz Demey (2014). Logical Geometries and Information in the Square of Oppositions. Journal of Logic, Language and Information 23 (4):527-565.
Similar books and articles
Juliano S. A. Maranhão (2009). Von Wright's Therapy to Jørgensen's Syndrome. Law and Philosophy 28 (2):163 - 201.
Michael J. Almeida (1990). Deontic Logic and the Possibility of Moral Conflict. Erkenntnis 33 (1):57 - 71.
Sven Ove Hansson (1997). Situationist Deontic Logic. Journal of Philosophical Logic 26 (4):423-448.
Leon Gumański (1980). On Deontic Logic. Studia Logica 39 (1):63 - 75.
Leon Gumański (1983). An Extension of the Deontic Calculus DSC. Studia Logica 42 (2-3):129 - 137.
Heinrich Wansing (1998). Nested Deontic Modalities: Another View of Parking on Highways. [REVIEW] Erkenntnis 49 (2):185-199.
Marcelo E. Coniglio & Newton M. Peron (2009). A Paraconsistentist Approach to Chisholm's Paradox. Principia 13 (3):299-326.
Sieghard Beller (2008). Deontic Norms, Deontic Reasoning, and Deontic Conditionals. Thinking and Reasoning 14 (4):305 – 341.
Richard Evans (2010). Introducing Exclusion Logic as a Deontic Logic. DEON 2010 10 (1):179-195.
Added to index2009-05-30
Total downloads73 ( #56,511 of 1,792,839 )
Recent downloads (6 months)2 ( #345,624 of 1,792,839 )
How can I increase my downloads?