David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal of Philosophical Logic 4 (2):237 - 252 (1975)
Recently, Bengt Hansson presented a paper about dyadic deontic logic,2 criticizing some purely axiomatic systems of dyadic deontic logic and proposing three purely semantical systems of dyadic deontic logic which he confidently called dyadic standard systems of deontic logic (DSDL1–3). Here I shall discuss the third by far most interesting system DSDL3 which is operating with preference relations. First, I shall describe this semantical system (Sections 1.1–1.3). Then I shall give an axiomatic system (Section 1.4) which is proved to be correct (Section 2) and complete (Section 3) with respect to Hansson's semantics. Finally, in face of these results Hansson's semantics will be discussed from a more intuitive standpoint. After emphasizing its intuitive attractiveness (Section 4.1) I will show that two objections often discussed in connection with preference relations do not apply to it (Section 4.2 and 4.3); more precisely, I will show that the connectedness condition for preference relations can be dropped and that, in a sense, it is not necessary to compare two possible worlds differing in infinitely many respects. (What exactly is meant by this, will become clear later on.) Yet there is a third objection to Hansson's semantics which points to a real intuitive inadequacy of DSDL3. A way of removing this inadequacy, which corresponds to Hansson's own intuitions as well as to familiar metaethical views, is suggested, but not technically realized (Section 4.4). In the last section (section 4.5) I shall briefly show that DSDL3 is decidable, as expected
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References found in this work BETA
Bengt Hansson (1968). Choice Structures and Preference Relations. Synthese 18 (4):443 - 458.
Jaakko Hintikka (1971). Some Main Problems of Deontic Logic. In Risto Hilpinen (ed.), Deontic Logic: Introductory and Systematic Readings. Sold and Distributed in the U.S.A. And Canada by Kluwer Boston 59-104.
Citations of this work BETA
Xavier Parent (2014). Maximality Vs. Optimality in Dyadic Deontic Logic. Journal of Philosophical Logic 43 (6):1101-1128.
Jörg Hansen (2006). Deontic Logics for Prioritized Imperatives. Artificial Intelligence and Law 14 (1-2):1-34.
Jennifer Carr (2014). The If P, Ought P Problem. Pacific Philosophical Quarterly 95 (4):555-583.
Lauri Carlson (1994). Logic for Dialogue Games. Synthese 99 (3):377 - 415.
Johan Benthem, Davide Grossi & Fenrong Liu (2014). Priority Structures in Deontic Logic. Theoria 80 (2):116-152.
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