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The Moral Law and The Good in Temporal Modal Deontic Logic with Propositional Quantifiers
Stockholm University, Faculty of Humanities, Department of Philosophy.
Number of Authors: 12020 (English)In: Australasian Journal of Logic, ISSN 1448-5052, Vol. 17, no 1, p. 22-69, article id 2Article in journal (Refereed) Published
Abstract [en]

The Moral Law is fulfilled (in a possible world omega at a time tau) iff (if and only it) everything that ought to be the case is the case (in omega at tau), and The Good (or The Highest Possible Good) is realised in a possible world omega at a time tau iff omega is deontically accessible from omega at tau. In this paper, I will introduce a set of temporal modal deontic systems with propositional quantifiers that can be used to prove some interesting theorems about The Moral Law and The Good. First, I will describe a set of systems without any propositional quantifiers. Then, I will show how these systems can be extended by a couple of propositional quantifiers. I will use a kind of T x W semantics to describe the systems semantically and semantic tableaux to describe them syntactically. Every system will include a constant . that stands for The Good. '.' is read as 'The Good is realised'. All systems that contain the propositional quantifiers will also include a constant * that stands for The Moral Law. 'star' is read as 'The Moral Law is fulfilled'. I will prove that all systems (without the propositional quantifiers) are sound and complete with respect to their semantics and that all systems (including the extended systems) are sound with respect to their semantics. It is left as an open question whether or not the extended systems are complete.

Place, publisher, year, edition, pages
2020. Vol. 17, no 1, p. 22-69, article id 2
Keywords [en]
The Moral Law, The Good, Temporal Modal Deontic Logic, Propositional Quantifiers, Semantic Tableaux
National Category
Philosophy, Ethics and Religion
Identifiers
URN: urn:nbn:se:su:diva-181379DOI: 10.26686/ajl.v17i1.5674ISI: 000524980200002OAI: oai:DiVA.org:su-181379DiVA, id: diva2:1429794
Available from: 2020-05-12 Created: 2020-05-12 Last updated: 2022-04-06Bibliographically approved

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Rönnedal, Daniel

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