According to the so-called golden rule, we ought to treat others as we want to be treated by them. This rule, in one form or another, is part of every major religion, and it has been accepted by many philosophers with various ethical views. However, if the literal golden rule is interpreted as an absolute rule, it is problematic. In this paper, I introduce a new version of this famous principle that is similar to various classical definitions. According to this variant, the rule can be formulated in the following way: If you want it to be the case that if 𝑥 were in your situation and you were in 𝑥’s situation then 𝑥 would do 𝐻 to you, and you have a good will, then you ought to do 𝐻 to x. I show how this version can be derived from a small set of highly plausible premises, and I defend it against some of the most interesting and/or common objections against the golden rule in the literature. I conclude that we have good reason to believe in this rendition of the principle.

The paper develops a set of quantified temporal alethic boulesic doxastic systems. Every system in this set consists of five parts: a 'quantified' part, a temporal part, a modal (alethic) part, a boulesic part and a doxastic part. There are no systems in the literature that combine all of these branches of logic. Hence, all systems in this paper are new. Every system is defined both semantically and proof-theoretically. The semantic apparatus consists of a kind of T x W models, and the proof-theoretical apparatus of semantic tableaux. The 'quantified part' of the systems includes relational predicates and the identity symbol. The quantifiers are, in effect, a kind of possibilist quantifiers that vary over every object in the domain. The tableaux rules are classical. The alethic part contains two types of modal operators for absolute and historical necessity and possibility. According to `boulesic logic' (the logic of the will), 'willing' (`consenting', 'rejecting', 'indifference' and 'non-indifference') is a kind of modal operator. Doxastic logic is the logic of beliefs; it treats 'believing' (and `conceiving') as a kind of modal operator. I will explore some possible relationships between these different parts, and investigate some principles that include more than one type of logical expression. I will show that every tableau system in the paper is sound and complete with respect to its semantics. Finally, I consider an example of a valid argument and an example of an invalid sentence. I show how one can use semantic tableaux to establish validity and invalidity and read off countermodels. These examples illustrate the philosophical usefulness of the systems that are introduced in this paper.

This paper discusses a new aporia, the aporia of future directed beliefs. This aporia contains three propositions: (1) It is possible that there is someone who is infallible that believes something about the future that is not historically settled, (2) it is necessary that someone is infallible if and only if it is necessary that everything she believes is true, and (3) it is necessary that all our beliefs are historically settled. Every claim in this set is intuitively plausible, and there are interesting arguments for or against each of them. Nevertheless, {(1), (2), (3)} entails a contradiction. Consequently, at least one of the sentences in this set must be false. I consider some possible solutions to the problem and discuss some arguments for and against these solutions. Five solutions, in particular, stand out. Three solutions reject (1), one solution rejects (2), and one solution rejects (3). No solution is without problems, and it is not obvious which one we should choose. Yet, we have to give up at least one sentence in {(1), (2), (3)}. This is the nature of an aporia.

In this paper, I will discuss boulesic and deontic logic and the relationship between these branches of logic. By 'boulesic logic,' or 'the logic of the will,' I mean a new kind of logic that deals with `boulesic' concepts, expressions, sentences, arguments and systems. I will concentrate on two types of boulesic expression: 'individual x wants it to be the case that' and 'individual x accepts that it is the case that.' These expressions will be symbolised by two sentential operators that take individuals and sentences as arguments and give sentences as values. Deontic logic is a relatively well-established branch of logic. It deals with normative concepts, sentences, arguments and systems. In this paper, I will show how deontic logic can be grounded in boulesic logic. I will develop a set of semantic tableau systems that include boulesic and alethic operators, possibilist quantifiers and the identity predicate; I will then show how these systems can be augmented by a set of deontic operators. I use a kind of possible world semantics to explain the intended meaning of our formal systems. Intuitively, we can think of our semantics as a description of the structure of a perfectly rational will. I mention some interesting theorems that can be proved in our systems, including some versions of the so-called hypothetical imperative. Finally, I show that all systems that are described in this paper are sound and complete with respect to their semantics.

This paper is about The Good and its relation to various kinds of goodness. I will investigate what it means to say that something is a highest good, a final all-inclusive, complete, or greatest good, and I will consider some definitions of ‘instrumental’ and ‘non-instrumental’ goodness. I will prove several interesting theorems about The Good and explore some of the essential relationships between various kinds of goodness.

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.

In this paper, I will develop a set of boulesic-doxastic tableau systems and prove that they are sound and complete. Boulesic-doxastic logic consists of two main parts: a boulesic part and a doxastic part. By 'boulesic logic' I mean 'the logic of the will', and by `doxastic logic' I mean 'the logic of belief'. The first part deals with 'boulesic' concepts, expressions, sentences, arguments and theorems. I will concentrate on two types of boulesic expression: 'individual x wants it to be the case that' and 'individual x accepts that it is the case that'. The second part deals with 'doxastic' concepts, expressions, sentences, arguments and theorems. I will concentrate on two types of doxastic expression: 'individual x believes that' and 'it is imaginable to individual x that'. Boulesic-doxastic logic investigates how these concepts are related to each other. Boulesic logic is a new kind of logic. Doxastic logic has been around for a while, but the approach to this branch of logic in this paper is new. Each system is combined with modal logic with two kinds of modal operators for historical and absolute necessity and predicate logic with necessary identity and 'possibilise quantifiers. I use a kind of possible world semantics to describe the systems semantically. I also sketch out how our basic language can be extended with propositional quantifiers. All the systems developed in this paper are new.

In this paper, I will discuss some examples of the so-called contrary-to-duty (obligation) paradox, a well-known puzzle in deontic logic. A contrary-to-duty obligation is an obligation telling us what ought to be the case if something forbidden is true, for example: 'If she is guilty, she should confess'. Contrary-to-duty obligations are important in our moral and legal thinking. Therefore, we want to be able to find an adequate symbolisation of such obligations in some logical system, a task that has turned out to be difficult. This is shown by the so-called contrary-to-duty (obligation) paradox. I will investigate and evaluate one kind of solution to this problem that has been suggested in the literature, which I will call the 'counterfactual solution'. I will use some recent systems that combine not only counterfactual logic and deontic logic, but also temporal logic, in my analysis of the paradox. I will argue that the counterfactual solution has many attractive features and that it can give a fairly satisfactory answer to some examples of the contrary-to-duty paradox, but that it nevertheless has some serious problems. The conclusion is that, notwithstanding the many attractive features of the solution, there seem to be other approaches to the paradox that are more promising.

In Symbolic Logic (1932), C. I. Lewis developed five modal systems S1 - S5. S4 and S5 arc so-called normal modal systems. Since Lewis and La.ngford's pioneering work many other systems of this kind have been investigated, among them the 32 systems that can be generated by the five axioms T, D, B, 4 and 5. Lewis also discusses how his systems can be augmented by propositional quantifiers and how these augmented logics allow us to express some interesting ideas that cannot be expressed in the corresponding quantifier-free logics. In this paper, I will develop 64 normal modal semantic tableau systems that can be extended by propositional quantifiers yielding 64 extended systems. All in all, we will investigate 128 different systems. I will show how these systems can be used to prove some interesting theorems and I will discuss Lewis's so-called existence postulate and some of its consequences. Finally, I will prove that all normal modal systems are sound and complete 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.

In this paper, I introduce a new aporia, the aporia of perfection. This aporia includes three claims: (1) Ought implies possibility, (2) We ought to be perfect, and (3) It is not possible that we are perfect. All these propositions appear to be plausible when considered in themselves and there are interesting arguments for them. However, together they entail a contradiction. Hence, at least one of the sentences must be false. I consider some possible solutions to the puzzle and discuss some pros and cons of these solutions. I conclude that we can avoid the contradiction that follows from (1) (3) and still hold on to our basic intuitions, if we instead of (1) (3) accept some slightly different propositions.