•  606
    Dyadic deontic logic and semantic tableaux
    Logic and Logical Philosophy 18 (3-4): 221-252. 2009.
    The purpose of this paper is to develop a class of semantic tableau systems for some dyadic deontic logics. We will consider 16 different pure dyadic deontic tableau systems and 32 different alethic dyadic deontic tableau systems. Possible world semantics is used to interpret our formal languages. Some relationships between our systems and well known dyadic deontic logics in the literature are pointed out and soundness results are obtained for every tableau system. Completeness results are obtai…Read more
  •  442
    Counterfactuals and semantic tableaux
    Logic and Logical Philosophy 18 (1): 71-91. 2009.
    The purpose of this paper is to develop a class of semantic tableau systems for some counterfactual logics. All in all I will discuss 1024 systems. Possible world semantics is used to interpret our formal languages. Soundness results are obtained for every tableau system and completeness results for a large subclass of these.
  •  224
    Doxastic logic: a new approach
    Journal of Applied Non-Classical Logics 28 (4): 313-347. 2018.
    In this paper, I develop a new set of doxastic logical systems and I show how they can be used to solve several well-known problems in doxastic logic, for example the so-called problem of logical omniscience. According to this puzzle, the notions of knowledge and belief that are used in ordinary epistemic and doxastic symbolic systems are too idealised. Hence, those systems cannot be used to model ordinary human or human-like agents' beliefs. At best, they can describe idealised individuals. The…Read more
  •  223
    Quantified Temporal Alethic Boulesic Doxastic Logic
    Logica Universalis 15 (1): 1-65. 2021.
    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$$T \times W$$T×Wmodels, and the…Read more
  •  219
    The Golden Rule and The Platinum Rule
    Journal of Value Inquiry 49 (1-2): 221-236. 2015.
    The purpose of this paper is to investigate the relationships between the so-called golden rule and the so-called platinum rule. According to the golden rule (GR) you ought to treat others as you want to be treated by them; and according to the platinum rule (PR), you ought to treat others as they want to be treated by you. In this essay I argue for the following propositions. (1) (GR) and (PR) are logically independent. (2) (PR) can be derived from (GR) given that you want to be treated by othe…Read more
  •  164
    Temporal alethic–deontic logic and semantic tableaux
    Journal of Applied Logic 10 (3): 219-237. 2012.
    The purpose of this paper is to describe a set of temporal alethic–deontic systems, i.e. systems that include temporal, alethic and deontic operators. All in all we will consider 2,147,483,648 systems. All systems are described both semantically and proof theoretically. We use a kind of possible world semantics, inspired by the so-called T x W semantics, to characterize our systems semantically and semantic tableaux to characterize them proof theoretically. We also show that all systems are soun…Read more
  •  161
    The Aporia of Future Directed Beliefs
    Acta Analytica 36 (2): 249-261. 2020.
    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 …Read more
  •  146
    The Moral Law and The Good in Temporal Modal Logic with Propositional Quantifiers
    Australasian Journal of Logic 17 (1): 22-69. 2020.
    The Moral Law is fulfilled iff everything that ought to be the case is the case, and The Good is realised in a possible world w at a time t iff w is deontically accessible from w at t. 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 exte…Read more
  •  146
    Quantified temporal alethic-deontic logic
    Logic and Logical Philosophy 24 (1): 19-59. 2014.
    The purpose of this paper is to describe a set of quantified temporal alethic-deontic systems, i.e., systems that combine temporal alethicdeontic logic with predicate logic. We consider three basic kinds of systems: constant, variable and constant and variable domain systems. These systems can be augmented by either necessary or contingent identity, and every system that includes identity can be combined with descriptors. All logics are described both semantically and proof theoretically. We use…Read more
  •  138
    Temporal Alethic Dyadic Deontic Logic and the Contrary-to-Duty Obligation Paradox
    Logic and Logical Philosophy 27 (1): 3-25. 2018.
    A contrary-to-duty obligation (sometimes called a reparational duty) is a conditional obligation where the condition is forbidden, e.g. “if you have hurt your friend, you should apologise”, “if he is guilty, he should confess”, and “if she will not keep her promise to you, she ought to call you”. It has proven very difficult to find plausible formalisations of such obligations in most deontic systems. In this paper, we will introduce and explore a set of temporal alethic dyadic deontic systems, …Read more
  •  114
    Perfect Happiness
    Symposion. Theoretical and Applied Inquiries in Philosophy and Social Sciences 8 (1): 89-116. 2021.
    In this paper, I will develop a new theory of the nature of happiness, or “perfect happiness.” I will examine what perfect happiness is and what it is not and I will try to answer some fundamental questions about this property. According to the theory, which I shall call “the fulfillment theory,” perfect happiness is perfect fulfillment. The analysis of happiness in this paper is a development of the old idea that happiness is getting what you want and can be classified as a kind of desire-satis…Read more
  •  112
    In Paradoxa Stoicorum, the Roman philosopher Cicero defends six important Stoic theses. Since these theses seem counterintuitive, and it is not likely that the average person would agree with them, they were generally called "paradoxes". According to the third paradox, (P3), (all) transgressions (wrong actions) are equal and (all) right actions are equal. According to one interpretation of this principle, which I will call (P3′), it means that if it is forbidden that A and it is forbidden that B…Read more
  •  108
    Bimodal Logic
    Polish Journal of Philosophy 6 (2): 71-93. 2012.
    Many interesting philosophical principles include two kinds of modalities, e.g. epistemic and doxastic, alethic and epistemic, or alethic and deontic modalities.The purpose of this essay is to describe a set of bimodal systems, i.e. systems that include two kinds of modal operators, in which it is possible to investigate some formalizations of such principles. All in all we will consider 4,194,304 logics. All logics are described semantically and proof theoretically. We use possible world semant…Read more
  •  103
    Boulesic-Doxastic Logic
    Australasian Journal of Logic 16 (3): 83-132. 2019.
    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…Read more
  •  100
    Contrary-to-Duty Paradoxes and Counterfactual Deontic Logic
    Philosophia 47 (4): 1247-1282. 2019.
    In this paper, I will discuss some examples of the so-called contrary-to-duty 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…Read more
  •  90
    The Ideal Observer Theory and Motivational Internalism
    Kriterion - Journal of Philosophy 29 (1): 79-98. 2015.
    In this paper I show that one version of motivational internalism follows from the so-called ideal observer theory. Let us call the version of the ideal observer theory used in this essay (IOT). According to (IOT), it is necessarily the case that it ought to be that A if and only if every ideal observer wants it to be the case that A. We shall call the version of motivational internalism that follows from (IOT) (moral) conditional belief motivational internalism (CBMI). According to (CBMI), it i…Read more
  •  90
    Contrary-to-Duty Paradox
    Internet Encyclopedia of Philosophy. 2022.
    A contrary-to-duty obligation is an obligation telling us what ought to be the case if something that is wrong is true. For example: ‘If you have done something bad, you should make amends’. Doing something bad is wrong, but if it is true that you did do something bad, it ought to be the case that you make amends. Here are some other examples: ‘If he is guilty, he should confess’, ‘If you have hurt your friend, you should apologise to her’, ‘If she will not keep her promise to him, she ought to …Read more
  •  90
    The Highest Good and the Relation between Virtue and Happiness: A Kantian Approach
    Symposion. Theoretical and Applied Inquiries in Philosophy and Social Sciences 8 (2): 187-210. 2021.
    The paper develops a Kantian view of the highest good and the relation between virtue and happiness. Several Kantian theses are defended, among them the thesis that the highest good is realized only if every virtuous individual is happy, the view that virtue is neither necessary nor sufficient for happiness, and the proposition that virtue is both necessary and sufficient for the worthiness of being happy. The author argues that the highest good ought to be realized and that it ought…Read more
  •  80
    Counterfactuals in Temporal Alethic-Deontic Logic
    South American Journal of Logic 2 (1): 57-81. 2016.
    The purpose of this paper is to describe a set of counterfactual temporal alethic-deontic systems, i.e. systems that include counterfactual, temporal, alethic and deontic operators. All systems are described both semantically and proof theoretically. We use a kind of possible world semantics, inspired by the so-called T x W semantics, to characterise our systems semantically and semantic tableaux to characterise them proof theoretically. Our models contain several different accessibility relatio…Read more
  •  79
    Commitment: some formal interpretations
    Disputatio 4 (33). 2012.
    We often use sentences that seem conditional in nature when we reason about normative issues, e.g. ‘If you have promised to do something, you should keep your promise’ and ‘If you have done something bad, you should apologize’. We seem to think that promise-making in some sense commits us to promise-keeping and that acting bad in some sense creates an obligation to apologize. It is, however, not obvious how we should symbolize such sentences in a formal language. The purpose of this essay is to …Read more
  •  72
    The Aporia of Omniscience
    Logos and Episteme 11 (2): 209-227. 2020.
    This paper introduces a new aporia, the aporia of omniscience. The puzzle consists of three propositions: (1) It is possible that there is someone who is necessarily omniscient and infallible, (2) It is necessary that all beliefs are historically settled, and (3) It is possible that the future is open. Every sentence in this set is intuitively reasonable and there are prima facie plausible arguments for each of them. However, the whole set {(1), (2), (3)} is inconsistent. Therefore, it seems to …Read more
  •  30
    Ought We to Believe the Truth and Nothing But the Truth?
    Logos and Episteme 14 (2): 179-196. 2023.
    According to the so-called truth norm, we ought to believe that A if and only if A is true. There are many possible interpretations of this norm. What does 'ought‘ in this norm mean? Does 'ought‘ have a wide or a narrow scope, etc.? In this paper, I will investigate one version of this norm and I will discuss two arguments for it. The 'ought‘ in the paper will be interpreted as a kind of 'rational‘ ought that takes wide scope. I will call the first argument for the truth norm 'the extrapolation …Read more
  •  22
    The Highest Good and the Relation between Virtue and Happiness
    Symposion: Theoretical and Applied Inquiries in Philosophy and Social Sciences 8 (2): 187-210. 2021.
    The paper develops a Kantian view of the highest good and the relation between virtue and happiness. Several Kantian theses are defended, among them the thesis that the highest good is realized only if every virtuous individual is happy, the view that virtue is neither necessary nor sufficient for happiness, and the proposition that virtue is both necessary and sufficient for the worthiness of being happy. The author argues that the highest good ought to be realized and that it ought to be that …Read more
  •  14
    Deontic logic is a branch of logic that investigates normative concepts, systems of norms and normative reasoning. The formal languages of deontic logic include normative concepts that correspond to natural language notions such as ought, obligatory, permissible, forbidden and optional. The present book is an introduction to this branch of logic. Several basic deontic systems are described and some of their properties are explored. Every system is characterized both semantically using possible w…Read more
  •  6
    Logiska Övningar är en övningsbok i logik och en introduktionsbok i teoretisk filosofi. Den är indelad i sju kapitel. Varje kapitel, förutom det första, behandlar en eller flera klassiska grenar av den teoretiska filosofin. Det första kapitlet är en allmän inledning till boken och till filosofi som ämne. Övriga kapitel behandlar följande områden. Logik & Argumentationsteori (kapitel 2). Hur bör vi tänka och argumentera? Kunskapsteori (kapitel 3). Vad är kunskap och hur får vi kunskap om verkligh…Read more
  •  5
    Den här boken är en övningsbok i logik och en kort introduktion till metaetik. Den innehåller nio kapitel. Det första kapitlet är en allmän inledning till moralfilosofin. Det innehåller information om vad metaetik är och om hur metaetiken förhåller sig till den normativa etiken, till praktisk (eller tillämpad) etik och till deskriptiv moralfilosofi. Kapitel 2 handlar om språkfilosofiska frågor. Kapitel 3 handlar om medvetandefilosofiska frågor. Kapitel 4 behandlar kunskapsteoretiska frågor. Kapi…Read more
  •  4
    Den här boken är en övningsbok i logik och en kort introduktion till politisk filosofi och rättsfilosofi. Tonvikten ligger på den politiska filosofin. Boken innehåller tio kapitel. Det första kapitlet är en allmän inledning till politisk filosofi och rättsfilosofi. Kapitel 2 handlar om konservatism. Kapitel 3 handlar om liberalism. Kapitel 4 handlar om socialism. Kapitel 5 handlar om anarkism. Kapitel 6 handlar om kommunism. Kapitel 7 handlar om ekologism. Kapitel 8 innehåller blandade övningar …Read more
  •  3
    The Golden Rule: A Defense
    Australasian Journal of Philosophy. forthcoming.
    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 formulate…Read more
  •  1
    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.
  •  1
    Quantified Counterfactual Temporal Alethic-Deontic Logic
    South American Journal of Logic 3 (1). 2017.
    This paper will introduce and explore a set of quantified counterfactual temporal alethic-deontic systems, that is, systems that combine counterfactual temporal alethic-deontic logic with predicate logic. I will consider three types of systems: constant, variable and constant and variable domain systems. Every system can be combined with either necessary or contingent identity. All logics are described both semantically and proof theoretically. I use a kind of possible world semantics, inspired b…Read more