Conflicting Obligations in Logic and Law

Transcription

1 Conflicting Obligations in Logic and Law Resolving conflicts of obligation with deontic modal logic Student Student: R.M. (Bob) Kersten ANR: Institution Tilburg University Department of Philosophy Master Philosophy of Science and Society Supervisors Supervisor: Dr. M. (Matteo) Colombo 2 nd Reader: Dr. R.A. (Reinhard) Muskens Submission Date 23 February 2017 Wordcount: Copyright 2017 All rights of this document are reserved by the author.

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3 Preface This essay and its defense will be the last piece of my academic training. When completed, I will have gotten a bachelors degree in law and a masters degree in philosophy. I will then go into the wide world to see what kind of contribution I can make with my acquired set of skills over the years. Studying for quite some time does teach you other things than just the knowledge. It teaches you about culture, about society, about friendship and life and I am grateful for this chance and have enjoyed it immensely. I am very thankful for my parents to stand by and believe in me all these years. The writing of a thesis can be a big task, and this work was certainly a big egg to lay, to use a colorful Dutch proverb. Over time I had to curb my (overly) ambitious plans and try to work out a manageable plan. With some effort it worked out. In the end, the result gives a lot of promise for further research, experimentation and philosophizing and I hope to be a part of that in the future. I would like to thank my supervisors. Matteo s excellent feedback helped to make my arguments as clear and well defined as they are. And without Reinhard s classes I would never have discovered logic at the level I know it today. I also thank a lot of friends who helped me through the years spell out, refine, defend and argue my ideas. I especially thank my girlfriend Aniek who supported me when I needed it, and gave me a kick in the butt when I required it. Without her I would probably still be in the conceptual phase. I conclude here now, and lets get to the beginning. Lastly, I wish you, reader, a pleasant read. - Bob Kersten - 3 -

4 Nulla: Abstract This thesis is about applying frameworks of deontic modal logic to lawmaking. Lawmakers can encounter problems when making new laws. Laws can bring obligations with them, and some laws can conflict with each other so obligations can conflict with each other. The hypothesis is that frameworks of deontic modal logic can aid to recognize, avoid or solve these conflicts of obligations. The two frameworks that are examined are Standard Deontic Logic and the Anderson-Kanger reductionist approach. The eventual aim is to see if an algorithm can be produced that could help lawmakers make better laws, i.e. to improve the harmony of law. The thesis uses actual world examples to illustrate conflicts of obligation a subject of law might encounter. It also uses philosophical dilemma s to point to problems the logical frameworks may have. Keywords: logic, modal logic, deontic logic, deontic modal logic, law, rules, rights, obligation, conflicts, application, applying logic, legal frameworks, logical frameworks, dilemma s, paradoxes, algorithm, standard deontic logic, SDL, Anderson-Kanger reductionist approach, McNamara, philosophy, legal philosophy, moral philosophy, ethics - 4 -

5 Table of Contents PREFACE NULLA: ABSTRACT TABLE OF CONTENTS I: INTRODUCTION I.1: Outset I.2: A case study: the Vreemdelingenwet I.3: What now? I.4: Qualities of a successful logical framework II: METHODOLOGY II.1: Method, literature and units II.2: Scope of the thesis II.3: Valorization III: RESULTS INTRODUCTION CHAPTER 1: MODAL LOGIC III.1.1: Kripke III.1.2: Deontic logic III.1.3: Deontic modal logic III.1.4: Rules III.1.5: Conclusion CHAPTER 2: STANDARD DEONTIC LOGIC III.2.1: Syntax and semantics III.2.2: Implications III.2.3: Conclusion CHAPTER 3: ANDERSON-KANGER REDUCTIONIST APPROACH III.3.1: A reduction of SDL axioms III.3.2: A different framework and implications III.3.3: Determinism III.3.4: Conclusion CHAPTER 4: DILEMMA S AND PROBLEMS III.4.1: What is a dilemma? III.4.2: Dilemma s and deontic logic III.4.3: The good Samaritan/the gentle killer dilemma III.4.4: Plato s dilemma: precedence of obligation and consequences for SDL III.4.5: The normative gaps puzzle III.4.6: The temporal dilemma, problems for d III.4.7: Conclusion IV: ANALYSIS IV.1: Two frameworks and four qualities IV.2: Potential

6 V: DISCUSSION V.1: Significance V.2: Limitations V.3: Recommendations and applications VI: CONCLUSION VII: LITERATURE

7 I: Introduction I.1: Outset The process of making rules can be difficult for lawmakers. Rules can have a regulatory or a constitutive character. Regulative rules are usually phrased as imperatives and can take the form of do X. Constitutive rules can also define actions and options, create new possibilities for regulation and they can qualify objects ( X counts as Y or In case of X, Y becomes Z see (Searle, 1969, pp )). Often, rules take the shape of imperatives, and imperatives imply obligations. If there was only one rule or obligation to follow, there would be little difficulties. But there are a lot of rules, so there is a multitude of obligation. A reason lawmaking is difficult is the problem how to fit a new law within a framework of existing law. It is also difficult to make new laws consistent with fundamental principles of a society, government or organization. For these also bring obligations with them. Sometimes these different laws, the different obligations, can conflict with each other. A popular example is the clash between the right of freedom of speech, and the right not to be insulted. Two different rights collide here, and it can be difficult to say which one ought to prevail above the other. Part of the problem is that you shouldn t want to follow just one law, you want to follow the law as a whole: to comply with the framework of your legal order. Especially since law is a framework of different obligations. Some obligations stem from a constitution, some from international treaties (e.g. Universal Declaration of Human Rights), some from jurisprudence or common law. Together, these laws build up the framework what we refer to as the law or a legal order. In an ideal world, none of these obligations would conflict with each other and there would be a harmony of law. There would be harmony when a subject of a legal framework could follow the framework as a whole without running into conflicting obligations between the laws themselves. This is at the moment not the case

8 I.2: A case study: the Vreemdelingenwet 2000 An example where one law collides with another is the animosity between the Vreemdelingenwet 2000 (Aliens Act 2000; AA2000 hereafter) and certain European directives and bylaws. The AA2000 is a law that regulates immigration. One of the concepts of the AA2000 was to give the Dutch state more instruments to deport (rejected) aliens and to elaborate on bureaucracy for new aliens, such that the Netherlands would become a less popular destination due to the multitude of rules and a slimmer chance of getting through that process. 1 However, some of the instruments the law provided were in conflict with certain European rules as we can see in ABRvS 28 December In this case, aliens were searched and frisked by the military police when they were near (but not crossing) border posts and places of importance. The AA2000 gave a legal basis for the searching and frisking. However, some of the instruments were in conflict with obligations derived from the Schengen-treaty, others were in conflict of article 8 of the European Declaration of Human Rights (EDHR), also known as the Family Life article. Some aliens were arrested and searched, in other cases some families were separated. The aliens that went to court found that a judge decided to let the European rules way heavier than the Dutch rules. The rules stated that the searching should no longer take place on the basis of the AA2000. The aliens were at the same time a person who could be searched, and a person who couldn t be searched, an impossibility. A problem is that these aliens had to go to court to let a judge resolve this impossibility stemming from a conflict between laws. That they could do this is a good thing, that they had to is not. The Dutch state could and should have known that the new rules in the AA2000 were in conflict with these international norms in the first place! If the law had been made in harmony with the legal framework, 1 See (Evaluatie Vreemdelingenwet 2000), a rapport describing the history, and some of the rationale, of the Aliens Act And also the letter from the RvS to the ministry of internal affairs, see literature

9 none of these cases would have had to been tried for a judge; and a lot of trouble, insecurity, money, time and effort would have been saved. I.3: What now? So, conflicts of laws and obligations can arise within a legal framework, this disturbs the harmony of law. It is usually up to a judge to resolve existing conflicts. When it comes to making new laws, a lawmaker has a chance to prevent this problem of conflicting obligations. And to prevent is better than to deal with the consequences. Conflicts of law can make a framework of law unstable: legal loopholes can arise and it can lead to legal insecurity. Would it be possible, when making new laws, to check if any conflict of obligation will arise, and if so how it could be averted? In this thesis, I ask whether frameworks of deontic modal logic can aid in this process. I examine two frameworks of deontic modal logic and try to find out if such a framework can help lawmakers; and if so, which of the two frameworks would work best. To use a framework, I will first examine how to understand and formulate obligations using deontic modal logic. After that I will examine how to formulate and recognize conflicts of obligations. I will use dilemma s and examples to see if deontic logic can help to recognize and resolve conflicts of obligations, and eventually make better laws. A better law can be understood as a law that fits well with other laws. It is a law that does not cause new conflicts of obligations and therefore promotes the harmony of law. With harmony of law, I mean the consistency of a legal framework with itself. As said before, one should aim to follow the law as a whole and not just certain particular laws. This is what being a subject of a legal framework entails. If you impose the obligation to follow the law as a whole on a subject, it should be at least possible to do so. This last premise entails that opposing or conflicting obligations should always be avoided: one cannot for instance do something and do something not at the same time. With this aim in mind, a logical framework that could improve the harmony of law is important

10 I.4: Qualities of a successful logical framework The success of a framework will depend on some qualities. It should be possible to: 1) turn the logical framework into an algorithm that a lawmaker can use; 2) introduce new and existing principles and work with these in the logical reasoning; 3) make a ordering relationship in case of multiple outcomes; 4) the framework should have some predictive power. Quality 1: Usability With an algorithm for a lawmaker I mean that any lawmaker should be able to use the framework when she makes new laws. This does not have to be a law in the legal sense or at a level of the nation state. Even corporations or organizations who make laws or rules should be able to use the algorithm. Since not all lawmakers are logicians, the algorithms formalities and difficulty will be important. Next to the level of sophistication, the level in which the algorithm can incorporate a framework is important. 3 Quality 2: Translatability With this I mean that principles and ideas of law should be convertible into logical formulae and that those formulae can be used in the logical reasoning. Quality 3: Ordering In case there are multiple outcomes (or that there are multiple possible worlds (see chapter 3)) a framework should offer some ordering relation. A dilemma is a good example where you have multiple, equal outcomes. The logic should be able to point out which outcome is most desirable from a logical point of view i.e. which causes none or the least conflicts. Ideally, you should be able to resolve the dilemma s c.q. conflicts. 3 Note that this thesis investigates whether such an algorithm could be made from a deontic logical framework; it does not provide the algorithm itself

11 Quality 4: Predictive Power The predictive power of the model lies its ability to predict whether a new law will cause no, a little or a lot of conflicts of obligation. A lawmaker can use that to assess whether a new law will lead to a lot of lawsuits or legal problems. This should also indicate if it is easy to follow the law or that it is likely that a law will be overturned in some court of law or dispute. If a logical framework has all these qualities it will fulfill the goal of this thesis. The goal is to promote the harmony of law by avoiding producing conflicts of obligations in new laws with the help of deontic modal logic. II: Methodology II.1: Method, literature and units The problem this thesis hopes to solve is a knowledge problem. It is not yet known if frameworks of deontic modal logic can help to improve the harmony of law by recognizing (and resolving) conflicting obligations. To gain this knowledge, I have chosen to do a literature study. Partially to understand the logical frameworks and also to look at the logical proofs and concepts in the literature. I have chosen not to emphasize on the formal aspects of deontic modal logic. This would make the focus of the thesis deontic logic itself, not its possible applications. Since I am interested in applying the logic, and to investigate if an algorithm can be made, I will not be treating a lot of proofs, or prove a lot of things myself. I will focus on literature about the logic and its applications. Paul McNamara s entry in the SEP, and his book co-authored with Hilpinen will form the backbone of this literature study (McNamaraHilpinen, 2012). I will also study essays by Anderson and Kanger. These four together will form an informed picture on the frameworks of 1) standard deontic logic, and 2) the Anderson-Kanger reductionist approach. These are the two frameworks that will be studied by this essay, and together with some secondary literature, will give a total picture of the systems

12 The units of research have been stated in the introduction (Section I.4). These are the 4 qualities that a framework will be measured by. As an overlapping quality it will be seen how well the framework succeeds in proving an answer to the problem of this thesis. These points will be presented in the conclusion (Section VI) and their significance will be debated in the discussion (Section V). II.2: Scope of the thesis As stated above, its not the goal of the thesis to give a formal critique on deontic modal logic. Its also not the aim of the thesis to incentivize lawmakers. The interest of the frameworks is in the formal relationship of laws within frameworks, the syntax of laws. The aim is to demonstrate what laws would lead to conflicts and what laws would promote the harmony of law via consistency. I am only interested in possible conflicts of obligations in schemes that lawmakers themselves choose. I intend to be as disinterested about the content of law as possible. Some factors which might influence the research, but which are not part of the research, are the legal implications of conflicting obligations. This thesis looks at the theoretical aspects and implications, not the practical, actual world consequences of these problems. I see that as an ex post facto problem that should be solved by lawyers, the essay is interested in an ex ante solution to the problem, before the damage is done. II.3: Valorization The product of the thesis is to benefit any form of lawmaker. This could be a nation state or a municipality, but also a commercial organization. Any organization that makes laws and that hopes to be in accordance with itself and its own principles could benefit from this thesis. The thesis also servers an academic purpose, as it gives a contribution to the discussion about deontic logic and its applications. The hypothesis of this essay is to see if frameworks of deontic modal logic can help to improve the harmony of law by creating an algorithm. What I expect from the results is that this is a promising lead, and such an algorithm can indeed be made. Such an algorithm would be of great benefit in a world with rapidly expanding, global and

13 complicated legal orders. This is a growing practical problem and I believe (legal) philosophy should do its best to give an answer to this problem. The interest of this thesis is theoretical, but its eventual implications are practical. Its important to see the tough, theoretical problems, but its just as important to focus on the practical problems they can relate to.. Research has been done on the relation between deontic logic, legal reasoning, obligations and lawmaking. Royakkers has done research on the connection between deontic logic and legal reasoning in his PhD dissertation. His focus was on the possible relation between artificial intelligence and lawmaking and on the limitations of deontic logic for the representation of legal rules (Royakkers, 1998, pp. 1-12). He also mentions the difficulties between confliction obligations in law, and tries to resolve these with deontic logic. His examples are about differences in conflicting legal obligations on the same level of legal obligation. This thesis also treats the multitude of legal obligations on different levels of legal rules, i.e.: from higher levels as in European bylaws to municipal rulings. (Nair, 2014) has specifically focused on the difficulties that dilemma s pose to deontic logic, especially in the principle of consistency, or D-rule. The question whether deontic logic needs to sacrifice some rules in order to incorporate these dilemma s, or the dilemma s merely illustrate the difficulty in making law coherent and harmonic is unanswered. Both mention that there is an interesting relationship between logics and reasoning about (legal) obligations and that it is an ongoing discussion. This thesis will help to bridge the gap between legal reasoning and deontic logical reasoning. An algorithm as intended will be very suitable for that purpose. III: Results Introduction In this section I will examine two systems of deontic modal logic: the system of standard deontic logic (SDL) and the Anderson-Kanger reductionist approach. I will first give a

14 background on what I understand as deontic modal logic. This will follow (McNamara, 2014) s view as stated in the Stanford Encyclopedia of Philosophy (SEP). McNamara also gives a formulation on the SDL, which will be the first system I will examine. After that I will give attention to the Anderson-Kanger reductionist approach, which is a variant of the SDL. I will first give a short recap on modal logic and then will focus on deontic modal logic. After that I will treat deontic logic dilemma s and problems. Chapter 1: Modal Logic III.1.1: Kripke Modality deals with relations between formulas. More specifically: Modal logic deals with operators expressing properties of propositions, such as it is necessary that, it ought to be the case that. (Muskens, 2015, p. 55). Some well-known modal operators include temporal ( it has been the case that, it has always been the case that ), epistemological ( he knows that, he believes that ) and deontic ( it is forbidden that, you ought to do ) operators. Saul Kripke started off modal logic with introducing certain operators, the necessity ( ) and possibility ( ) operators. This is also called the weak logic and often denoted by the letter K. It deals with two rules Rules of K Necessitation Rule: If A is a theorem of K, then so is A Distribution Axiom: (A B) ( A B) (Garson, 2016) As Garson notes, the operators behave in a similar way to the existential and universal quantifiers. The accessibility relationship that deals with deontic concepts is called the deontic accessibility relationship. This will be our area of interest. These deontic concepts deal with obligation, permissibility and omissibility of actions and concepts. These concepts are also studied in ethics and moral philosophy and I consider them ethical concepts

15 III.1.2: Deontic logic To follow McNamara s interpretation of deontic modal logic, I will subscribe to his definition of deontic logic from the SEP 4 : Deontic logic is that branch of symbolic logic that has been the most concerned with the contribution that the following notions make to what follows from what: permissible, impermissible, obligatory, omissible, optional, ought, must, supererogatory, indifferent/significant, the least one can do, better than/best/good/bad, claim/liberty/power/immunity (McNamara, 2014) Note that these concepts are similar to concepts that are important in lawmaking and in a framework of law. One can say that the lawbook of a country is its summation of what a certain legal framework thinks about these questions: what is right, what is obligatory, what is liberty etc.. For this reason, I think its likely that there is a link between deontic logic and lawmaking. McNamara continues to state that logics usually focus on the theoretical questions of philosophy. That is, they focus on thinking and the rules and axioms for thinking. Deontic logic is a logic that falls under this category. However, from the notions it investigates it can be seen that deontic logic focusses on the doing of things: what is permitted and forbidden. This falls under the practical philosophy i.e. ethics. So it is a theoretical field which focusses on the practical philosophy. Therefore it is thought that this style of reasoning can be of help to difficult practical questions such as the making of laws. 4 It is not the aim of this thesis to give a background or historical view on deontic logic; for this see the SEP entry by (McNamara, 2014) and also the entry on Mally s Deontic Logic referred therein

16 III.1.3: Deontic modal logic Deontic modal logic is, for the parts we are interested in, analogues to modal logic. McNamara states that you can speak of deontic truth or deontic necessity just as you can speak of modal necessity. Both use the same rules and inferences; the one focusses on truth, the other on obligations. McNamara builds up what he calls the Traditional Scheme (TS) with five normative statuses of deontic logic. These are: Traditional Scheme it is obligatory that (OB) it is permissible that (PE) it is impermissible that (IM) it is omissible that (OM) it is optional that (OP) (McNamara, 2014) 5 The first three of these are of the biggest interest to us, since the last two say that an outcome doesn t really matter. They do not matter because when something is omissible, the outcome can be ignored. When something is optional, the claim do p and do not p hold the same value. In both OM and OP outcomes, there is no incentive to give sanction or reward to the consequences of an action. This is an important notion as we will see later on in the Anderson-Kanger reductionist approach. In moral theory, attributing blame or praise is also a key concept. It does seem intuitively correct that 5 Some other authors use O, F or [OB] as expressions of the deontic operators standing for obligatory c.q. forbidden. Since I am following McNamara s view on deontic logic, I will also subscribe to his style of abbreviations

17 when a claim does not merit either of these consequences, a claim is not of interest to us. To illustrate an optional scenario, imagine going to someone to buy a second-hand guitar. You can inspect the guitar for its qualities, and hear what the price is. On that moment you can either accept the deal and buy the guitar or decline the deal and just leave. Both outcomes have the same value, although they might have other consequences (either you have the guitar or not). From a normative point of view, both outcomes are possible and you could do either. Things that are omissible are simply not relevant, at least not in a deontic manner. You can imagine everything that would not qualify as a normative status or moral issue. Also, if we recap on the AA2000 from the introduction, when the judge decided that the aliens were right and the European guidelines were more important than the Dutch (illegitimate) nation-level laws, the obligations and rights stemming from the Dutch law became omissible: no longer relevant for the discussion because their power had stopped working. The first three notions can be defined in either one of them and its negation. For example: something is permissible if and only if (iff) it is not obligatory to not do it (PE OB p, just as p can be defined as p) Normative statuses are statuses that ought to lead to action, or at least give a guideline on what the subject of the status ought to do. It is a claim about a judgment, not a factual claim about the world. It can be a logical possibility that it is obligatory for a human being to travel faster than the speed of light, but that doesn t mean that it is a physical necessity. The physical necessity accessibility relation is a different modal logic. That accessibility relation does deal with the relations between possible worlds that concerns physical possibility and necessity. Deontic logic is interested in the normative statuses of concepts, and to analyze these over possible worlds. To make the connection between Kripke-style logics and deontic modal logic, you can say that You must do p is equivalent to It is necessary that you do p, where p can be

18 any action or concept. Deontic logic especially focusses on duty, and therefore there is a connection between ethics and this kind of logic because analyzing the implication of duty is an important part of the study of ethics. It is important to note that modal logic and deontic logic work similar, but do entail different aspects. It is the case in modal logic that if it is necessary that p, then p is true. This does not flow over to deontic logic. If something is obliged, that does not make it true. The same goes for if p is true then it is permitted. This is turning an is claim into an ought claim, where the first is a statement of truth (or fact) and the latter is a judgment. Since the goal is to help make judgments I will only speak of deontic truth or deontic necessity and refrain from making fact-claims about the world. This is something different than the physical accessibility modality, which broadly states that if you ought to do something, it should be possible to do it. As stated before, this deals with the difference between the physical necessity relationship and the deontic necessity relationship. III.1.4: Rules McNamara concludes the set-up of the deontic logic with some presuppositions and rules that will be used throughout the SDL but also in other versions of deontic logic so I will name them shortly. Rules of Deontic Logic 1) OB-RE: if p<->q is a theorem, so is OBp<->OBq 2) OD: OB 3) DS: (OBp<-> OMp)... (Imp OMp) 4) TTC: (OBp OPp IMp) (~(OBp IMp) ~(OBp OPp) ~(OPp IMp)). 5) NC: (OBp OB p) (McNamara, 2014)

19 Where 1) is the rule that if something is a equivocal statement, so is the statement with the deontic preface, this is similar to the Necessitation Rule in K, 2) if something is logically invalid, it can never be obligatory, 3) shown in a shorter version here, but this rule derives all deontic forms from one form (in this case stemming from OB, where the first example says when something is obligatory, it is also relevant ), 4) this groups the different deontic forms from each other, this works together with 3 to map out the general rules of deontic logic, 5) similar to the doctrine of double negation, something cannot be obligatory and non-obligatory at the same time. These rules together form the basis of what McNamara defines as deontic logic and they lead up to the standard system of deontic logic: SDL. III.1.5: Conclusion We have introduced deontic modal logic. Modality deals with different accessibility relations over possible worlds. Possible worlds can be thought of as different scenarios; the way things might have been or be otherwise. The accessibility relations deal with the different kind of modal operators. We are interested in deontic logic, which focusses on normative concepts like obligation and permissibility. It is based on the Kripkelanguage K, which deals with necessity and possibility. Because deontic logic focusses on practical concepts like duty and obligation, it seems there is a link between the logic and legal frameworks. We have seen that the normative statuses are guidelines on what to do, on what action to take. They are similar to the making of judgments. The making of judgments is about what is right to do, this is different from what is there in the world or what is actual or factual. We have introduces the Traditional Scheme and Rules of Deontic Logic. These are rules that together from the basis of deontic modal logic and especially of the Standard Deontic Logic. Some of these rules can bring problems with them (as we will see in a later section). All in all, this chapter gives us the basic rules and logical language to understand the following chapters

20 Chapter 2: Standard Deontic Logic III.2.1: Syntax and semantics To start off, we assume he normal rules of propositional logic, and the rules as mentioned in the first chapter. SDL also assumes OB-K and OB-D axioms. K is the axiom used for distributing the modal operator, in this case the OB operator. The D-rule is a no conflicts or a doctrine of double negation-style argument: that something is only obligatory if its also not obligatory to not do it. The D stands for Deontic and the K for Kripke. Formally these basic axioms look like this: SDL A1. All tautologous well formed formulas of the language (TAUT) A2. OB(p q) (OBp OBq) (OB-K) A3. OBp OB p (OB-D) R1. If p and p q then q (MP) R2. If p then OBp (OB-NEC) (McNamara, 2014) Where MP stands for Modus Ponens and the NEC-rule, which is debated by McNamara later on, tells us that if something is a theorem, the deontic operator-variant of that thing is also a theorem. Together with the following rules, this is the set of axioms for SDL:

21 OB OB OB(p q) (OBp OBq) (OBp OBq) OB(p q) OBp OPp IMp If p q then OBp OBq If p q then OBp OBq (OB-N) (OB-OD) (OB-M) (OB-C / Aggregation) (OB-Exhaustion) (OB-RM) (OB-RE) (McNamara, 2014) These rules seem straightforward and similar to the ones named above, although sometimes given a different name. The OD-rule declares that it is not obligatory to do that which is logically invalid, i.e. it cannot be a duty to do something and to do that something not at the same time. The same goes for the exhaustion rule: something must be either obligatory, optional or impossible. These three rules are exhaustive; something must fall under one (or more) of these categories else it is apparently not something that qualifies as a normative status; not to say its omissible, its something completely unqualifiable. McNamara gives proof for (most) of these stated rules, or refers to those who do. The aggregation rule says that if you have two separate obligations to do a and b, you can conjunct those duties into one duty to do a and b. In natural langue this would be for instance I must do the dishes and I must clean the kitchen into I must do the dishes and clean the kitchen. Later on it shall become clear that grouping obligations together like this can potentially make reasoning about complex obligations easier, but more on this later on. To reason with these rules, we have to introduce semantics. Like other normal modal logics, deontic modal logic uses a Kripke-style possible world semantics scheme. In

22 this, you can introduce possible worlds to see under what condition certain sentences can be logically valid or will uphold in certain possible world, given the normal rules. This works by having a set of possible worlds, W, and a relation symbol A. This relation shows how worlds are acceptable (or accessible ) to each other. This says that Aij is to be read that a world i is acceptable through j iff everything that is obligatory in i also holds in j. Seriality is then added; that is that every world there is at least one xacceptable world, if only itself. That brings us closer to the core of SDL. The fundamental idea here is that the normative status of a proposition from the standpoint of a world i can be assessed by looking at how that proposition fairs at the i-acceptable worlds. (McNamara, 2014). To explain this, I will first show the Kripke-style semantic truth rules: Derivative Rules Let M i p denote p's truth at a world, i, in a model, M 6 [OB]: M i OBp: j[if Aij then M j p] Derivative Truth-Conditions: [PE]: M i PEp: j(aij & M j p) [IM]: M i IMp: ~ j(aij & M j p) [OM]: M i OMp: j(aij & M j ~p) [OP]: M i OPp: j(aij & M j p) & j(aij & M j ~p) p is true in the model, M (M p): p is true at every world in M. This leads to the following: something is obligatory iff in all j-worlds, p holds. Something is permitted if in some j-world p holds. Something is impermissible if in no j-world p 6 A model can be seen as a logical map where different propositional variables truths can be seen and tested. It shows in what world under which circumstances some proposition will hold or not

23 holds. Something is omitted if in some j-world p doesn t hold and something is i-optional if in some world p holds and in some it doesn t. Additionally, you can have a set of worlds greater than 2, consisting of an actual world (from where we reason) to a non-empty set of possible worlds. This opens the possibility for a world-relative ordering relationships. This can be understood as the following: if j k, and k l then j l. This of course makes a relationship between multiple worlds clear, where each world is as good as itself (j=j). In the first example, it is said that a world is as good as, or better than, another world. If we see j, k and l as the total set of possible worlds, we can make the relationship clearer by saying for instance that p occurs in j, also in k but not in l. Let p be something desirable, for instance to love ones neighbor, then we could say that j is as good as k, but l is not as good as k nor as j since here is no occurrence of p. Doing this helps us to order the different worlds and see if 1) the actual world is a desirable world and 2) if we have a large set of possible worlds, to see which world would be more desirable than the actual world. Especially (2) shows us how we could make the ordering relation. Imagine that its desirable that there is an obligation, say -p, from a perspective of a lawmaker. It would be a good thing than if there is a world where there is all -p. That would be better than a world with just some -p or much better than a world with no -p at all. A last assumption then is The Limit Assumption : that there is at least one world which is as good as all worlds, or that there is one the i-best world. With seriality, this makes it so that you can always reason from a world which is the best possible world and make a shift in what ranks the other worlds. III.2.2: Implications What SDL does is that it makes it possible to transfer sentences from the natural language into a logic. This can make it easier to reason with them, because there is less chance of introducing bias into the reasoning. With this I mean that the sentence all drugs should be legal holds a different political and moral status than the formula Ld

24 The goal of the thesis is to see if deontic logic can help recognize and resolve conflicting obligations in law. Part of the reason that I formed this hypothesis is that the logic could give a more disinterested outcome in this reasoning. An outcome closely related to what is logically possible or impossible and not so much related to what is politically or socially desirable. It is thought that the first approach tends to be of more contribution to the harmony of law because making sure that there are no logical contradiction in duties is a key part of the reasoning (the OB-N rule for instance). Making laws on the basis of political or irrational arguments does not necessarily improve the harmony of law because they can have other more important interests. These interests could be a wider range of reasons, to solidify political power or to impose a conservative or progressive view. However, if these lawmakers would use a tool as intended in this thesis, the tool would prevent them from making logical inconsistent laws and therefore not disrupt the harmony of law. In an ideal world, SDL would be able to take in all sentences from the natural language concerning normative propositions. SDL would then be able to reflect upon these propositions using the tools of modal logic to see which claims are true i.e.: which ones lead to obligation, which lead to permissible claims and which to impermissible claims or contradictions. This last claim is because something which is logically invalid cannot be obliged; and if there is no world in which it could hold it is impermissible. However, SDL also helps us to understand norms via other tools such as the analyses of paradoxes, dilemmas and puzzles. Philosophical puzzles and dilemmas can help us to distinguish what is right about something, and why something is wrong. For example, there is the paradox of the gentle murderer (Forrester, 1984, pp ). In which it says in natural language: a) It is obligatory that you do not kill b) If you kill, you ought to kill gently

25 c) You do kill someone Transferred to logical forms we get 1) OB k 2) k OBg 3) k From 2 and 3 by MP it follows that OB-g, however, you can only kill gently if you kill; and given that it is obliged to kill gently, it follows from a logical truth that you are now obliged to kill as well. This leads to two possible outcomes, either the rules aren t right or we must change the premises. This last part is important since the aim of the thesis is to test which laws work and which not. Before we will investigate other dilemma s we will first look at the Anderson-Kanger reductionist approach. III.2.3: Conclusion The SDL-rules are further introduced and explained in this chapter. To reason with these rules, we introduce possible worlds and we introduce accessibility relations between the possible worlds. Together with derivative rules, you can make logical models to see in which possible world a certain sentence p will hold, to see what is obligatory, permissible or impermissible. You can make sentences like if p does not hold in this world, p cannot be obligatory. This is used to evaluate possible worlds. With these rules, and the rules from chapter 1, you can transfer sentences from natural language into the logic. This allows a logician or lawmaker to reason with the concepts in the language in a disinterested manner, because this logic is more free of bias than natural language. It is also shown that the logic can be used as a tool to point out certain unexpected consequences certain obligations bring with them, as is shown in the example of the gentle murderer. This example shows that logic can reveal certain aspects that natural language would have some trouble with

26 Chapter 3: Anderson-Kanger reductionist approach III.3.1: A reduction of SDL axioms The AK-ra reduces all axioms of SDL (see III.2.1) into constant d, and uses the standard modal language K to make a new deontic framework: Kd. The constant d stands for all (relevant) normative demands are met. This makes up the next scheme of rules. Kd scheme A1: All Regular Tautologies (TAUT) A2: (p q) ( p q) (K) A3: d (d) R1: If p and p q then q (MP) R2: If p then p (NEC) (McNamara, 2014) So what it does is it reduces the axioms of deontic logic into modal logic, the standard language of K with A3 makes Kd. Where A3 can be read as that it is possible that there exists a world where all relevant normative demands are met. It is possible with just the constant d and the standard modal operators to formulate all deontic operators (see (McNamara, 2014) for proofs on this). The term all (relative) normative standards have been met is a bit vague since it is not obvious what the standards are and why they are relevant. I think this is on purpose. It tries to envelop all terms we have seen in the TS in the SDL-framework. Given the fact that you then have to coin a term that covers obligatory as well as omissible requires some degree of vagueness. A definition too sharply defined would almost certainly leave out one or more of the deontic terms used in the SDL and therefore d would not be an complete a logic as SDL, so it trades in completeness over non-ambiguity. One difference between regular modal logic is the axiom that all the deontic elements are contained in d. When using the language of Kd, we try to look for a world where d

27 is satisfied. Or rather: the world in which all normative demands are met, this is an d- ideal world as to say, the best world. This means that, when using Kd, you end up with two sets of possible worlds Those where the demands are all met (DEM-worlds) and those where they are not. Something, like p, can be obligatory iff it appears in a DEM world; if not it can only be one of the other outcomes. This feature has a strong point, that there is always an ideal world where all demands are met, and you can always made an ordering relation easy, because there is always one best world and you can check if a world is as good as that world. 7 III.3.2: A different framework and implications However, usually there is added a fourth axiom to the rules of Kd, namely T (or sometimes referred to as M). T states that if something is necessary it is true. In modal logic this seems to offer little problems, this has already been addressed in Rules for K (see III.1.1). But as noted there, modal logic like alethic logic usually focusses on truth, not duty. If the axiom is added and you make the language KTd, it shows that SDL cannot be reduced into d because it does generates more axioms on its own, so its more than just a reduction. KTd is a deontic framework of itself. The T axiom is a truth implicating axiom, which poses little problems in language KT. For instance, you can state that if A is the case, it should be possible that A is the case (A A) and also that if it is necessary that A than it should be possible that A, and even that A then is the case (( A A) ( A A)). This is sometimes informally said that if something is necessary it should be possible, and if something is necessary the case, 7 See also footnote 31:. Note that we could add an ordering-relation semantics like that described at the end of our section on SDL in order to generate the DEM component of these models. The main difference would be that instead of a set of world-relative ordering relations, one for each world (e.g., i) there would be just one ordering relation,, whereby all worlds in W (in a given model) would be ranked just once. This relation would be reflexive, transitive and connected, while satisfying the Limit Assumption in W. DEM would then be the set of all the best worlds in W, and then the truth conditions for d and the five deontic operators would be cast via DEM so generated. (McNamara, 2014)

28 than there is the actual world where it is the case. Else there could be situations where something is necessary, but is not the case in the actual world, which seems wrong at the sight of it. However, in KTd this poses difficulties. Because a deontic system involves duties, and the T axiom involves a truth implication function. This entails that the deontic framework SDL cannot be reduced into KTd because SDL s axioms are not concerned with truth, but duty. Therefore KTd is either 1) not a reduction (since SDL cannot be fitted into d ) or, 2) KTd is a system on its own and d is not so much a constant as a set of axioms. III.3.3: Determinism Also, in normal modal logic, introducing the rule of determinism (Det) is no problem. Determinism says that if something is the case, it is necessary that it is the case: Det: p p. If p is true then it is necessary that p holds, this seems right when it comes to truth. However, his evokes a long standing argument between determinists and ethics: if Det is assumed, then if something is true, then it can also become an obligation (through the NEC rule). This is of course turning fact or truth claim into a judgment and that is something that judgments are better without. So by adding the Det-rule, it appears that our logic is either too strong for a regular ethical view, i.e. to soundly make judgments. Or it shows a connection between an obligation and the actual world. Perhaps it is the case that facts in the real world do entail certain obligations with them, but I cannot just imagine it being the other way around, although it might be logically possible. In the next section I will review, with the help of a dilemma, if there are more challenges for d or rather KTd. III.3.4: Conclusion The Anderson-Kanger reductionist approach reduces the SDL-rules into a new constant d, which stands for all (relevant) normative demands have been met and reasons while using the normal rules of (modal) logic. When introducing possible worlds, this leads that there is always one world where all demands are met: DEM-worlds. You can always reason from this world, via an accessibility relation, so making an ordering

29 relation is straightforward. You can measure with a model in what way a world matches up to a world where all demands are met. We also introduce an axiom T which makes the language of KTd complete. T is a truth functioning axiom, making the reduction a separate language from the regular SDL. It can be seen as a strong point to make a connection between truth and duty, but there are also some problems with it. One of these problems is determinism. This states that if something is the case, it must also be true. However, if used together with the deontic constant, this can turn a state of affairs as they are into a state of affairs that it ought to be: this is a fact-judgement problem and it should be avoided. It seems that the Kd-language is a framework on its own, with certain differences from SDL, but that its stronger variant KTd might be too strong to work with. Chapter 4: Dilemma s and problems III.4.1: What is a dilemma? Normally, when people talk about a dilemma they refer to a hard choice they have to make. This often involves choosing between two or more options that all have distinctive drawbacks. An often used example from William Styron s Sophies Choice is the following. Sophie is at a nazi-concentration camp with her two children. She is told that one of her kids is to live, the other is to die, and she must choose which one. Sophie can prevent the death of either of her children, but only by condemning the other to be killed. if she chooses neither, then both will be killed [she] has a morally compelling reason to choose one of her children. But for each child, Sophie has an apparently equally strong reason to save him or her. (McConnell, 2014) This dilemma shows the difficulty, and indeed the seemingly impossibility, of a (good) choice. In this essay, I will use a dilemma in a slightly different way. My view is that a dilemma is to philosophy what an experiment is to science. It is a tool you can use to test ideas and reflect on concepts. You can test if there are faults in reasoning, or if there are consequences to ideas that you haven t forseen

30 What this dilemma-tool will look like: I refer to (McConnell, 2014): the agent is required to do each of two (or more) actions; the agent can do each of the actions; but the agent cannot do both (or all) of the actions. (McConnell, 2014). He continues to state that whatever the agent does, it is a moral failure. Either to comply to something that is obliged, or that she is obliged to do something wrong. In other words, a dilemma is something where you have to do something, but all possible options contain features so that either a choice is impossible to make or the outcomes are undesirable to bring about. Moral dilemmas can point to problems in reasoning or gaps in concepts. I think this doesn t mean that you should then abandon the idea, it is just something you have to be aware of. Such as that the concept of gluttony shouldn t stop you from eating altogether. III.4.2: Dilemma s and deontic logic However, McConnell argues that moral dilemma s can point to logical inconsistency and that they therefore are problematic for deontic logic. He demonstrates this by conjoining two principles of deontic logic, rules we have seen before: the principle of deontic consistency (OBA OB A) and the principle of deontic logic ( (A B) (OBA OBB)). Where we have phrased the latter as the Distribution rule in SDL and as Axiom 2 in K(T)d 8, and the former as the D-rule (which is part of the reduction in K(T)d. After that he lays out what a moral dilemma is: that you are obliged to do A, obliged to do B, but you cannot do A and B. The claim is that if this kind of moral dilemma exist, they do lead to logical inconsistency. The argument from McConnell is the following: (1) OA (2) OB (3) C (A & B) [where C means cannot ] (4) (A B) (OA OB) [where means physical necessity] (5) (B & A) (from 3) 8 I use K(T)d here, when the bracketed (T) means that this applies to system Kd as well as KTd