Project topics and materials
Get Complete Project Material File(s) Now! »
Schema-based theories of analogical reasoning
Brewer’s notion of analogical reasoning
The basic idea of Brewer (1996) in his paper is that analogical reasoning is essentially a three-step process where each step is necessary and together they form sufficient conditions for reasoning by analogy. According to Brewer it is a combination of abduction, induction and deduction.
The first step is called abduction in a context of doubt. A context of doubt occurs if a judge or a lawyer cannot clearly take some standpoint in a case. It can be uncertainty whether to apply a certain concept or not. The abduction arises when the lawyer or the judge have some examples and establishes a rule to sort these examples. Brewer calls this kind of rule an analogy-warranting rule. (Brewer 1996, p. 962) The second step is the sorting of the examples. It means to apply the potential analogy-warranting rule to some examples and see if it gives the desired, or at least an acceptable, result. The application is done on some separate set of propositions. This set of propositions are distinguished by what Brewer calls analogy-warranting rationales. If the potential analogy-warranting rule does not yield an acceptable result by the application on the items given by the analogy-warranting rationales, it should be discharged and a new potential analogy-warranting rule should be made according to the first step. If it yields an acceptable result, it can be used in the third step. (Brewer 1996, p. 962) The third step is simply to apply the analogy-warranting rule found in the first step, and confirmed in the second step, to the example that was the motivation for the reasoning in the first place. (Brewer 1996, p. 963) Intuitively, each step corresponds to a different reasoning process. The first step is based on abductive reasoning, by finding an appropriate explanation. The second step is based on some kind of inductive reasoning, justifying the rule from the first step by several similar examples. The third step is based on deductive reasoning, by the application of a general rule to a specific case. The theory that is presented by Brewer (1996) will be called the AWR-model.
The first step is an abductive step where one should make a potential analogy-warranting rule. Analogy-warranting rules are abbreviated AWR in Brewer (1996). We will also use this abbreviation.
In an analogical argument, the source is the basis of the analogy. It is what we build our analogy from. The target is what is known to have some shared characteristics with the source and where we do not have knowledge about the characteristic in question. An AWR is a rule that states the logical relation between the different characteristics in one domain. In fig. 2.1, the horizontal arrows represent similarities between characteristics of the source and the target. The vertical arrows represent the AWR. (Brewer 1996, p. 965) These vertical relations in the source and target are things that have to be discovered. (Brewer 1996, p. 978) This is why the first step can be seen as some kind of abduction. The relation, the AWR, is not there already, but it has to be discovered or created outside of the framework. This is the background for using abduction, namely to find the best possible explanation of the specific relation.
The abduction of an AWR should occur in a context of doubt. Brewer argues that there are several ways to have a context of doubt. One of them is vagueness in norms. This occurs when the norm cannot be deductively applied to the case, that we do not know whether it is possible to apply a predicate to a particular case. A term that has the possibility of being vague is called an open-textured term. An open-textured term might not be vague in a specific setting, but if the setting changes, it might become a vague term. Another kind of vagueness may occur if a group of users disagree about the meaning of some term. It is not necessarily a term that is vague in itself as the individual users may look at the term as deductively applicable to the case, but because of disagreements between individuals, we do not know what interpretation to choose. Brewer therefore distinguishes vagueness related to an open-textured term and vagueness related to disagreements about meaning. (Brewer 1996, pp. 993-994) The context of doubt where the potential AWR may be made is then explained as vagueness of some term. The creation of potential AWRs is not a mechanical process. It is in some sense an area where logic cannot help you. A relation between characteristics may have many different explanations and logic itself does not seem to help you in sorting the good from the bad ones. One may therefore create a very high number of potential AWRs that may have different effects on the outcome of the analogical argument. The procedure for creating relevant or good AWRs is then first to refer to a requirement of entailment, together with some ideals or virtues of abduced explanations. The entailment requirement is the requirement that the AWR has to make the argument deductively valid. The AWR needs to be broad enough to make the premises entail the conclusion. It also needs to be precise enough to be applicable in the specific argument. The entailment requirement makes us able to look at juridical arguments as deductive. (Brewer 1996, pp. 993, 997, 999).
Even after imposing the entailment requirement, there may still be many po-tential AWRs that fulfil the entailment requirement without being very « good ». Another restriction on the AWRs is that they should strive some values or ideals, like predictability, notice and governmental accountability. Even if we admit that the AWRs may not completely fulfil these ideals, we may still look at them as idealised goals that we try to achieve. The exact values may be discussed, but Brewer (1996, p. 1003) mentions three values (clarity, notice and accountabil-ity) that can be considered important in this aspect. The process of creating an AWR stays fundamentally dependent on non-logical aspects, even though it may have some grounds in legal theory. The potential AWR should also be supplied with a proper justification, some analogy-warranting rationals, AWRas. AWRas provide the background or the explanation of the potential AWR and should be independent of the AWR itself. (Brewer 1996, pp. 991-993, 1021).
John Woods’ notion of a GS
In Is Legal Reasoning Irrational? An Introduction to the Epistemology of Law by Woods (2015, pp. 271-279), we are presented with an epistemological frame-work for arguments by parallel reasoning or analogical arguments for handling precedents. The main motivation in the book by Woods is to examine the logi-cal and epistemological foundations that lies as a background in legal reasoning, and particularly so for criminal law in the Canadian legal system. The book goes through many notions used in legal reasoning that seem to depend on an (implicit) epistemological or logical description. Amongst these, we have the notion of ar-gumentation by analogy and the notion of precedent. (Woods 2015, pp. 57-82, 271–279).
The general idea of argumentation by analogy and the role of a precedent here is that they can be described by a schema. This schema is introduced in order to implement the requirement found in analogical reasoning of sufficient relevant similarity. Woods (2015, p. 276) introduces what he calls a generalization schema (GS). The idea behind this GS is that it should be a general description where the analogue (source) is an instance, so that the analogised (target) also is an instance of this general description.
Stare decisis and applying precedents
Stare decisis is a legal feature, typically found in Common Law. It is the principle for the legal bindingness of a previous legal decision or precedent. It is used to embody the principle of like cases should be treated alike. If stare decisis is an accepted principle, a judge may not choose to treat a case differently from a previously decided case when both cases are similar. Woods (2015, pp. 57-58) identifies six features for the principle of stare decisis:
1. The decisions of a higher court are binding on all courts below. These are called vertical precedents.
2. Courts at all levels must not disoblige their own prior decisions. These precedents are called horizontal.
3. Lower court decisions from other common law jurisdiction can have « persuasive authority » for sister courts domestically.
4. Binding decisions are precedent-setting.
5. Non-binding decisions can be treated, and frequently are, as having « persuasive authority ».
6. A decision is binding when it rests upon something with a capa-ble judge would be able without unnatural effort to construe as a « general legal principle » or « rule of law ».
There is a distinction between binding and non-binding precedents in the fea-tures listed. That a decision is binding means that the reasons for decision provides a rule of law that one cannot disoblige. A decision might be non-binding in the situation that the reasons given for the decision are not coherent, that they cannot be seen as a general principle of law. If a precedent is given several reasons for a decision, these reasons might be in conflict with each other and it would therefore not be possible to take out some general rule to be used in a later decision. Woods uses an example of a decision in Canadian law, R. v. Morgentaler, 1988. 1 S.C.R. 30, that considered section 251 in the Criminal Code related to the illegality of abortion as unconstitutional. This decision was provided with three opinions or reasons for the decision, where no individual opinion had a majority in the jury of five members. Even though none of the reasons received a majority in the jury, the decision received a majority based on these three different opinions:
— the unfairness of procedures,
— autonomy of the woman and
— unjustness in the security of the person.
These three reasons were not compatible, and neither did receive a majority in the jury, and could therefore not be used to create a rule of law and therefore a binding decision. In spite of the non-bindingness of this decision, it was decisive, so section 251 is decided to be unconstitutional. (Woods 2015, pp. 58-59) A precedent that is legally binding is covered by the principle of stare decisis. This means that it stands in all cases of sufficient relevant similarity. A court that will treat a similar case cannot ignore the decision of the precedent. In the case of a binding precedent, the decision is therefore not only a solution to the actual case at hand, but also a finding for the ages. (Woods 2015, p. 59) According to Woods, judges might decide a case ’stupidly’ or ’wisely’, and in both situations, the case might serve as a precedent for later decisions. If a case is decided ’wisely’, the later application should not encounter an immediate problem. However, in the case that we are speaking about a ’stupid’ or ’unwelcome’ precedent, the future judges still have to apply this precedent, though stay aware that the precedent was ’stupid’. This motivates the following rules of thumb:
1. The more unwelcome the precedent, the more narrowly it should be inter-preted;
2. The more welcome the precedent, the more widely it should be interpreted.
The principle of stare decisis is found mainly in common law systems. It binds the future judges on the ratio decidendi from previous decisions. According to this principle, a ratio, when it is internally consistent and coherent, can and must be taken account of when deciding a similar case at a later stage. We might then say that the ratio embodies a rule of law. (Woods 2015, pp. 60-61)
Describing generalization schemas
In order to describe arguments based on generalization schemas, Woods (2015, pp. 274-277) uses an example by Judith Jarvis Thomson, called the Violinist Ar-gument, which is a philosophical argument for the permissibility of abortion. The example is described in the following way in A Defence of Abortion by Thomson (1971, pp. 48-49): But now let me ask you to imagine this. You wake up in the morning and find yourself back to back in bed with an unconscious violinist. A famous unconscious violinist. He has been found to have a fatal kidney ailment, and the Society of Music Lovers has canvassed all the avail-able medical records and found that you alone have the right blood type to help. They have therefore kidnapped you, and last night the violin-ist’s circulatory system was plugged into yours, so that your kidneys can be used to extract poisons from his blood as well as your own. The director of the hospital now tells you, « Look, we’re sorry the Society of Music Lovers did this to you–we would never have permitted it if we had known. But still, they did it, and the violinist is now plugged into you. To unplug you would be to kill him. But never mind, it’s only for nine months. By then he will have recovered from his ailment, and can safely be unplugged from you. » Is it morally incumbent on you to accede to this situation? No doubt it would be very nice of you if you did, a great kindness. But do you have to accede to it? What if it were not nine months, but nine years? Or longer still? What if the director of the hospital says. « Tough luck. I agree. but now you’ve got to stay in bed, with the violinist plugged into you, for the rest of your life. Because remember this. All persons have a right to life, and violinists are per-sons. Granted you have a right to decide what happens in and to your body, but a person’s right to life outweighs your right to decide what happens in and to your body. So you cannot ever be unplugged from him. » I imagine you would regard this as outrageous, which suggests that something really is wrong with that plausible-sounding argument I mentioned a moment ago.
Inference-based approaches to analogical reasoning
Bartha’s (2010) project is to make a general, normative theory of analogical arguments. It means to explain them from a logical point of view. The theory is based on what he calls horizontal and vertical relations. According to Bartha, the vertical relations have been neglected in the literature in favour of the horizontal relations. By introducing the articulation model, he intends to reintroduce the vertical relations to the field of analogical arguments. (Bartha 2010, p. 93)
Frames for Bartha’s articulation model
In his book, By Parallel Reasoning : The Construction and Evaluation of Ana-logical Arguments, Bartha (2010) introduces what he calls the articulation model. It is a framework that he claims can represent analogical arguments in a satisfac-tory way, in addition to have the ability to distinguish good from bad analogical arguments. The book focuses on analogical arguments in scientific disciplines, but his theory would seem to be applicable more generally to other kinds of analogical arguments. We will only introduce the kinds of analogies that seem relevant for legal reasoning, which here means to exclude the so-called deductive forms. We use P to symbolise a factor that is found in the source domain and P ∗ to symbolise a factor that is found the target domain. Q symbolises a factor that is found in the source domain, that is being used as background for the hypothetical analogy. Q∗ symbolises the factor that is analogised in the target domain, it is the factor that is not observed. The horizontal relations are relations between factors of the two different domains. The vertical relations are relations between the factors internal in one domain. The relations are described by fig. 2.2 (Bartha 2010, p. 24)
Table of contents :
Contents
Extended summary in French
Introduction
Analogy and meaning
Immanent reasoning
Conditions on analogies
Analysing analogy
Informal analysis of procedure
Dialogical rules
Dialogical procedures
Results
Dialogues and counterexamples
Initial permission of analogy
Proportionality and dialogues
Conclusion
Introduction
Project description
Structure of dissertation
Intention, motivation and goal
I What is analogy?
1 Preliminary remarks regarding the notion of analogy
1.1 Civil Law
1.2 Common Law
1.3 Analogical arguments of two forms
2 Theories of analogical reasoning
2.1 Categorising theories
2.2 Schema-based theories of analogical reasoning
Brewer’s notion of analogical reasoning
Alchourrón’s arguments a fortiori and a pari
John Woods’ notion of a GS
2.3 Inference-based approaches to analogical reasoning
Bartha’s notion of analogical reasoning
Prakken and Sartor’s dialogical model of legal reasoning
Rahman and Iqbal’s dialogical theory of co-relational inference
3 Comparison of contemporary theories
3.1 Horizontal relations
3.2 Vertical relations
3.3 Multiple analogies
II Formal and informal background
4 Constructive type theory
4.1 Judgments
Categorical judgments
Propositions
Hypothetical judgments
4.2 Rules in CTT
Cartesian product of a family of sets
Disjoint union of a family of sets
Disjoint union of two sets
4.3 Specification and contexts
Modality
Contexts in possible worlds
Specification by context
5 Immanent reasoning
5.1 Preliminary notions of dialogical logic
Particle rules
Structural rules
General definitions of the dialogical language
5.2 Standard dialogical logic
Rules of dialogical logic
Equality and example of a play
Extensive forms and strategies
5.3 Dialogues with play objects
The local and the global level
Strategy level and example
Example of dialogue in immanent reasoning
6 Imperatives, precedents and relations
6.1 Dialogical implementation of heteronomous imperatives
Heteronomous imperatives
Logical analysis of heteronomous imperatives
Conditionals and heteronomous imperatives
6.2 Capturing the notion of precedent
A model of analogy
The notion of a case
Initial conditions
6.3 Explaining relations
Horizontal relations
Vertical relations
Other relations?
III Analysing analogy
7 CTT analysis
7.1 General precedent-based reasoning
Performing analogical reasoning
Representing source cases
Representing the analogical procedure in CTT
7.2 Precedent-based reasoning with heteronomous imperatives
Performing analogical reasoning
Representing source cases
Representing the analogical procedure in CTT
7.3 Steamboat example
Assumptions and description of example
Informal analysis
Formal analysis
8 Dialogical implementation
8.1 Precedent-based reasoning
Terminology
Challenge rules
Explanation rules
8.2 Explaining and extending the analysis
Explanation of the dialogical approach
Formation plays and permitted analogies
Introducing heteronomous imperatives
8.3 Dialogical example
Steamboat example
Dialogical analysis
Results
9 Theoretical considerations
9.1 Logical, actual and real assumptions
Potentiality and actuality
Propositions
Assumptions, possibility and actuality
9.2 Distinction of steps and future contingency
Characteristics of a conditional right
There will be a sea-battle tomorrow
CTT and moral conditionals
9.3 Linking performance and deontic qualification
Good Shoemakers
CTT and hypotheticals
Deontic logic and hypotheticals
Conclusion
Project
Results
Further research
Bibliography
